1. Integrated optical realizations of
qudits
Masters thesis
Thomas Balle
Department of Physics and Astronomy
Faculty of Science
University of Aarhus
Denmark
1st
of July, 2011
Advisory committee
Supervisor: Prof. Dr. Martin Kristensen
Co-supervisor: Dr. Nathaniel Groothoff
3. Integrated optical realizations of qudits
Thomas Balle
2005-1903
Department of Physics and Astronomy, University of Aarhus,
Denmark
Submitted in partial fulfillment of the requirements for the degree of
Master of Science in Optics and Electronics
1st
of July 2011
Abstract Quantum communication has for many years been subject of much
research. The reason for this, is that it is possible to produce very secure cryptog-
raphy systems using quantum communications. If the present security systems are
to be replaced, this is a reasonable candidate, but this system is not fully developed
yet. At the moment, quantum cryptography systems are still too large and bulky
to fit inside a computer or other electrical systems, thus making it unhandy for
commercial use. The purpose of this project is to design and create a prototype of
a system that is directly compatible with existing optical communication systems
and is small enough for potential implementation in computers and other electrical
systems. The system designed in this project will not be in the desired size-range,
but the key components for encoding photons will be manufactured on integrated
optical chips, which are far smaller than the existing systems. The purpose of this
thesis is therefore not so much to create a small enough system, but instead to
show that it is possible to create it.
4. Danish summary
Dette projekt er blevet sponsoreret af MOBISEQ, som er et samarbejde mellem
sikkerheds og kryptologi gruppen ved Datalogisk Institut, Århus Universitet, iNano
centret og firmaet Ignis Photonyx.
Formålet med dette projekt er at designe og udvikle et kvantekryptografi system
der er baseret på integreret optik og som er direkte kompatibelt med nutidig optisk
kommunikations teknologi og er lille nok til implementering i eksisterende elektro-
niske systemer.
Til dette formål har vi foreslået at bruge fase-kodning med B92 protokollen, som
blev foreslået af Bennett i 1992, udvidet til at bruge fire fase tilstande i to uorthog-
onale baser. Til dette designede Ph.D. Jacob Selchau et intergreret optisk kom-
ponent der ved brug af Bragg gitre reducerer den påkrævede størrelse af det
ubalancerede Mach-Zehnder interferometer således at det benyttede interferom-
eter minder mere om et Michelson-Morley interferometer.
I dette speciale bliver baggrunden, metoder og sikkerheden af kvantekryptografi
diskuteret, de designede komponenter bliver karakteriseret så det er muligt at
bruge disse til kodning og dekodning af enkelt-fotoner og til sidst vil opbygning og
test af det fulde system blive gennemgået, diskuteret og dokumenteret. Det bliver
vist at det ved at bruge B92 protokollen med de designede integrerede optiske kom-
ponenter er muligt at kode og dekode enkelte fotoner i fase og at skælne mellem de
forskellige tilstande. Det bliver desuden vist at, grundet ikke-ideelle komponenter
og for lille separering af de ikke-interfererende signal dele, at støj-niveauet er for
højt til at opnå et regulært konceptuelt bevis for at dette system kan virke uden
at visse forbedringer bliver implementeret.
Af disse forbedringer er den primære fremtidige forbedring en implementering af en
intensitets modulator til at modulere laser-pulsernes længde sådan at der forekom-
mer mindre overlap i tid mellem de forskellige dele af signalet og derved bedre
signal/støj forhold.
iv
6. Acknowledgements
I would like to thank my supervisor Martin Kristensen for his great help and
advices in gaining understanding of the physics behind these experiments. Special
thanks goes to Dr. Nathaniel Groothoff, without whom a lot of days in the lab
would have be terribly boring, and Dr. Jacob Selchau, MSc Jeff V. Cruz, MSc
Laura Meriggi, MSc Anders S. Thomsen and Dr. Asger C. Krüger whose work,
assistance and help with the experiments have been invaluable. Thanks also to
bachelor student Kristian Sigvardt who helped on the final stretch before the
deadline. And also a very great thanks to MSc David Hansen who kept my spirits
up when the stress settled in 25 hours before the deadline.
vi
7. Chapter 1
Introduction
Quantum cryptography, or Quantum Key Distribution (QKD), has for several
years been subject of much research. There are several reasons for this, but the
main reason is that if the quantum computer is invented, the security systems
used presently in net banking, for credit cards etc are obsolete. This is due to
the fact that the presently used security systems are based on the difficulty in
factorizing products of large prime numbers and the computation time of this is
greatly reduced for quantum computers. A new secure system is therefore needed
and a potential candidate for this is quantum cryptography.
There are already commercial quantum cryptography systems available, but these
systems are still too large and bulky to fit inside a computer or other electrical
systems, thus making it unhandy for many applications. An other concern is the
effectiveness of the system, or rather, the time it takes to create a proper key for
the encryption/decryption. The goal of this project is to make a mobile and com-
mercially viable component for quantum cryptography that is directly compatible
with existing optical communication systems at a wavelength of 1550nm, and is
small enough for potential implementation in computers and other electrical sys-
tems. Since this is a prototype of such a system, we will only develop the key
components on integrated optical chips and base the remaining of the set-up on
optical fibres. The chosen protocol for quantum cryptography is, in this project,
phase coding since this solves many problems regarding stability.
The project was founded by the Mobile Quantum Security Project (MOBISEQ),
which is a collaborative effort between the security and cryptology group from the
Institute of Computer Science, Aarhus University, the iNano centre and the com-
pany Ignis Photonyx. The requirements set by MOBISEQ was that the component
must be small enough for successful implementation in existing electrical systems
and that it must be able to use existing light sources for optical communication.
For this reason, the system is designed to be used with a commercial short pulse
laser source with a centre wavelength of 1549.3nm.
1
8. 1.1. BACKGROUND CHAPTER 1. INTRODUCTION
The system designed in this project will not be in the desired size-range, but the
key components for encoding photons will be manufactured as silica-on-silicon in-
tegrated optical components, which are far smaller than existing systems. The
purpose of this thesis is therefore not so much to create a sufficiently small sys-
tem, but instead to show that it is possible to do, using integrated optics.
This thesis is a continuation of the work discussed in the Ph.D. thesis by Jacob
Selchau[1], the Masters thesis by Jeff Vale Cruz[2] and the pre-masters thesis of
this masters thesis[3]. In this thesis we will summarize the work done in these pa-
pers, discuss the theory behind the system and show our experimental realizations
using integrated optical components and suggest further developments.
1.1 Background
In order to fully understand the basic principles of quantum communication, we
have to have an understanding of classical cryptography and the reasons for de-
veloping quantum cryptography.
The science of secure communication, known as cryptology, has for millennia been
something people have wanted to perfect. The origin of cryptology is still un-
known, but it is known that several cryptological methods was developed in many
of the ancient civilizations, such as Mesopotamia, Egypt, India and China. One of
the first known breakthroughs in cryptology in Europe, was the Spartan develop-
ment of the so-called SCYTALE[4] (Greek for baton) in the ancient Greece. The
SCYTALE consisted of a wooden rod of a certain shape. Around this rod, a strip
of cloth or parchment was wrapped and the message was then written across the
strip, as shown in figure 1.1.
Figure 1.1: The ancient Greek SCYTALE.
When the parchment was unwrapped, the text would then appear unintelligible
and the message would be sent to the recipient of the message. The recipient
would then wrap the strip around a similarly shaped rod and could then read the
message. This form of encryption is known as transposition, since the letters in
the message is moved around.
Another form of encryption is substitution, where the letters in the message are
substituted with other letters or numbers. It is supposed that Julius Caesar used
this form of encryption, by substituting every letter in the message with the letter
three places further ahead in the alphabet. This resulted in the letter A being
substituted with the letter D, B with E and so on.
2
9. CHAPTER 1. INTRODUCTION 1.1. BACKGROUND
Transposition and substitution are the two basic methods of encryption used to-
day. Though the encryption methods used today are more complicated than the
before mentioned examples, they are still based on the same principles. The main
difference between now and then, is that the method of encryption and decryption
is no longer needed to be kept a secret. What needs to be kept a secret is the
specific key used for the encryption and decryption and in many cases it is only
the decryption key that needs to be kept a secret. This leads us to the two forms
of keys used in modern cryptography: symmetric and asymmetric keys.
Keys
Cryptography that uses symmetric keys means that the same key is used for en-
cryption and decryption and this is the most basic form of cryptography. An ex-
ample of this type of cryptography is the One-Time Pad[4][5], invented by Gilbert
Vernam, AT&T Bell Labs, in 1917. In the binary system, this works as shown in
figure 1.1.
Message 11000
Key 01001
Cryptotext 10001
Key 01001
Resulting message 11000
Table 1.1: One-time Pad.
The One-Time Pad method works by generating a random sequence of characters,
i.e. the key, of the same length as the message. This sequence is then added to the
message, thus generating a random, but known, perturbation of the message. In
the binary system, as shown in figure 1.1, a random sequence of ones and zeroes
is generated and is added to the message (0 + 0 = 0, 1 + 0 = 1 and 1 + 1 = 0) to
encrypt the message and then subtracted from the so-called cryptotext to decrypt
the message. This form of cryptography is completely safe, as long as the key re-
mains a secret, since the perturbation of the message is completely random. This
method is also the only method to have been proven completely safe mathemat-
ically (Claude Shannon, Bell Labs, 1949). The only down-side of One-Time Pad
is that it requires the key to be of the same length as the message, thus making it
impractical and time consuming when sending larger amounts of data.
The problem with the length of the key can be solved by using less secure meth-
ods, which are still based on the One-Time Pad. The security of these methods
requires that the calculation-time to crack the encryption has to be sufficiently
3
10. 1.1. BACKGROUND CHAPTER 1. INTRODUCTION
high. An example of such methods is DES (Data Encryption Standard)[4], where
the message is split up into small blocks and each block is encrypted with a 56 bit
key. To increase the security of this method, the message is split up in blocks in a
complex way, including permutations and non-linear functions, so that the blocks
have to be decrypted in a certain order. The security of this method is thus based
on the complexity of the calculations required to crack the encryption. The DES
algorithm thus has the advantage of having a short 56 bit key, sufficiently high
security and a short encryption/decryption time. Other algorithms are also based
on this principle, such as IDEA (International Data Encryption Algorithm) and
AES (Advanced Encryption Standard)[4]. Whereas DES is based on a 56 bit key,
the AES algorithm uses 128, 196 or 256 bit keys, thus increasing the security but
still having acceptably short keys.
We now arrive at the main problem in cryptography: only the recipient may be
able to read the message. The thing the above methods have in common, is that
the key has to be sent to the recipient in a secure way, so that the recipient can
decrypt the message. In earlier times, this was solved with a trusted courier, but
in modern times almost all communication happens electronically, where other
people can listen in. This gives rise to the main problem with algorithms using
a symmetric key; how do you exchange the key without risking anybody else to
intercept the key? This is solved by using an asymmetric keys, also called public-
key cryptosystem.
The use of asymmetric keys was published for the first time by Rivest, Shamir and
Adleman at MIT in 1978 and is called the RSA algorithm (from their surname
initials)[6]. This is based on that the recipient, Bob, has a secret key. From this
key Bob creates a public key, for encrypting the message, which he sends to the
transmitter of the message, Alice, through a public channel. Alice now uses this
key to encrypt her message and sends the encrypted message back to Bob, who
then decrypts the message using his own secret key. The advantage of this algo-
rithm is that the public key can only be used to encrypt the message and that the
encrypted message can only be decrypted with Bob’s secret key. The security of
this algorithm is based on the complexity and difficulty in factorizing the product
of to large prime numbers, meaning that it is easy to calculate p · q = n, but it is
difficult to calculate p and q from only knowing n. The best known algorithm to
calculate p and q from n has a calculation-time of:
T(n) = exp c · (ln(n))
1
3 · (ln(ln(n)))
2
3 (1.1)
Where c is a constant. The length of the keys used today in this algorithm, are
between 1024 and 2048 bit, which makes the calculation time sufficiently large for
the algorithm to be regarded as secure. Since the security of the RSA algorithm
is based on the difficulty in factorizing the product of two large prime numbers, it
4
11. CHAPTER 1. INTRODUCTION 1.1. BACKGROUND
is vulnerable to technological advances and development of faster algorithms for
calculating p and q.
The downside of the RSA algorithm is that it is relatively slow to encrypt and
decrypt the message or data and that it requires a large key. For this reason, the
RSA algorithm is usually used together with cryptosystems based on symmetric
keys, where the RSA algorithm is used to exchange the key for the symmetric key
cryptosystems. This has the advantage that the slow RSA algorithm is only used
to encrypt end decrypt the short key for the, e.g., DES algorithm and the faster
DES algorithm is then used to encrypt and decrypt the arbitrarily long message.
In this way, the security of the system is kept sufficiently high and the calculation
time sufficiently low. As an example of the security of this system, a 77 bit long
key for a cryptosystem based on a symmetric key has a security equivalent to
having a 2048 bit long key for the RSA algorithm[7].
Quantum computer
Even though the security in the above is high, it is still determined by the difficulty
of the calculations required to gain the key. We cannot know if someone tomorrow,
in a week or in 10 years comes up with a new algorithm, for factorizing products
of prime numbers that makes the present cryptography systems obsolete. In ad-
dition to this, the development of the quantum computer causes a great threat
to the present cryptography systems. Peter Shor at MIT published in 1994[8] a
quantum algorithm, called Shor’s algorithm, that can factorize products of large
prime numbers in the time:
T(n) ≈ O (ln(n))3
(1.2)
This means that if the quantum computer is developed, the time it takes to crack
the RSA algorithm is no longer exponential. This causes the security of the all the
places that uses the RSA algorithm to collapse, which includes banking, internet,
credit cards etc.. A new cryptography system is therefore needed and quantum
cryptography is a potential candidate for this purpose.
The purpose of quantum cryptography is to solve the problem of exchanging keys
for cryptosystems using symmetric keys. Through this, the transmitter and re-
ceiver creates the key together instead of exchanging it and thus avoiding the
problem of transmitting the key. In order to understand the concept of this, we
first have to understand the theory behind it.
5
12. Chapter 2
Quantum cryptography
Quantum cryptography sets itself apart from classical cryptography methods be-
cause it provides a means for encrypting information that no amount of analysis
can break. This is referred to as “unconditional secrecy”. The big advantage is
that this property of quantum cryptography is not a consequence of some “hard”
mathematical problem that might be solved some day, nor of some devilishly clever
algorithm or fiendishly intricate hardware design that might be reverse-engineered
one day, but instead is due to what are believed to be inviolable principles of
the laws of physics: the physics of Quantum Mechanics. If our understanding of
quantum mechanics is correct, and after three-quarters of a century of research
we know of no reason to believe it to be incorrect1
, quantum cryptography is and
always will be unconditionally secret, irrespective of whatever advances are made
in mathematics or computer science, and probably in any other sphere of human
activity. More specifically, the security of quantum cryptography is due to the
fact that it is impossible to gain complete knowledge of any given system. The
security of quantum cryptography can thus be expressed as four separate quantum
mechanical laws[4][9]:
• It is not possible to perform a measurement on a system without causing a
perturbation of the system.
• Heisenberg’s uncertainty principle: It is not possible to know both the posi-
tion and momentum of a particle with an arbitrarily high precision.
• It is not possible to form an image of individual quantum processes.
1
One should still keep in mind the words of Einstein on the subject of randomness in his letter
to Max Born on the 4th of December 1926 (translated by Irene Born): Quantum mechanics is
certainly imposing. But an inner voice tells me that it is not yet the real thing. The theory says
a lot, but does not really bring us any closer to the secret of the “old one.” I, at any rate, am
convinced that He does not throw dice.
6
13. CHAPTER 2. QUANTUM CRYPTOGRAPHY 2.1. THE QUANTUM BIT
• The no-cloning theorem[10][11]: It is not possible to copy an unknown quan-
tum state.
The effect of these laws is that any interaction imposed on the system can be
detected, since any observations or manipulations will cause a perturbation of the
system. Any measurement or manipulation performed by a third-party eavesdrop-
per will therefore be detectable by the transmitter and recipient.
This principle is used for quantum communication where single particles, with spe-
cific quantum states, are sent from the transmitter, Alice, to the recipient, Bob.
The particles used for this can be photons, atoms, electrons or any other particles
where it is possible to manipulate and maintain specific quantum states. In this
thesis we will focus on photons but the theory can be generalized for any particles.
2.1 The quantum bit
In order to send information from Alice to Bob we introduce the quantum bit,
or qubit, which is the quantum mechanical version of the binary system, which
is information in its purest form and consists of distinguished eigenstates of a
quantum mechanical system. An eigenstate of a hermitian operator ˆH in quantum
mechanics represents a state corresponding to a measurable outcome of the physical
property of which the operator ˆH represents the actual measurement. Analogous
to the binary system, the relevant eigenstates of a qubit are generally called | 0
and | 1 . Since the qubit is governed by the laws of quantum mechanics, an
arbitrary qubit | Q is not necessarily one of the two states. Instead, this can be
generalized to:
| Q = α | 0 + β | 1 (2.1)
Where α and β are the probability amplitudes fulfilling the condition |α|2
+|β|2
= 1.
The qubit is therefore a particle where we manipulate a single quantum state in
two specific ways and assign one value to a binary “0” and the other value to a
binary “1” corresponding to β = 0 and α = 0 respectively.
The concept of qubits was unknowingly introduced by Stephen Wiesner in 1983
when he published his proposal for unforgeable quantum money and this laid
the groundwork for the idea of quantum key distribution. In the following year
(1984) Charles H. Bennett and Gilles Brassard published the first protocol for
quantum cryptography[12]. This protocol is called the BB84 protocol, after their
surname initials and when it was published, and was the first milestone in quantum
cryptography.
7
14. 2.2. THE BB84 PROTOCOL CHAPTER 2. QUANTUM CRYPTOGRAPHY
2.2 The BB84 protocol
In the BB84 protocol, Alice wishes to send a private key to Bob, or rather; Alice
and Bob wishes to create a key. This is done by choosing two non-orthogonal
bases where each basis consists of two orthogonal bit values. Using polarization,
we let the first basis be defined by the horizontal and vertical polarization and the
second basis be defined by the two diagonal polarizations. These bases are known
as the + and × bases respectively. The polarization states are denoted as | ψij
where i is the basis and j is the bit value and from equation (2.1) we obtain:
| ψ+0 =| 0 =|→ | ψ×0 =
| 0 + | 1
√
2
=|
| ψ+1 =| 1 =|↑ | ψ×1 =
| 0 − | 1
√
2
=|
To create a key for an arbitrary cryptosystem, Alice begins by transmitting single
photons where she randomly chooses, from the four polarization states shown
above, which polarization to send each photon in. Bob the randomly chooses
which polarization to measure in and writes down what polarization he measured
and what result he got. Alice and Bob then exchange which polarizations they
used and the results where Bob measured correctly are retained as the key. This
imposes a risk in our protocol, since exchanging what polarizations Alice and Bob
used over a public channel gives information about the values that were sent. In
the ideal case, where there is no loss or noise in the system, this is solved by
considering what possibilities Bob has for detecting a photon.
If Alice sends a photon with vertical polarization and Bob measures the vertical
polarization, then Bob detects the photon. If instead Bob measures a diagonal
polarization he will have a 50% probability of detecting the photon and if he
measures the horizontal polarization he will have 0% probability of measuring the
photon. It is therefore not important to note which polarization he measures, but
only which basis he uses because if he measured in the correct basis and he did
not detect a photon he know that he measured the wrong bit vaule and therefore
know what bit value was sent. In this way, Bob has 50% probability of measuring
the correct value and thus only half of the photons sent will be used for the key.
When creating the key, Bob now only has to tell Alice which bases he used, which
gives no information about values he measured, and this is then used to obtain
the key. This is shown in figure 2.1.
8
15. CHAPTER 2. QUANTUM CRYPTOGRAPHY 2.2. THE BB84 PROTOCOL
Figure 2.1: BB84 protocol using polarized photons.
Let us now consider the case where an eavesdropper, known as Eve, has access to
the photons before they reach Bob and where it is assumed that Eve is infinitely
clever, with infinite resources and that she knows which bases Alice encodes the
photons in. The simplest type of attack Eve can perform is known as the intercept-
resend attack where Eve intercepts the photon, measures in a random basis and
sends a photon corresponding to her result to Bob. As before, Eve has a 50% prob-
ability of measuring correctly and Bob then has a 50% probability of measuring
the photon he receives from Eve “correctly”. There is therefore a 25% probability
that Bob measures the correct value with respect to what Alice sent. When Alice
and Bob then exchanges which bases they used, this pertubation does not show
up. In order to detect Eve they have to sacrifice some measurements where they
used the same bases in order to calculate the error rate or the percentage of the
results that was measured incorrectly. In this case, it well be discovered that 50%
of the retained qubits have incorrect values and Eve is thereby discovered and the
entire key is discarded.
If Eve instead only intercepts 10% of the photons and then send her results to
Bob, Eve will gain 5% of the information sent from Alice to Bob and she will only
cause a 2.5% higher error rate for Bob. Even though Eve only gains a small part
of the key, this still poses a problem since Eve can be considered to be infinitely
clever and it can therefore be assumed that she is able to determine the entire key.
In order to counter this, Alice and Bob either have to use exchange a larger part of
9
16. 2.2. THE BB84 PROTOCOL CHAPTER 2. QUANTUM CRYPTOGRAPHY
the retained qubits or implement a privacy amplification protocol after the initial
exchange of a certain amount of qubits. In the privacy amplification protocol,
Alice and Bob decide how much the remaining sequence of qubits should be short-
ened, even though Eve has not been present, so that the amount of information
that Eve might have gotten is below a certain threshhold. To do this, Alice and
Bob chooses an amount τ by which the sequence of qubits needs to be reduced.
Alice now produce a random matrix of the size (n − τ) × n, where n is the length
of the sequence of qubits and multiply it with the qubit vector. This matrix is
now sent through a public channel to Bob, who also multiplies it with the qubit
vector. Alice and Bob now have a resulting key of the length n − τ, which can be
used to encrypt the message, since it is assumed that Eve does not have enough
information to pose a threat.
Further information about polarization manipulation can be found in chapter 9.1.4
in [13] and a more detailed discussion of the BB84 protocol can be found in section
3.2 in the pre-thesis[3], in section II.C in [5] or the original article [12]. The BB84
protocol in noisy environments is also discussed in some detail in sections II- V
in [14].
Polarization is the simplest way of encoding photons, but it is not the ideal solution
when using optical fibres, since polarization is in general not conserved in these.
The reason for this is that optical fibres works by total internal reflection inside the
fibre core and since the interface between the core and the cladding is curved, the
polarization of the photon becomes elliptical or circular. It is still possible to use
optical fibres for polarization encoding, but it is essential to know exactly how the
polarization is changed through the system and this change is highly sensitive to
the slightest bend or temperature fluctuations, which makes optical fibres highly
problematic to use for polarization encoding. Since most quantum cryptography
systems, including the system used in this pre-thesis, are based on optical fibres,
we have to use an other form of encoding: phase encoding.
When using phase encoding, the phase of the photon is modulated instead of the
polarization and Bob then detects the interference. In order to do this, we first
need the means for obtaining this interference. This brings us to the so-called
Mach-Zehnder interferometer.
10
17. CHAPTER 2. QUANTUM CRYPTOGRAPHY 2.3. MACH-ZEHNDER
2.3 Mach-Zehnder
The Mach-Zehnder interferometer was developed by Ludwig Mach and Ludwig
Zehnder in the late 19th century and consists of two symmetric 50/50 beam split-
ters where the two outputs of the first splitter are the inputs of the second splitter.
A schematic of this is shown in figure 2.2 where a phase modulator is added on
one of the arms.
Figure 2.2: Unbalanced Mach-Zehnder interferometer with
beam splitters BS and mirrors M.
To explain this system, we first need to know the action of a single symmetric
beam splitter. This is given by the simple rule:
|In → |Transmitted + |Reflected =
1
√
2
|In +
ei π
2
√
2
|In =
1
√
2
|In +
i
√
2
|In
(2.2)
Where the fraction 1/
√
2 is due to unity and the π/2 phase shift comes from unity,
the beam splitter being lossless and the fact that it is a symmetric beam splitter.
The origin of the phase shift was shown by Degiorgio in 1980[15] and Zeilinger in
1981[16] and it is discussed in greater detail by Holbrow et al. in 2001[17].
We now consider the case where we inject a single photon into input 1 and nothing
in input 2. Applying equation (2.2) we see that the arms |1 and |2 are given by:
|1 =
1
√
2
|In1 |2 =
i
√
2
|In1 (2.3)
Depending on the nature of the two mirrors, the photon will either receive a π
phase shift or no phase shift, but since this affects both arms this effect cancels
11
18. 2.3. MACH-ZEHNDER CHAPTER 2. QUANTUM CRYPTOGRAPHY
out and we will therefore omit this. We therefore have that:
|4 = |1 =
1
√
2
|In1 |3 = eiφ
|2 =
ieiφ
√
2
|In1 (2.4)
Where the phase shift φ is imposed by a modulator that merely delays the photon
by φ by changing the length of the optical path. Using equation (2.2) again we
then obtain the following results for the outputs:
|Out1 =
i
√
2
|4 +
1
√
2
|3 =
i
2
|In1 +
ieiφ
2
|In1 =
1
2
+
eiφ
2
i|In1 (2.5)
|Out2 =
1
√
2
|4 +
i
√
2
|3 =
1
2
|In1 +
i2
eiφ
2
|In1 =
1
2
−
eiφ
2
|In1 (2.6)
From this we can see that if we let the phase shift φ on |3 be 0 we get:
|Out1 = i|In1 (2.7)
|Out2 = 0 (2.8)
Where the phase shift i is an overall phase shift and does not affect any detection.
If we instead phase shift |3 by π we obtain:
|Out1 = 0 (2.9)
|Out2 = |In1 (2.10)
It is therefore possible to determine the phase difference between the signal |3 and
the reference |4 by measuring the output of one or both output arms. This can
now be used to build a quantum key distribution system based on phase encoding.
Since most optical communication systems are based on optical fibres, we first
have to introduce the fibre equivalent of the Mach-Zehnder interferometer.
This is done by using so-called fibre couplers, which consists of two fibres on which
the cores are exposed on a small section. The two fibres are then joined together
over a certain length, so that the two fibres effectively share the core over that
distance. An incoming signal then oscillates between the two cores as a function
of its wavelength. By controlling the length of the coupler, it is therefore possible
to split the signal up in a specific ratio. In a symmetric coupler the length of
the coupler is so that, at a certain wavelength, half of the signal is in each core.
Fibre couplers are therefore passive components equivalent to beam splitters and
split the incoming signal up in two parts in a ratio depending on the length of the
coupler and the wavelength of the signal.
Using symmetric fibre couplers, where the ratio is 50/50, an optical fibre Mach-
Zehnder interferometer can be made as shown in figure 2.3.
12
19. CHAPTER 2. QUANTUM CRYPTOGRAPHY 2.4. FABRY-PÉROT
Figure 2.3: Mach-Zehnder interferometer where FC are fibre
couplers.
As for the Mach-Zehnder interferometer shown in figure 2.2, the output |Out1 is
maximum when the length difference between the two arms is n · π, where n =
{0, 1, 2, ...}, and minimum when the length difference is n · π/2.
2.4 Fabry-Pérot
In the case of continuous wave (CW) light, the unbalanced Mach-Zehnder interfer-
ometer will act like a cavity with a length equal to the length difference between
the two arms. Constructive or destructive interference will therefore occur de-
pending on the wavelength, since only certain wavelengths are supported. For a
wavelength to be supported in a given cavity, the length of the cavity must be
2 · n · λ, where n is an integer and λ is the wavelength. This gives rise to a periodic
Fabry-Pérot structure in intensity as a function of wavelength as the length of the
cavity becomes a multiple of the wavelength. The distance between two peaks in
this periodic structure is called the free spectral range (FSR) and is given by:
FSR = ∆λ =
λ2
0
2 · n · L + λ0
(2.11)
Here, ∆λ is the distance between two peaks in the periodic structure, λ0 is the
central wavelength, n is the index of refraction of the media and L is the length
of the cavity. We can from this see that if the cavity length decreases, the FSR
must increase.
When using CW light, the Fabry-Pérot structure can therefore be used as a mea-
sure of the phase shift, since a change of FSR corresponds to changing the optical
path length a wavelength and therefore corresponds to a phase shift of 2π. Simi-
larly, a change of FSR/2 corresponds to a phase shift of π. It is therefore possible
to use a CW light source to characterize an unbalanced Mach-Zehnder interferom-
eter and determine the phase shifts by measuring the Fabry-Pérot structure as a
function of wavelength.
We now have the means to measure phase differences and can therefore now go on
to discuss phase encoding.
13
20. 2.5. THE B92 PROTOCOL CHAPTER 2. QUANTUM CRYPTOGRAPHY
2.5 The B92 protocol
The use of phase shifting for encoding photons was first published by Bennett
in 1992 and thus this protocol was called the B92 protocol. Here he suggested
a simplified version of the BB84 protocol using two identical unbalanced Mach-
Zehnder interferometers, meaning that the arms of the interferometers are not the
same length. A schematic of the system is shown in figure 2.4.
Figure 2.4: Schematic of the B92 protocol Laser, modulators
and Detector.
Recalling the discussion about how the signal is split up in two parts in the inter-
ferometer and the fact that this system is supposed to use single photons which
is the smallest amount of light possible, one might have trouble grasping how
this would work. To explain this, we have to turn back to quantum mechanics.
When a photon reaches a beam splitter, it has 50% probability of going in each
direction and if one then positions a detector in either of the outputs, a detection
will then occour 50% of the time. Now the quantum mechanics steps in; if we
do not detect which path the photon will take, it will take both paths, or rather
a superposition of both paths2
. This has been shown several times for photons,
electrons[19], neutrons[20], atoms[21] and other particles, where a single particle
gains information about both paths even though it logically should travel through
only one of the paths. The conclusion is therefore that it is possible to make a
single particle interfere with itself as long as we do not try to determine where it
is. In the same way, one should not think of the signal as having an intensity but
instead a probability distribution.
An incoming photon is thus split up in two parts separated in time in Alice’s in-
terferometer, where the front part is a reference and the second is the signal which
has been phase shifted φA by the modulator. Since half of the signal will be sent
out through the second output, each of the two parts will ideally (i.e. no loss or
noise) contain 1/4 of the probability distribution. When the two parts arrive at
Bob’s Mach-Zehnder interferometer, both parts are split up in two parts and the
parts travelling through the long arm are phase shifted. Given that the two in-
terferometers are identical, the output from Bob’s interferometer will now consist
2
This should be seen as equivalent to the Schrödingers Cat paradox[9].
14
21. CHAPTER 2. QUANTUM CRYPTOGRAPHY 2.5. THE B92 PROTOCOL
of four parts of equal size of ideally 1/8 of the probability distribution and where
two of the parts have been phase shifted φB. The part that went through the
short arm of both interferometers will arrive before the others and the part that
went through both long arms will arrive late and these two parts can therefore
be ignored since they cannot be used for interference. This is done by gating the
detector so that it is off at their time of arrival. The two remaining parts will have
travelled similar distances, where the difference is given by the difference between
the phase shifts φA and φB. These two parts will therefore arrive at the last beam
splitter or coupler at the same time and will therefore cause interference where the
resulting output will depend on the phase difference, as discussed in section 2.3.
How the four probability distributions are separated in time is shown in figure 2.5.
Figure 2.5: The output from Bob’s interferometer where “s”
and “l” represents going through the short and
long arm respectively.
If Alice and Bob imposed the same phase shift, constructive interference will appear
and the detector will therefore detect a signal. If there is a π difference in the phase
shifts, destructive interference will appear instead and the light will be sent out of
the other output arm and the detector will therefore not see a signal. If instead the
phase difference is π/2, Bob will have 50% probability of measuring the photon.
It is of course possible to place a detector on the second output arm so that both
outputs can be detected, but in practise this causes as many problems as it solves
due to imperfect detectors. This is because both detectors have to be completely
identical in any sense for this to work properly. Since this is not feasible in practise,
this would result in a rather more complex error rate and data analysis, since each
detector must be analyzed separately, and a single detector is therefore preferred.
In order to actually detect a single photon, we have to use a special detector called
an avalanche photo diode (APD) single photon detector. A schematic of how this
is build is shown in figure 2.6.
15
22. 2.5. THE B92 PROTOCOL CHAPTER 2. QUANTUM CRYPTOGRAPHY
Figure 2.6: Principle of the avalanche photo diode.
This can be called a PIPN semiconductor diode, since it is built up by a p-doped
part with excess electrons, an intrinsic part, which is a pure semiconductor, another
p-doped part and a n-doped part with excess holes. The terms p- and n-doped
semiconductors means that the semiconductor is doped with other atoms that
increase or reduce its total amount of electrons respectively. When a photon hits
the intrinsic part it generates an electron-hole pair, where the electron travels
towards the right and the hole travels towards the left due the the electric field
across the diode. The field strength is shown in figure 2.6 as well, and indicates the
force with which the electrons and holes are moved. When the electron reaches the
PN junction to the right, where the electric field strength increases, the electron
gains enough energy to break free several other electrons, creating an avalanche
effect. One electron thus becomes many and there is now enough signal to show
that a photon was detected. The reason for having the avalanche effect happen
in a small region instead of throughout the diode is because photons will not
be absorbed by the intrinsic layer at the same place each time and the amount
of electrons will therefore be different for in each detection. This causes some
problems for the electronics that determines if there was a detection and in order
to ensure that approximately the same signal is produced each time, the avalanche
effect is restricted to a small region.
Bennett originally proposed this system using any two non-orthogonal states, but
to increase the security of the system, we will use two non-orthogonal bases each
consisting of two orthogonal states, as discussed for the BB84 protocol in section
2.2. We therefore define φ = 0 and φ = π to be “0” and “1” respectively in the
first basis and φ = π/2 and φ = 3π/2 to be “0” and “1” respectively in the other
basis. From the previous discussions it is clear that these states qualifies for use
in this protocol, since measuring in the wrong basis will give Bob 50% probability
of measuring a photon.
From the above discussions we can now look at what results Bob would obtain
when using the various phase shifts. This is shown in table 2.1.
16
23. CHAPTER 2. QUANTUM CRYPTOGRAPHY 2.5. THE B92 PROTOCOL
Alice Bob
Qubit φA φB φA − φB Qubit
0 0 0 0 0
0 0 π
2
π
2
?
0 0 π π ?
0 0 3π
2
3π
2
?
1 π 0 π ?
1 π π
2
π
2
?
1 π π 0 1
1 π 3π
2
π
2
?
0 π
2
0 π
2
?
0 π
2
π
2
0 0
0 π
2
π π
2
?
0 π
2
3π
2
π ?
1 3π
2
0 3π
2
?
1 3π
2
π
2
π ?
1 3π
2
π π
2
?
1 3π
2
3π
2
0 1
Table 2.1: The B92 protocol using four states and where “?”
denotes uncertain result.
From this it is clear that Bob will only measure the correct bit value 25% of the
time and in the realistic case where we have loss and noise in the system, this will
be reduced to one correct measurement out a few thousand pulses.
The security of this system is, as in the case of polarization encoding, given by
the randomness of the measurements and the known probabilities for what Bob
measures. The basic attacks Eve can perform on this system is therefore the same
as in the case of polarization encoding, as discussed in section 2.2.
A more thorough description of phase coding is given in section 3.2 in the pre-
thesis[3] and in [5]. It should be noted that photons can also be encoded using
frequency, or rather in the relative phase of the side-bands of the central frequency,
as discussed in section 3.2 in the pre-thesis[3] and the original publication by
Goedgebuer in 1997et al.[22]. In addition, it should also be noted that phase
encoding can also be done using entangled photons[23], where entangled photons
are discussed in some detail in the pre-thesis[3] and in the original publication on
using this for QKD by Ekert in 1991[24].
The discussions so far have mainly concerned ideal systems without loss or noise
present. Since this very rarely is the case in practise, we have to be able to take
this into account in our data analysis and in the ways we try to detect Eve.
17
24. 2.6. SECURITY CHAPTER 2. QUANTUM CRYPTOGRAPHY
2.6 Security
The security of any system depends on how much information any third party
might obtain and how to prevent this from happening. In classical cryptography
this is done by making it sufficiently difficult for any third party to obtain the
information by using products of large prime numbers, as described in chapter
1.1. In quantum cryptography however, the security is determined by the ability
to detect the perturbations caused by Eve. Because there is noise and loss in all
systems this makes it increasingly difficult to detect Eve, since she is no longer the
only source of perturbations and it is therefore necessary to establish a measure
of the amount of incorrectly measured photons compared to the total amount of
received photons. This is known as the quantum bit error rate and is given by[4]:
QBER =
Ne
N
=
Re
R
(2.12)
Where N is the amount of photons measured, Ne is the amount of photons that
was measured incorrectly and R and Re are the corresponding detection rates. The
QBER is then measured for the system and from this, any excess perturbations
can then be detected and thus determining if Eve is present.
The main sources of errors or noise are visibility imperfections due to interference
edge-contrast and dark counts in the detector. The visibility imperfections gives
rise the error rate 1−V
2
where V is the interference-visibility. The reduction of this
requires that the system is kept stable over time and a visibility of 98%, yielding
an error rate of 1%, indicates a stable and well adjusted system.
The dark counts are due to imperfect detectors where there is a certain probabil-
ity over time that an electron will spontaneously detach itself from an atom and
thus will be detected as a photon count. This can be reduced by using a small
detection period and setting a bias voltage over the diode so that this probability
is reduced. Because a bias over the diode also reduces the detection probability
this is a trade-off between noise rate and the probability that a photon is detected
and this is often set so that there is a 10% detection probability of the incomming
photons. Additionally, this value is the prime reason for limitations in transmis-
sion distance, since the error rate due to visibility imperfections is independent of
length.
The maximum QBER that is usually required for a system to be sufficiently secure
can range from in the order of 10% and up to 50% depending on the dark count
rate. This should be seen in contrast to the acceptable error rates used in classical
telecommunication, where it usually is in the order of 10−9
or in some cases down
to 10−15
.
Since the effective bit rate depends on the noise rates, it is possible to calculate
the bit rate as a function of distance. This is done from the knowledge of both
18
25. CHAPTER 2. QUANTUM CRYPTOGRAPHY 2.6. SECURITY
Alice’s and Bob’s mutual Shannon information, I(α, β), and the maximum Shan-
non information that Eve might have gained without compromising the security
of the system, Imax
(α, ), which is seen with respect to Alice’s and Bob’s mutual
Shannon information. The Shannon information depends on the specifics of the
system, including the distance, and the bit rate as a function of distance can then
be written as:
Rb = Rc · (I(α, β) − Imax
(α, )) (2.13)
From this, it is possible to calculate that the maximum transmission distance for
a 1550nm signal is in the order of 50 to 100km.
In order to correct the noise counts, we have to consider what actions Alice and
Bob can perform. When Alice has finished the transmission of the photons, Alice
and Bob first have to determine the raw key material. This is done by Bob sending
a register of the incidences where he detected a photon, since this in the ideal case
should be the only incidences where Bob should detect a photon. They then select
a set number of incidences and compare the phase states they used and from this
calculates the QBER. Because the incidences that were used for this comparison
is now compromised, they are therefore discarded. If the QBER is close enough
to the initially calculated QBER for the system, since there will always be an
uncertainty on the QBER, Alice and Bob now have to correct these errors. This is
done by first splitting the detected photons into blocks as shown in the following
table:
A 01001010 10011001 11010010 10011101
B 01011010 10011001 11010010 10111101
A 00100010 10011111 00100010 11011011
B 00100010 10011110 01100010 11011011
A 01101100 00110001 10010110 01000111
B 01111100 00110001 10010110 01000111
A 11100010 00010100 11110111 11000110
B 11100010 00010100 11110110 11000110
Table 2.2: A sample of Alice’s (A) and Bob’s (B) raw key
material generated by QKD.
The key material above contains errors arising mainly from detector noise and
these are removed by a simple block-parity check procedure. This is done by cal-
culating the binary sum of each block, yielding either 0 or 1, and if this value differ
for a certain block, it means that there is an odd number of errors in the block
and it is therefore discarded[25]. Since this is based on the assumption that there
19
26. 2.6. SECURITY CHAPTER 2. QUANTUM CRYPTOGRAPHY
are no more than one error in any block, this procedure has to be performed a
number of times where the blocks are changed each time to reduce the risk that
two errors can be present in a block.
The size of the blocks is a trade-off between having small enough blocks so that
less information is lost when blocks are discarded, but being large enough so that
less information about the key material can be obtained by Eve. In the case of 8
bit blocks, a single bit is dropped from each block that passes the parity check to
compensate for the information revealed publicly. If further security is required,
the privacy amplification method, as discussed in section 2.2 can be applied.
Another major concern is that Eve might gain information about the key by only
intercepting pulses containing more than one photon, measure each photon in-
dividually and thus obtain the correct value and then send a photon with the
resulting value to Bob. This problem arises due to imperfect single-photon sources
and this attack is called a photon splitting attack. Even though this is not possible
with present day technology, it cannot be assumed that Eve cannot figure out how
to do this in practise and it is therefore necessary to introduce a security measure
to detect photon splitting attacks. This is done by extending the protocol to use
decoy states, the idea of which was first proposed by Hwang in 2003[26]. The secu-
rity of decoy states was proved by Lo et al. in 2004[27] and the first experimental
implementation of it was reported Zhao et al. et al. in 2006[28].
Decoy states are pulses that contains more than one photon on purpose and Alice
chooses at random what pulses she sends as decoy states. After the transmission,
Alice then informs Bob which pulses were sent as decoy states and this can now be
used to detect Eve’s photon splitting attack. Because the decoy states will have a
higher detection rate and because Eve cannot distinguish between ordinary pulses
containing more than one photon and decoy states, Alice and Bob will therefore
be able to see her attack when analysing the results. The decoy states are usually
chosen to contain 1 − 5 photons on average, in contrast to the ordinary pulses
that usually contains 0.1 photons on average. To increase the effectiveness of the
decoy states, decoy states with different numbers of photons on average can be
transmitted. Any change in the relative incidence of the different photon numbers
that are registered at Bob can then be used to detect the presence of Eve.
For more information about the security of the QKD protocols, see [29], [30] and
[31]. In addition, the security of imperfect photon sources and detectors is dis-
cussed in [32].
Now that we have discussed the basic mechanics and methods of QKD, we can
now look at what realizations have been made in this subject.
20
27. CHAPTER 2. QUANTUM CRYPTOGRAPHY 2.7. REALIZATIONS
2.7 Realizations
Fibre optical QKD systems have been available commercially for some years now
but systems using integrated optical components[33] are still under development
but working systems have been realized. In 2001, Bonfrate et al. published their
proposal of a system based on germanium-doped silica waveguide interferometers
[34], using the set-up shown in figure 2.7[34].
Figure 2.7: Two waveguide asymmetric Mach-Zehnder inter-
ferometers combined on optical fibre link to pro-
duce QKD interferometric system.
Where the integrated optical components are similar the the one shown in figure
2.8[38] except with a thermo-optical modulator on the short arm.
Figure 2.8: Schematic of a typical planar light-wave circuit.
Using this set-up, they obtained pulses that were separated in time by 1.1ns and
with the centre pulse being the interference pulse. This is shown in figure 2.9[34]
where the inset shows the interference peak intensity when scanning the phase,
exhibiting the expected sinusoidal dependency of the phase.
21
28. 2.7. REALIZATIONS CHAPTER 2. QUANTUM CRYPTOGRAPHY
Figure 2.9: Scope trace of combined output.
When using an InGaAs APD detector with a 3ns gate width and a repetition rate
of 100kHz, they obtained a QBER of ≈ 2%.
In 2004, Honjo et al. reported a QKD system using an integrated-optic inter-
ferometer based on the B92 protocol for the first time[35]. In this system, Alice
transmits a intensity and phase modulated signal and Bob measures the inter-
ference with an asymmetric Mach-Zehnder interferometer with detectors on both
output ports. With this system, they were able to achieve a raw key generation rate
of 3076 bits per second with a 5.0% QBER over 20km of fibre. In the same year,
Kimura, Nambu et al. reported a system using two asymmetric Mach-Zehnder
interferometers[36] as in figure 2.7 where the relative phase shift between the two
arms in the interferometers was changes by controlling the temperature of the en-
tire chip. With this set-up, they were able to create raw key material over 150km
with a interference visibility of more than 80%.
In 2004[37] and 2008[38], Nambu et al. reported two systems using phase and po-
larization coding respectively, using integrated optical asymmetrical Mach-Zehnder
interferometers, and proposed a number of examples of how to expand the use of
planar light-wave circuits for implementation of other protocols.
In this thesis we propose a new system using a different version of the asymmetric
Mach-Zehnder interferometer.
22
29. Chapter 3
Chip characterization
The components used in this project was designed to fulfil the requirements set by
MOBISEQ:
• The components must be portable and be able to be integrated into existing
systems.
• The components must contain wave guides capable of guiding light at TELE-
COM wavelengths and, more specifically, that of the laser we intend to use
which produces approximately ≈ 300ps long pulses at ≈ 1549.3nm.
• The components must be identical so that one component is to serve as
encoder for Alice and one as decoder for Bob. Any difference between the
two components is therefore likely to introduce a source of error.
These requirements form the motivation behind the design of the component where
we wish to use the B92 protocol extended to four quantum states in two bases as
discussed in detail in section 2.5.
3.1 The design
The integrated optical SiO2 on Si chips containing the components were designed
by Jacob Selchau as a part of his Ph.D. thesis[1] and then manufactured by Dan
Zauner at Ignis Photonyx and Henrik Rokkjær Sørensen at NKT Photonics. The
design was based on the development of an idea first proposed by Kashyap in
1993[39], which involved using Bragg gratings in fibres as mirrors, with an early
integrated optics implementation by J. M. Jouanno, D. Zauner and M. Kristensen
in 1997[40].
The Bragg grating is in this case a sinusoidal change in the refractive index of the
waveguide with grating spacing Λ and a schematic of this is shown in figure 3.1.
23
30. 3.1. THE DESIGN CHAPTER 3. CHIP CHARACTERIZATION
Figure 3.1: Schematic of Bragg grating.
Where the core has refractive index n and the refractive index of the grating is
nB. This results in an effective refractive index, neff , of the Bragg grating. Using
this, we can write the following expression for the wavelength that is reflected by
this grating:
λB = 2 · neff · Λ (3.1)
This is because only a certain wavelength is subject to constructive interference
when reflected. The bandwidth of this reflection is then given by:
∆λ =
2 · δn0 · η
π
λB (3.2)
Where δn0 is the variation in the refractive index (n − nB) and η is the fraction of
power in the core. The bandwidth therefore depends on the shape of the grating
where any change in the refractive index of the grating will results in a larger
bandwidth.
Because the grating is written from the top of the chip by doping the silica with
germanium, the effective index of refraction of the waveguide is different for hor-
izontally and vertically polarized light. It is therefore important that only one of
these polarizations is used because the result would otherwise be a superposition
of two slightly different unbalanced Mach-Zehnder interferometers. The polariza-
tion of the light is for this reason controlled using a polarization controller before
entering the chip so that the dips in the structure are as deep as possible since any
superposition of the two structures will result in more shallow dips due to different
FSR values.
The Bragg grating can therefore be used as a mirror at the wavelength λB ±∆λ/2
as it transmits all other wavelengths. By using this, it is possible to reduce the
size of the component. This is done by folding the asymmetric Mach-Zehnder
interferometer onto itself and thus producing a Michelson-Morley interferometer
where we only use one of the input/output arms. This is shown in figure 3.2.
24
31. CHAPTER 3. CHIP CHARACTERIZATION 3.1. THE DESIGN
Figure 3.2: The designed component with symmetric cou-
pler SC, Bragg gratings BG and thermo-optical
modulator TOM.
In this way, the component is effectively an unbalanced Mach-Zehnder interfer-
ometer at a certain wavelength range, depending on the Bragg grating. The
phase difference between the two arms is then changed by placing a voltage over
the thermo-optical modulator (TOM) so that the temperature of the waveguide
changes, resulting in change of the refractive index and thus effectively changing
the optical path length. As discussed in section 2.5, the pulses are separated in
time by the time it takes the light to travel the length difference between the two
arms. In our components, the length difference is approximately 4cm and with an
index of refraction of 1.54, the delay becomes in the order of 400ps. The signal
parts are therefore separated by 400ps in time and their widths are 300ps at full
width half maximum (FWHM). Since the tails are far longer than the FWHM,
the non-interfering parts of the signal will overlap in some degree resulting in an
offset of the interfering parts.
A schematic of the chip containing 12 components is shown in figure 3.3.
Figure 3.3: Schematic of the chip containing 12 components
with thermo-optical modulators.
25
32. 3.2. BASIC SET-UP CHAPTER 3. CHIP CHARACTERIZATION
A picture of one of the chips is shown in figure 3.4.
Figure 3.4: Picture of one of the chips.
One should notice that the chip in figure 3.4 is turned 180◦
with respect to the
schematic in figure 3.3 and the input side of the chip is therefore the right hand
edge in the picture.
3.2 Basic set-up
The basic set-up used in the characterization measurements consists of a narrow
band CW laser source controlled by a spectrum analyser, polarization control
before the chip and the platform with the chip and fibre launch platforms, as seen
in figure 3.5.
Figure 3.5: Sketch of basic set-up with three dimensional,
high precision fiber launch platforms on an iso-
lated platform.
The platform with the chip mount and fibre launch platforms is isolated from the
lower platform and allows the upper platform to move in both horizontal directions
under a microscope. In this way, it is possible to look at any part of the chip
26
33. CHAPTER 3. CHIP CHARACTERIZATION 3.3. CHIP SELECTION
through the microscope without compromising the alignment. The fibre launch
platforms are equipped with micro-precision positioning screws and the horizontal
axis screws are equipped with piezoelectrical elements for fine-tuning. The manual
screws on the fibre launch platforms allow movement over approximately 3mm and
the piezoelectrical elements allow movement over 25µm over a voltage change of
approximately 100V. This allows us to position the fiber and butt-couple it with
the chip with high precision in three dimensions and makes it easy to switch to a
different component on the chip. In addition, the centre stages is equipped with
a micrometer screw, so that it can be moved several cm in the horizontal axis
perpendicular to the fibers. This makes it easy and practical to switch component
without having to move each fibre individually over relatively long distances.
Before the light enters the chip, we also have a circulator. A circulator is a passive
fibre-optic component that is used to separate light going in different directions.
It is a three-port device designed such that light entering any port exits through
the next. This means that if light is sent into port 1, it will exit through port
2. If the light that came out through port 2 is then reflected and enters the
circulator through port 2, this light will exit through port 3. This makes it ideal
for our experiments, since it gives us the opportunity for using and measuring the
reflected light from the chip.
3.3 Chip selection
Because the manufacturer of the chips did not have the equipment to determine at
what wavelength the Bragg gratings reflected light, the chips were sent to us so that
we could characterize the chips. This was done by measuring the transmitted light
through the long arm and the reflection from the chip as a function of wavelength
and through this determining at what wavelength the grating reflects and the
strength of the grating. Out of 8 attempts, only one chip was suitable for our
experiments[1][2], with a reflection wavelength of approximately 1549.5nm and
with a grating strength given by a 16 − 20dB decrease in transmission. This chip
had been damaged at some point and a corner of the chip had broken off. Together
with the fact that the last three components were defective, this resulted in only
components 5−9 was usable, out of which components 6−8 was the best. Because
this was the only usable chip, we chose to use components 6 and 8[3]. The first
measurements of the transmission and reflection of components 6 and 8 are shown
in figures 3.6 and 3.7.
27
34. 3.3. CHIP SELECTION CHAPTER 3. CHIP CHARACTERIZATION
Figure 3.6: Transmission and reflection spectra for compo-
nent 6 using lower input arm.
Figure 3.7: Transmission and reflection spectra for compo-
nent 8 using lower input arm.
28
35. CHAPTER 3. CHIP CHARACTERIZATION 3.3. CHIP SELECTION
Where the centre wavelength, at which the grating in the long arm reflects light,
is given by the minima in the transmission spectra and the strength of the grating
is given by the depth of the dip in the spectra. In addition, it can be seen that
the bandwidth of the grating is approximately 0.5nm. The characterization and
selection of the chip is discussed in great detail in [1] and [2].
It should be noted that the maximum transmission level at approximately −17dBm
is due to unoptimized alignment. The reason why this was not better aligned is
because it is the shape of the spectra and not the intensity that is important at
this point. In addition, it is not always possible to achieve the same maximum
intensity level due to defects on the end facets of the optical fibres, dust on the
chip or other factors that can change from day to day.
The “noise” on the reflection spectrum is the Fabry-Pérot structure as discussed
in section 2.4. Since this structure is not a “clean” structure with fixed spacings
between the peaks, this suggests the presence of other cavities in our system so
that the structure becomes a superposition of several structures. To identify these
other cavities, we first notice that the reflection outside the grating bandwidth
is very high compared to the intensity change in transmission. The main cause
of this is reflections from the end facet of the fibre and of the chip, since there
is a large change in refractive index due to a gap between the fibre and the chip.
Because this gap is edged by two large changes in refractive index, the gap becomes
a cavity with cavity length in the order of tens of µm and thus a large FSR. In
order to remove this cavity and decrease the reflection, the gap has to be filled
with something with an index of refraction closer to that of the fibre core and the
waveguide in the chip.
29
36. 3.4. OPTIMIZATION CHAPTER 3. CHIP CHARACTERIZATION
3.4 Optimization
For this purpose, we use an optical coupling compound called index-matching gel
with an index of refraction of approximately 1.46. This is applied as shown in
figure 3.8.
Figure 3.8: Schematic of application of index-matching gel.
The change in refractive index at the interfaces then becomes less that 0.1 and
the effect of the cavity is greatly reduced. Two new properly aligned measure-
ments of the transmission and reflection spectra of components 6 and 8 were then
obtaine.and a reference measurement without the chip, yielding approximately
−2.95dBm, was subtracted from the data. This is shown in figures 3.9 and 3.10.
Figure 3.9: Transmission and reflection spectra for compo-
nent 6 using lower input arm with index gel.
30
37. CHAPTER 3. CHIP CHARACTERIZATION 3.4. OPTIMIZATION
Figure 3.10: Transmission and reflection spectra for compo-
nent 8 using lower input arm with index gel.
The Fabry-Pérot structure is here seen more clearly, but even though the reflection
at wavelengths outside that of the grating is far lower and some of the oscillations
have disappeared, there are still other slow oscillations present. In addition, it
should be noticed that the reflection and the transmission spectra does not seem
to match; the reflection is still relatively high compared to the transmission at
wavelengths shorter than the centre wavelength of the transmission dip. This is
likely to be due to a small difference in the grating spacing between the gratings
in the short and the long arm, but because the short arm is terminated in the
middle of the chip, it is impossible to measure the transmission spectrum of this
grating. We can therefore only guess the cause of this mismatch between reflection
and transmission spectra, leaving this subject open for debate and turn back to
the oscillations in the reflection spectra.
In order to characterize the oscillations present in the reflection spectra, we have
to look at what contributors there might be. In order to do this, we first we have
to determine the FSR of the component.
We have that the length difference between the two arms is approximately 4cm,
which corresponds to the length of the “cavity”. Using that the index of refraction
of the waveguide is n = 1.54 and that the wavelength is λ0 = 1549.5nm, we then
obtain the following free spectral range (FSR) from equation (2.11):
FSRcomponent = ∆λ =
λ2
0
2 · n · L + λ0
=
(1549.5nm)2
2 · 1.54 · 4cm + 1549.5nm
= 0.02nm (3.3)
31
38. 3.4. OPTIMIZATION CHAPTER 3. CHIP CHARACTERIZATION
The fast oscillations are therefore clearly due to the component, but there are still
oscillations with an FSR in the order of 0.2nm that are not accounted for. Since
these are not seen when measuring before the chip, they must be due to something
in the chip or the input fibre. We can therefore calculate the cavity length for an
FSR of 0.2nm at λ0 = 1549.25nm by using n = 1 for air and n = 1.54 for the
waveguide. This yields:
L =
λ2
0
FSR
+ λ0
2 · n
=
6mm for n = 1
4mm for n = 1.54
(3.4)
A 6mm cavity in free air is not likely, because such a cavity would be easy to find
and the cavity must therefore be within in the chip and be approximately 4mm
long. Looking at the chip, we see that the most likely source is the Bragg gratings
themselves, which are approximately 4mm long. The most likely explanation for
why this cavity arises is that the manufacturing of the gratings is not ideal so that
the edges of the gratings are doped with more germanium than the centre of the
gratings, resulting in reflections from the ends of the gratings. Since the gratings
are inside the chip it is not possible for us to reduce the effect of this cavity, but
since the oscillations does not have a severe impact on the quality of the grating,
these cavities can be ignored.
Due to the fact that we are going to use this system for single photons, it is nec-
essary for the bit rate that any part of the system that can be considered to be
outside Alice’s domain has the lowest possible loss. From looking at the figures 3.9
and 3.10, we therefore assign component 6 to Bob since this has the lowest loss.
This is because every part of the system located before the point where the pulses
are sent towards Bob is considered a part of Alice and it is therefore only at the
exit of Alice that the average number of photons per pulse has to 0.1. In order
to avoid cross-talk between the two components, component 8 is then assigned to
Alice, leaving component 7 as the separation between the two used components.
In order to characterize the components further, it was first necessary to stabi-
lize the temperature of the chip. The reason for this, is that the chip is very
temperature sensitive, since the coding happens through changes in temperature.
The sensitivity of the chip was discovered as soon as close-up scans were made of
the Fabry-Pérot structures. In a single 2nm wavelength scan, that would take a
few minutes, the structures drifted up to 0.02nm, making analysis of the Fabry-
Pérot structures impossible. The instability was removed by implementing a tem-
perature stabilizer developed by MSc Anders S. Thomsen for another on-going
experiment[41] and the instability was therefore assumed to be due to temperature
fluctuations in the laboratory. The controller is able to stabilize the temperature
with a precision of 0.03◦
C in the range 20◦
C to 60◦
C.
Using the temperature control, it is then possible to use the Fabry-Pérot structure
32
39. CHAPTER 3. CHIP CHARACTERIZATION 3.4. OPTIMIZATION
to determine the required voltages for the phase shift. As discussed in section
2.4, the phase shift as a function of modulation can be determined by using a
CW light source and look at the change in the Fabry-Pérot structure. A close-up
of the structure measured by sweeping the CW laser source over a 0.5nm wave-
length span and detecting the intensity of the reflected light by using a standard
semiconductor detector is shown in figure 3.11.
Figure 3.11: Fabry-Pérot structure of component 8.
It is here clearly seen that the fast oscillating structure has a period of approxi-
mately 0.02nm as calculated for the structure of the component in equation (3.3).
The significant change in amplitude towards the edges of the figure is due to the
structure of the Bragg gratings, as discussed earlier.
In [3], some initial voltages was determined for the phase shift and measurements
were then conducted where the system switched between the different phase states.
It was first theorized that the system would be able to work at a 1kHz transmission
rate, but experiments showed that the settling time for the phase change in the
long arm was in the order of 2.5 milliseconds and the highest operating frequency
therefore becomes in the order of 400Hz. An example of this with more recent
voltage settings and at a frequency of 100Hz is shown in figure 3.12.
33
40. 3.4. OPTIMIZATION CHAPTER 3. CHIP CHARACTERIZATION
Figure 3.12: Switching phase states every 10 milliseconds.
The phase shift is here seen where the Fabry-Pérot structure is at a maximum at
the lowest voltage and at a minimum at the third voltage level, corresponding to
0 and π or a shift of a half wavelength. The second and the fourth voltage level
corresponds to phase states π/2 and 3π/2 or a shift change of 1/4 of a wavelength
and 3/4 of a wavelength respectively. It is here seen that the shift stabilizes more
quickly when at a maximum or a minimum in the structure than when on the
slope. Changing the switching frequency so that the phase state changes every 10
seconds instead of every 10 milliseconds, in order to look for long term effects, now
yields the spectrum shown in figure 3.13.
34
41. CHAPTER 3. CHIP CHARACTERIZATION 3.4. OPTIMIZATION
Figure 3.13: Switching phase states every 10 seconds.
This demonstrates a potentially serious problem: the long term settling time is
far to large. From figure 3.12 it is seen that the settling time of the phase change
of the long arm is in the order of milliseconds, but over time the heat used to
modulate the long arm spreads out into the chip and heats up the entire chip
causing a large time-constant. The reason for this problem is that every time the
phase state is changed, the total amount of power transferred through the chip
changes and it will therefore warm up or cool down depending on the change in
power. It was seen that this long-term settling time for the phase shift was in
the order of 20 seconds of which the first 10 seconds are shown in figure 3.13.
At relatively high switching rates and with a constant average power over time,
this is not a problem. In practise however, this could cause problems since the
phase changes will be chosen randomly. Even though the average power over time
statistically should be constant in the case of randomly chosen states, there is a
finite probability that it will change causing the chip to change overall temperature.
It is therefore necessary to keep the total amount of power transferred through the
chip constant. This is done by using so-called dummy heaters.
35
42. 3.5. DUMMY HEATERS CHAPTER 3. CHIP CHARACTERIZATION
3.5 Dummy heaters
The dummy heaters are used only to maintain a sufficiently constant temperature
of the chip and does not affect the phase shift as such. Since the chips were
not designed with dummy heaters for this purpose, the heaters of neighbouring
components were used. The dummy heaters are therefore located approximately
a millimetre away from the heaters where the optimum is usually chosen to be
around 200µm as a trade-off between minimal overall temperature change and
minimal effect on the phase shift by the dummy heater. The optimal solution
would therefore be to use the neighbouring components on both sides, but because
there is only a single component between Alice and Bob (component 7), this would
be problematic since the power transferred through this component then would
depend on both Alice and Bob. Security-wise, this causes another problem, since
calculating this power requires knowledge of both Alice’s and Bob’s phase states.
Components 5 and 9 are therefore chosen to be the dummy heaters for Bob and
Alice respectively.
This brings us to the next problem. Two electrical connections to the chip using
micro-precision needle probes are required for each heater and eight needle probes
are therefore required. Since the stage on which the chip is located can only
accommodate four needle probes, it was necessary to reduce the needed amount
of needle probes. This was solved by short-circuiting all the connection pads on
one end of the chip and connect them to ground. This is shown in figure 3.14.
Figure 3.14: Schematic of the chip where the connection
pads on one side are short-circuited and con-
nected to ground.
36
43. CHAPTER 3. CHIP CHARACTERIZATION 3.5. DUMMY HEATERS
Using this, it was then possible to use just four needle probes; one for each heater.
A picture of the connection with the needle probes is seen in figure 3.15.
Figure 3.15: Picture of the chip with connections to heaters
and dummy heaters.
In order to select the proper voltages to put across the dummy heaters, we first
have to consider the voltages required for the heaters. The modulators on our
chip are thermo-optical modulators (TOM) which consists of a 3cm long heater
located on top of the waveguide with a resistance of approximately 200Ω. The
temperature of the heater is then proportional to the power transferred by the
heater and thus the voltage squared:
T ∝ P = V · I =
V 2
R
(3.5)
Since the phase shift is proportional to the temperature, the phase shift is linear
as a function of the power and quadratic as a function of voltage. The power
required for the four phase states are therefore four equally spaced points on the
linear phase versus power curve since the phase states are equally spaced. In order
to avoid having to use a power supply for each phase state for each heater and
dummy heater, we can use that if the total power transferred through the chip
is set to be P3π/2 + P0, the total power can be kept constant by only using the
voltages used for the heaters. This is because P3π/2 + P0 = Pπ/2 + Pπ due to the
linearity. For each phase state, the required powers then becomes:
37
44. 3.5. DUMMY HEATERS CHAPTER 3. CHIP CHARACTERIZATION
Desired phase state
0 π/2 π 3π/2
Heater : P0 Pπ/2 Pπ P3π/2
Dummy : P3π/2 Pπ Pπ/2 P0
Table 3.1: Required powers on heater and dummy heater for
a given phase state.
To implement this, the electrical system in figure 3.16 is built.
Figure 3.16: Schematic of the electrical system to control
the voltages.
Where the voltages required for the phase states are supplied by voltage regulators
designed and built by MSc Anders S. Thomsen and MSc Laura Meriggi for which
great thanks are owed(see section 4.3:Switching in [3]). The switches are fast
voltage switches that can switch between two input voltages between 1.25V (due
to the voltage regulators) to 14V (1V below breakdown voltage for the switch) with
a 300ns turn-on and turn-off time, but with a 2µs turn-off delay time due to the
reaction time of the components when changing to a lower voltage. The switches
are controlled with a transistor-transistor logic (TTL) signal where a logical true
sets the output to the higher of the two inputs (input 2) and a logical false sets
the output to the lower of the two input voltages (input 1). It is important that
the lower of the two voltages is set to input 1, since this is blocked by a diode with
reverse bias V2 − V1 when input 2 is selected.
From the table 3.1 and the voltages that the switches switch between in figure
3.16, we can now set up the following switching table:
38
45. CHAPTER 3. CHIP CHARACTERIZATION 3.5. DUMMY HEATERS
Desired phase state
0 π/2 π 3π/2
Switch 1 : Low High High Low
Switch 2 : High Low Low High
Switch 3 : Low Low High High
Switch 3 : High High Low Low
Table 3.2: Table of rules for the trigger signals to get the
desired phase states. Due to the TTL inverters,
3’ is always the opposite of 3.
Using the dummy heaters, the settling times now becomes as shown in figure 3.17
where the phase state is changed every 10 seconds.
Figure 3.17: Switching phase states every 10 seconds with
dummy heaters.
It is here seen that the settling times have improved greatly and the small change
over time is due to a difference in resistance between the heater and dummy heater
causing a small change the total power. The resistance difference is usually less
than 1Ω and the resistances change day by day do to dust, vibrations etc. and the
difference therefore changes as well.
Changing the switching frequency so that the phase state changes every 10 mil-
39
46. 3.5. DUMMY HEATERS CHAPTER 3. CHIP CHARACTERIZATION
liseconds instead of every 10 seconds, in order to see the fast change, now yields
the spectrum shown in figure 3.18.
Figure 3.18: Switching phase states every 10 milliseconds
with dummy heaters.
Comparing this to figure 3.12 shows that the fast settling time has decreased
as well. Using the dummy heaters therefore increases the maximum operating
frequency and ensures that the temperature of the chip is kept sufficiently stable
so that instability due to changes in total power occurs.
With the system stabilized, it is now possible to determine the required powers for
the phase states from knowing the resistances of the heaters and by determining
the voltages.
40
47. CHAPTER 3. CHIP CHARACTERIZATION 3.6. PHASE SHIFT
3.6 Phase shift
In order to measure the voltages required for the phase states and match the phase
states for the components so that Bob can properly decode the photons, it is first
necessary to establish the set-up for these measurements. A schematic of this is
shown in figure 3.19 where the voltages for the heaters are supplied by the electrical
set-up shown in figure 3.16.
Figure 3.19: Schematic of the set-up used to optimize the
phase.
The system first have to be optimized by aligning the fibres properly and opti-
mizing the polarization to ensure that only one of the two possible Fabry-Pérot
structures are used. The first polarization controller, also known as Mickey Mouse
ears due to the three pads, and the polarizer is used to ensure that the light enter-
ing the system is linearly polarized and at maximum intensity. The polarization of
the light entering Alice’s component is now optimized by setting Alice’s component
to switch between the phase states so that the the structure at some point moves
through a minimum, as seen in figure 3.18 at phase state π and when switching
between 3π/2 and 0. By measuring continuously, it is then possible to optimize the
polarization of the light entering Alice’s component by manipulating the polariza-
tion with the second polarization controller so that the minimum in the structure
is minimized in intensity. The polarization of the light entering Bob’s component
41
48. 3.6. PHASE SHIFT CHAPTER 3. CHIP CHARACTERIZATION
is now optimized by fixing the light that exits Alice to a maximum by manipulat-
ing the wavelength of the light. The polarization optimization procedure is now
repeated for Bob.
Because Alice acts as the reference point of the phase states, the voltages required
for her phase states have to be determined first. This is done by setting Alice’s
component to switch between all four phase states or just the 0 and 3π/2 states
and then manipulate the wavelength so that the 0 state is set to certain position in
the Fabry-Pérot structure (e.g. a maximum). The voltage for the 3π/2 state can
now be manipulated so that the phase change corresponds with a movement in the
Fabry-Pérot structure of 3/4 of a wavelength as is approximately the case in figure
3.18. Due to the minimum voltage from the voltage regulators and voltage drops
over the switches, the power corresponding to the 0 state for Alice’s component
is determined by the resistance of the heater and the voltage over the chip, which
we chose to measure over the input side of switch 3 in figure 3.16 and ground:
P0 =
V 2
0
RA
=
(1.012V)2
187.3Ω
= 5.5mW (3.6)
Through the method described above, it was then determined that the voltage
required for the 3π/2 state was 9.22V and the power therefore becomes:
P3π/2 =
V 2
3π/2
RA
=
(9.36V)2
187.3Ω
= 467.8mW (3.7)
Due to the linearity in power, the powers required for the phase states π/2 and π
are then calculated by:
Pπ/2 =
1
3
(P3π/2 − P0 + P0 = 159.6mW ⇒ Vπ/2 = 5.47V (3.8)
Pπ =
2
3
(P3π/2 − P0 + P0 = 313.7mW ⇒ Vπ = 7.66V (3.9)
Where the calculated voltages requires that the resistance is 187.3Ω. It should be
noted that the resistance changes when the temperature of the heater changes and
the powers that are calculated here are therefore not the correct powers but relative
powers with respect to the initial resistance. The reason why the resistances are not
measured at the different voltages or powers is that a measurement of the resistance
requires that there is no voltage across the heater. It is therefore necessary to to
turn off the voltage before measuring the resistance and the temperature therefore
begins to decrease, making the measurement unreliable.
The powers required for Bob’s phase states can now be determined by matching his
Fabry-Pérot structure to Alice’s and both detectors in the set-up shown in figure
42
49. CHAPTER 3. CHIP CHARACTERIZATION 3.6. PHASE SHIFT
3.19 are therefore required so that both structures can be measured simultaneously.
This is done by setting Alice and Bob to the two phases that are to be mached
and then scanning the CW light source over a small wavelength range of e.g.
0.1nm or 0.5nm so that a suitable number of peaks in the structure are seen on
the oscilloscope. The following measurement, where both Alice and Bob is set to
phase state 0 and the structures are matched by manipulating the voltage on Bob,
was measured over a wavelength range of 0.5nm. The oscilloscope data, where the
time axis is converted to an approximated wavelength from the knowledge of the
scan range, is shown in figure 3.20.
Figure 3.20: Oscilloscope data of the matched structures of
Alice and Bob at phase state 0.
The structures are matched such that the peaks in the structure of Alice and Bob
together match the peaks in Alice’s structure. Alternatively, the structures can be
matched when Alice and Bob are out of phase where Bob is set to the phase state
that we want to optimize and Alice is set to π shifted state. An example of this is
shown in figure 3.21 where Alice is set to state 0 and Bob is set to state π.
43
50. 3.6. PHASE SHIFT CHAPTER 3. CHIP CHARACTERIZATION
Figure 3.21: Oscilloscope data of the matched structures of
Alice and Bob where Alice is set to state 0 and
Bob is set to state π.
Here, the structures are matched by manipulating the voltages so that the least
possible signal is transmitted from Bob or so that the small peaks are of equal
height. It is also seen that due to the Fabry-Pérot structure of the Bragg gratings,
the effective FSR changes where the structure of the gratings approaches a mini-
mum. The structures of Alice and Bob therefore no longer have the same effective
FSR since the gratings are not identical. This is being studied by bachelor student
Kristian Sigvardt who is writing his bachelor project on this subject.
The voltage, and therefore the power required for phase state 0 for Bob, is effec-
tively an offset between the Alice’s and Bob’s structures, since the components
are not completely identical. The offset therefore has to be applied to either Al-
ice’s or Bob’s powers, depending on whether the offset is between 0 and π or −π
and 0 respectively, indicating in which direction the structures has to be moved.
Because the phase shift has a quadratic dependency on the voltage, the lowest
possible voltages are desired, since the phase shift will then be least sensitive to
jitter in the voltages.
Repeating this process for Bob at state 3π/2 and Alice at either 3π/2 or π/2 then
yields the voltage and thus the power required for state 3π/2 for Bob’s structure
with respect to Alice’s structure. The following values for P0 and P3π/2 for Bob
44
51. CHAPTER 3. CHIP CHARACTERIZATION 3.6. PHASE SHIFT
was determined:
P0 =
V 2
0
RB
=
(3.326V)2
182.9Ω
= 60.4mW (3.10)
P3π/2 =
V 2
3π/2
RB
=
(9.88V)2
182.9Ω
= 533.4mW (3.11)
The powers required for the phase states π/2 and π then becomes:
Pπ/2 =
1
3
(P3π/2 − P0 + P0 = 218.1mW ⇒ Vπ/2 = 6.32V (3.12)
Pπ =
2
3
(P3π/2 − P0 + P0 = 375.8mW ⇒ Vπ = 8.29V (3.13)
As before, the voltages calculated here only apply for the case where the resistance
is 182.9Ω.
With the powers determined and the voltages set, it is possible to re-optimize the
polarization of the light entering Bob’s component. This is done by setting Alice’s
component to switch between all four states, as shown in figure 3.18, and changing
the wavelength so that one of the phase states is located at a maximum in the
Fabry-Pérot structure. Bob is then set to the state that is π shifted with respect
to the state that was set to maximum transmission on Alice’s component and the
polarization is then manipulated so that the signal from Bob is minimized when
Alice is at maximum transmission. In this way, it is not just Bob’s Fabry-Pérot
structure we use to optimize the polarization but instead the phase difference
between Alice and Bob and thus ensuring that the structures match.
We have now characterized and optimized the system, but before we move on to
the experiments, we first have to make sure that the wavelength of the short-pulse
laser source matches the reflection wavelength of the components.
45
52. 3.7. SHORT-PULSE LASER CHAPTER 3. CHIP CHARACTERIZATION
3.7 Short-pulse laser
The laser that we intend to use is an ID Quantique id300 short-pulse laser source
that produces ≈ 300ps long light pulses at full width half maximum (FWHM) and
with a 0dBm peak intensity. This is done at a wavelength of ≈ 1549.3nm with a
bandwidth of ≈ 1nm and at repetition rates of single-shot to 500MHz.
When the short-pulse laser is turned on and is being triggered, it takes some time
for it to warm up. This is seen in figure 3.22 where the laser was turned on and
triggered by a 1MHz trigger signal while being heated up by a heating element
below the laser and the laser output was measured as a function of wavelength.
The temperature was measured with a thermometer below the laser.
Figure 3.22: Measurements of short-pulse laser output while
the laser is being heated up.
From this, we can see that the wavelength spectrum of the laser changes signifi-
cantly as a function of temperature and it is therefore important that we determine
at what temperature we need to use the laser when using it for our experiments.
In figure 3.23, measurements of the intensity as a function of wavelength for the
laser output and for transmission through the Alice and Bob are shown for room
temperature (24◦
C) and for 25◦
− 26◦
C where the exact temperature is unknown
since the thermometer was only able to show integers.
46
53. CHAPTER 3. CHIP CHARACTERIZATION 3.7. SHORT-PULSE LASER
Figure 3.23: Wavelength spectra of the laser output and
through the system at different temperatures.
These measurements are part of a larger series of measurements for different tem-
peratures but in order to avoid an overcrowded figure, only these measurements
are shown, where the measurements at 24◦
C is the initial temperature and the
measurements at 25circ
− 26◦
C was found to be the ideal temperature. The band-
width of the measurements of the intensity versus wavelength of the transmitted
light trough Alice and Bob is limited by the reflection bandwidth of the gratings
and higher or lower centre wavelengths of the laser output therefore causes a less
ideal output profile. We therefore heat the laser up to approximately 25 or 26◦
C
for all the experiments where we use this laser. In addition, the heating of the laser
is a slow process since we want to avoid overheating it and it therefore requires at
least an hour before the temperature has stabilized and the laser can be used.
Single photons are then obtained by attenuating the laser source so that the pulses
on average contain 0.1 photons so that sufficiently few pulses contain more than
one photon and where the probabilities are given by a Poisson distribution:
P(k) =
αk
k!
e−α
(3.14)
Where P(k) is the probability of a pulse containing k photons and α is the ampli-
tude of the electric field of the pulse, proportional to its intensity.
47
54. Chapter 4
The experiment
We now turn to the single-photon experiments where we want to use the system
for quantum key distribution (QKD) which is the prime purpose of this thesis. We
start by establishing the set-up required for the single-photon transmission.
4.1 The set-up
The set-up is built to be controlled by two computers controlled by Labview Real-
Time (RT) which is an operating system that can only be controlled over an
Ethernet connection by a separate host computer and that enables us to use µs
time resolution in contrast to the ms time resolution that is available on a stan-
dard Windows computer due to available processing time. The two computers are
each equipped with a high-speed National Instruments PCI-6236 data acquisition
(DAQ) card that have four analogue inputs, four analogue outputs, six digital in-
puts and four digital outputs. Of these inputs and outputs, three digital outputs
on both Alice and Bob are used to control the switches, an additional analogue
output is used by Alice to trigger the laser and two digital inputs are used by Bob
to receive detection signals from the single-photon detector module. The two RT
computers are then controlled by the host computer by deploying a Labview pro-
gram that automatically controls the set-up using a set of pre-determined param-
eters and randomly chosen phase states. In order to get a proper understanding of
this set-up, we start by recollecting the electrical system for controlling the heater
and dummy heater voltages, as discussed in section 3.5. This set-up is shown again
in figure 4.1.
48
55. CHAPTER 4. THE EXPERIMENT 4.1. THE SET-UP
Figure 4.1: Schematic of the electrical system to control the
voltages.
Where the three transistor-transistor logic (TTL) trigger signals controlling the
voltages for Alice’s heater and dummy heater are controlled by Alice’s RT com-
puter and the three TTL signals for Bob are similarly controlled by his RT com-
puter. As discussed in section 3.6, the voltages on the voltage regulators are set to
correspond to the powers calculated in equations (3.6)-(3.13) where the voltages
are set to the determined values on the input side of switch 3, which was chosen
due to easy access and consistency in measurements.
We now turn to the optical part of the system, which is shown in figure 4.2. The
optical system is triggered by an analogue 5V trigger pulse created by an analogue
output in Alice’s RT computer and which has a rise time of approximately 1µs.
Since the timing of the system has to be accurate down to less than 1ns, it is
necessary to have clean pulses with small rise times in order to avoid jitter in the
timing due to noise on the rising slope of a comparatively slow-rising pulse. A
pulse generator is therefore triggered by the pulse from Alice’s RT computer, since
any jitter here is merely a small offset in time, and the pulse generator generates
a 3V pulse with a rise time in the order of 10ns. This pulse is now used to trig-
ger the ID Quantique id300 short-pulse laser source after which the laser emits
a ≈ 300ps long pulse and the trigger signal is sent on towards the ID Quantique
id201 single-photon detection module (SPDM).
49
57. CHAPTER 4. THE EXPERIMENT 4.1. THE SET-UP
After emission, the polarization of the pulse is manipulated in order to minimize
any loss due to polarization in the attenuator or the 80/20 optical fibre coupler.
The attenuator is used to attenuate the light pulse so that the average number of
photons per pulse when reflected from Alice’s component and sent towards Bob is
0.1. The light is then sent into an 80/20 optical fibre coupler which allows us to
optimize the system using CW light without having to disconnect any fibres and
thus avoiding changes in polarization, damages to fibre ends and collection of dust
on fibre ends. The output from the 80/20 coupler is therefore 80% of the incoming
intensity of the short laser pulse or 20% of the intensity of the incoming CW light.
The loss of signal through this coupler is irrelevant, since it is not before the output
side of Alice’s component that the average number of photons is required to be
0.1. By using a polarization controller and a polarizer, it is now ensured that the
polarization is linearly polarized the polarization is then controlled to ensure that
only one of the two possible Fabry-Pérot structures is used, as discussed in section
3.6. Inside the chip, the pulse is encoded by the thermo-optical modulator which
is controlled by the voltages from the electrical set-up. The reflected light from
Alice’s component is now transmitted through port three in the circulator, after
which it is sent through a 10/90 optical fibre coupler to allow us to measure the
reflected light from Alice’s component without having to disturb the set-up. By
using that the 10% output is 9.5dB weaker than the 90% output, the 10% output
can also be used to optimize the attenuation level so that 0.1 photon per pulse is
transmitted from the 90% output port. As before, the photon is then decoded in
Bob’s component and the resulting signal is sent towards the SPDM.
The trigger signal that triggered the laser was, as mentioned above, sent towards
the SPDM. This is to ensure that the delay is stable to less than 1ns. The length of
the cable is then chosen so that the time it takes the trigger pulse to travel through
the cable is in the order of 10ns less than the time it takes the light to arrive at
the SPDM. The reason for this is that the SPDM has a built-in adjustable time
delay of between 0 and 25ns1
and any fine-tuning of the timing can therefore be
done by changing the delay in the SPDM. The SPDM can then be set to use a
2.5ns gate width which results in a ≈ 0.5ns long detection window when at 10%
detection probability. Using this, it is possible to gate the signal from Bob which
consists of four pulses, as discussed in section 2.5 and 3.1 and seen in figure 2.5,
and thereby only measure the interfering signal parts.
If a photon is detected, a trigger pulse is then sent to Bob’s computer where the de-
tection is logged and if no photons were detected, the trigger signal informs Bob’s
computer that no photons was detected. The trigger signal therefore ensures that
the photons that Bob measures are indexed correctly so that Alice and Bob can
1
In reality, this delay is either zero where the delay system is bypassed or 14ns to 39ns due to a
timing offset in the delay circuit.
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