Electromagnetically induced transparency in atomic physics

1. ELECTROMAGNETICALLY
INDUCEDTRANSP
ARENCYIN
R
UBIDIUM 85
Amrozia Shaheen

2. Electromagnetically induced
transparency
 The concept of E
ITwasfirst given by Harris et al in
1990. When a strong coupling laser field is used to
drive a resonanttransition ina three-level atomic
system,theabsorption of a weak probe laser field
can be reduced or eliminated provided the two
resonanttransitionsare coherentlycoupled to a
commonstate.
 E
ITwasfirst observed in lambda type systemof
strontiumvapors using high pulsed laser in 1991.

3. Stimulated absorption
 StimulatedAbsorption: When a photon of energy
equalsto theenergy difference between two
atomiclevelsinteractswith theatom.The atom in
thelower energy state,absorbsthephotonand
jumps to the higher energy state (excited state).

4. Spontaneousemission
 Spontaneous emission: A processby which an
atom in the excited state undergoes a transition to
thelower energy state (groundstate) and emitsa
photon.

5. Stimulated emission
 Stimulatedemission:Aprocessby whichanatomic
electron (inexcited state) interactswith an
electromagnetic wavedrop to a lower energy level
transferring its energy to that field

6. Electromagnetically induced
transparency
 EITconfigurations:
Ladder V-type Lambda-type

7. R
ubidium85
 R
ubidiumis a silvery white metallic element alkali
metal group.
 Electronic configuration:
 Fine structure splitting:
For electron
Ground state

8. R
ubidium85
 First excited state:
P
ossible states
 Second excited state:
possible states

9. R
ubidium85
 Hyperfine splitting:Thisisinteraction of nuclear
spin (I) with the electron angular momentum (J).
 HFsplitting of ground state is,
 HFsplitting of the 1st and 2nd excited statesis,

10. Energy level diagram of 85Rb

11. Three level Ladder type system
 Two laser beams are used to excite the electronic
transitions.
 Probe beam
transition
beam for
for the
, coupling
.
probe beam

detuning while
is the
coupling beam detuning.

12. Ladder type system
 The initial state of the systemis,
 The state of the system evolves after time t, so the
time dependent wave function is,

13. Hamiltonian
 The total Hamiltonian of the system can be find out
using perturbative approach,
 Unperturbed part:
using orthonormality condition, i.e.,

14. Hamiltonian
 Perturbedpart:Whenanelectromagnetic field
interacts with the atom, the interaction Hamiltonian
is,
under parity conservation

15. Hamiltonian
 T
otal Hamiltonian:

16. Time evolutionof the density matrix
 Using density matrix has its own significance as an
in physical systemsthe exact state of the systemis
hardly known but only probabilities are known.
 The density operator is,
 The time evolution of the density matrix can be find
out by Liouville (Von Neumann) equation,

17. Time evolutionof the density matrix
 Generalized form of the density operator
equation of motion:
and the density matrix elements are,

18. Time evolutionof the density matrix

19. Time evolutionof density matrix
The matrix elements are,

20. Time evolutionof the density matrix
initial conditions are,
substituting,

21. Time evolutionof the density matrix
Now the equation of motion becomes,
Introducing the transformations,

22. Time evolutionof the density matrix
These equationsare of the form,
Steady state solution can be obtained by solving,

23. Time evolutionof the density matrix
Here Bis a matrix of cofactors.

24. Time evolutionof the density matrix
similarly,

25. Complex susceptibility
 The real and imaginary parts of the complex
susceptibilty are used to define the dispersion
and absorption
coefficients,
 The complex susceptibility and polarization is
related by,
 Atomic polarization for N number of atoms per unit
volume is,

26. Complex susceptibility
 Doppler broadening effects: The atom moving towards
the probe beam will feel an up shift in its frequency by
an amount
by the factor
and downshifted for the coupling beam
.
As number of atoms per unit volume is , and
isof Maxwellian form,

27. Complex Susceptibility
substituting,

28. Complex susceptibility
 Ignoring two photon transition:

29. Complex susceptibility
 The error function is the integral of normalized
gaussian function,
and the susceptibility is,

30. Complex susceptibility
 Including two photon transition:

31. Complex susceptibility
so two complex roots are,
The integral can be written as,
Mathematica gives,

32. Complex susceptibility
the constants C1 and C2 are,
where,
Logarithm of any complex number is,
and,

33. Complex susceptibility
Defining the function,
where sgn is the signum function defined as,
and the susceptibility expression becomes,

34. R
esults

35. R
esults

36. Applications of EIT
 Fundamental and commercial applications of EITin
atomic physics and quantumoptics include,
 Lasing without inversion,
 R
eduction of the speed of light,
 Quantummemory,
 Optical switches,
 All optical wavelength converters for
telecommunications,
 Quantum information processing.