Introduction to group members and research conducted in the Quantum Theory group at Glasgow.

1. Quantum Theory Group:
research overview
Frances Crimin
University of Glasgow
Optical sciences seminar series

2. Group Members
Academic staff
Research
Fellows
Research
Associates
PhD
Students
Steve Barnett Sarah Croke Jörg Götte
Thomas BroughamJim Cresser Frances Crimin
Neel MacKinnon Sijia (Scarlett) GaoKieran Flatt Atirach (Can) Ritboon Anette Messinger
Fiona Speirits

3. Research Areas
Quantum Optics & Quantum Information Light-Matter Interactions
• Quantum information
Quantum key distribution
Quantum state transfer
Boson sampling
High-dimensional temporal quantum states
• Quantum measurement
Minimum error state discrimination
Restricted classes of measurement
Experimental implementations
“Learning” with a quantum probe
• Quantum foundations
Structure & uniqueness of the formalism of quantum theory
Foundation & applications of quantum measurement
• Quantum optics & thermodynamics
Coherence as a catalytic resource
Open quantum systems
Quantum fluctuation theorems
• Chiral molecules & media
Scattering of light from chiral molecules
Sources and sinks of helicity
Electric-magnetic (a)symmetry
• Optical angular momentum
Natures of spin and orbital angular momentum
Angular momentum transfer from light to media
• Optical forces on atoms and molecules
Chiral rotational spectroscopy
Discriminatory forces for optical isomers
• Radiative properties of atoms near and
within a medium
• Electron vector vortex beams

4. Quantum Optics & Quantum
Information

5. Boson Sampling
• Demonstrates advantage of quantum systems on small scale
Other uses?
Resource of computationally hard decision and function problems
Phys Rev A. 94, 012315 (2016).
• Samples from the probability distribution of
identical bosons scattered by a linear interferometer
• Solve classically intractable problems
Sapienza lab, www.3dquest.eu
S. Takeuchi, Jpn J. Appl. Phys. 53 030101 (2014).
quantum cryptography

6. Minimum error state
Discrimination
• A system is prepared in one of a number of possible states with known
prior probabilities .
̂ρi
Pi
• Two state problem: well-known solution
Best probability (minimum error) of obtaining
correct state?
AS Holevo, J. Multivariate Analysis 3, 337 (1973);
HP Yuen, RS Kennedy, and M Lax, IEEE Trans. Inf. Theory IT-21, 125 (1975);
CW Helstrom, Quantum Detection and Estimation Theory (New York: Academic, 1976)
• Trine states (with arbitrary probabilities)
G Weir, C Hughes, SM Barnett, and S Croke, Q Sci. Technol. 3, 035003 (2018).
Dark grey: region in which
3 outcome measurement is
optimal.
Light grey: 2 outcome
measurement is optimal.

7. Foundations & Applications
of quantum measurement
Understanding quantum measurement
How do these interpretations guide what is experimentally possible?
Born Rule:
• States represented by |i⟩, | f⟩
• Probability of measurement resulting in | f⟩ : P( f |i) = |⟨f |i⟩|2
Any other rule for calculating probabilities allowed?
• Busch-Gleason theorem: no
What about sequential measurement?
• Extension of Gleason’s theorem: recover state update rule for ̂ρ
Phys. Rev. A 96, 062125 (2017)
• Quantum cryptography: post-measurement information is often made available
•• QKD: security contingent on the laws of quantum mechanics being correct:
axiomatic approach assumptions underlying security proofs.

8. Open quantum systems
& quantum thermodynamics
Master Equations: implications
1. MEs predict transport of heat when there should be none, or none occurring when it should.
2. Generation of quantum coherence from noise.
3. Violation of detailed balance in steady state, i.e., does it occur or not.
• Describe dynamics of “small” quantum system interacting with a much larger thermal environment
̂H = ̂HS + ̂HR + ̂V
̂χ(t) = ̂U(t) ̂χ(0) ̂U†
(t)
̂U(t) = exp {i ̂Ht/ℏ}
̂ρS(t) = TrR [ ̂χ(t)]• Combined system
• Approximations:weak interaction, large separation of timescales associated with dynamics
• Advent of quantum thermodynamics
Cresser and Facer arXiv:1710.09939
+ quantum optics problems:

9. Quantum fluctuation theorems
(due to Crooks)
Crooks fluctuation theorem:
• Reversible dynamics: forward time trajectory exponentially more likely than the reverse
+ QFT: Second law of thermodynamics at microscopic level: P(t > t0)
P(t < t0)
• Micromaser: MW cavity field pumped by beam of excited atoms: single atoms provide sufficient pump
arXiv:quant-ph/0203052v1
• Quantum optical setup: ̂HJC = ℏω ̂a† ̂a
atom
+ ℏΩ ̂σ†
̂σ
field
− ℏg(t)( ̂a†
̂σ + ̂σ† ̂a)
interaction
• Time reversal processes in micromaser relationship between micromaser field & atomic beam
correlation properties
(Time-reversed quantum trajectory analysis of micromaser correlation properties and fluctuation relations)

10. “Catalytic” coherence & the
Jaynes-Cummings model
Two-level atom, coherent state field
|Ψ(0)⟩ = |α⟩|e⟩
|Ψ(t)⟩ = e−|α|2
/2
∞
∑
n
αn
n!
(cos( n + 1gt)|n⟩|e⟩ − sin( n + 1gt)|n + 1⟩|g⟩)
Can we re-use the coherent state as a
coherence resource without degrading the field?
• At , project into states | ± ⟩ =
1
2
(|e⟩ ± |g⟩)
• Repeat process with many atoms…
arXiv:quant-ph/1804.05154
• Field state looks approximately like
A coherent state again:
⟨ + |Ψ(t1)⟩ = e−|α|2
/2
∞
∑
n
αn
n! (
cos( n + 1gt1) +
n
α
sin( ngt1)
)
|n⟩
t1

11. Conditional success probability
increases after every atom
Pr
− ∼
1
¯nr
Failure probability
decreases with increase in
average photon number
(more classical)
• c.w. reservoir field:
Pr
− invariant w.r.t equivalent scaling parameter
Green: new coherent state
Orange: re-cycled state
Blue: no adjustment of interaction times

12. Light-Matter Interactions

13. Optical angular momentum
Momentum density of EM field: ⃗p = ε0μ0 (
⃗E × ⃗H)
Angular momentum density: ⃗j = ε0μ0 ⃗r × (
⃗E × ⃗H)
⃗J =
∫
⃗jdV
=
∫
ε0μ0 ∑
j
Ej ( ⃗r × ⃗∇) Aj + ⃗E × ⃗A dV
orbital
spin
S. M. Barnett et al 2016 J. Opt. 18 064004
phase gradient
of wavefront
sense of rotation
of field vectors
High-order LG beams

14. Angular momentum transfer
from light to dielectric media
Dove Prism: M-shaped Dove Prism:
inverts image
changes polarisation
ΔJphoton = − ℏ (2l + 1) → ΔJDove = ℏ (2l + 1)
Mechanism of momentum & angular momentum transfer?
• Quantized, single photon approach torque per photon due to TIR in dielectric
angular momentum transfer

15. Momentum transfer Angular momentum transfer

16. Chiral molecules & the
angular momentum of light
https://www.uni-muenster.de/Physik.PI/
Zacharias/en/research/chiral_molecules
Right-handed B-DNA L-amino acids
https://universe-review.ca/F11-monocell03.htm
Right-handed sugar
: non-superimposable upon mirror imageχειρ
• “Enantiomers” react differently to L and R circularly polarised light
https://atlasofscience.org/l-amino-acids-key-for-the-evolution-of-life-
came-from-extraterrestrial-space/

17. Discriminatory forces for chiral
molecules
• Chiral molecules interacting with ⃗E, ⃗H : coupled system of ⃗d , ⃗m
mixed electric-magnetic dipole polarizability ±b
u = −
1
2 [⟨ ⃗d ⟩ ⋅ ⃗E + ⟨ ⃗m⟩ ⋅ ⃗B] = − awe + bh
• Light-matter interaction:
electric dipole - electric dipole polarizabilities &
electric energy density
electric dipole - magnetic dipole polarizabilities &
helicity density
Cameron et al., Phil. Trans. R. Soc. A 375, 20150433 (2017)

18. Chiral optical force
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Cameron et al., NJP 16, 013020 (2014) Canaguier-Durand et al., NJP 15, 123037 (2013)
⃗F = − ⃗∇u = a ⃗∇we ± |b| ⃗∇h
if ⃗∇we = 0, ⃗F = ± |b| ⃗∇h

19. Helicity & Electric-Magnetic
symmetry
Noether: Conservation laws are reflections of symmetries
• Translational symmetry: conservation of momentum
• Rotational symmetry: conservation of angular momentum
• Electric-magnetic symmetry: conservation of helicity
Helicity: Projection of angular momentum
into linear momentum direction*
*W.-K. Tung, Group Theory in Physics (World Scientific, Singapore,
1985)
Phys. Rev. A. 86, 013845 (2012)
⃗J
⃗P /| ⃗P | :
⃗J ⋅ ⃗P = ( ⃗L + ⃗S ) ⋅ ⃗P = ⃗S ⋅ ⃗P = ⃗∇ ×
⃗∇ × ⃗E = −
·
⃗B
⃗∇ × ⃗H =
·
⃗D
Helicity not conserved
E-M symmetry broken
Probe helicity
generation
within materials

20. Electron vector vortex beams
• OAM vortex beams: phase singularities/dislocation of phase fronts
Electron vortex beams
ℋ Ψ( ⃗r, t) = E Ψ( ⃗r, t) ∇2
Ψ( ⃗r, t) + k2
Ψ( ⃗r, t) = 0
• Skyrmions: nm-sized spin textures of topological origin
https://en.wikipedia.org/wiki/Magnetic_skyrmion
• Consider topological charge of beams: single electron beams with vortex & spin structure possess
“Skyrmion number” (integer topological charge): robust against any deformation during its propagation
Skyrme T H R 1962 Nuclear Physics 31 556–569

21. “When mysteries are very clever,
they hide in the light”
Jean Giono (1895-1970)