Induced Electromagnetically Transparency and Slow Light
Joyce Poon Oct. 29, 2003
Outline
What is EIT? Overview of light-atom interaction EIT physics: derivation, experimental results Dispersive properties and slow light Other interesting effects
EIT
Proposed independently by Kocharovskaya and Khanin (Inst. of Applied Physics, Russia) in 1988, and Stephen E. Harris (Stanford) in 1989 Electromagnetically Induced Transparency is "a technique for eliminating the effect of a medium on a propagating beam of electromagnetic radiation." Renders an opaque medium transparent The physical basis for EIT is Coherent Population Trapping (CPT)
Quick Review of Light-Matter Interaction
2 level atom, semiclassical picture Hamiltonian: Unperturbed part: Perturbation:
|2 |1
Rabi Frequency:
2 Level Atom, Semiclassical Picture
Solve the system of equations using TDPT. Ansatz:
"interaction picture"
After RWA:
Solution: (no detuning) Probability amplitudes: and
sine and cosine
Physics of EIT
Consider lambda system (3 level atom):
|3 coupling |2
c p
probe Nominally, medium absorbs the probe (resonant transition).
|1
In EIT, medium can be transparent to probe beam by tuning the coupling beam (for a certain initial state of atoms). Quantum interference of the transition probabilities between 2 3 and 1 3
Some Math
Unperturbed Hamiltonian: Perturbation: Wavevector: Solution:
2 Rabi frequencies corresponding to the probe and coupling
Neglected damping, decay, broadening
Transparency Solutions
Consider various initial conditions: (i)
atom is not absorbing for all t. for all t "un-coupled/dark state" population trapped in lower states
More typical EIT situation: (ii) A coherent superposition is required (phase is very important): (iii)
"coupled state"
for all t
Adiabatic Preparation
How to prepare coherent state? 1. Assume initially, the population is in the ground state |1 . 2. Turn on coupling (probe off, p=0), this is an eigenstate! 3. The population is all in the ground state |1 . 4. Then increase both the control and probe slowly (adiabatically) and the atom will remain in the eigenstate. Condition for adiabatic preparation:
Experimental Results
First demonstration by K.J. Boller, A. Imamoglu, and S.E. Harris in Strontium (Sr) vapour (1991)
Energy Diagram
Transmission vs. Probe Detuning
Transmission at resonance changed from exp(-20) to exp(-1) !
Transmission of probe laser. Top: No coupling laser, Bottom: With coupling
Dispersion and Slow Light
Refractive index changes rapidly with frequency near resonance slow group velocity
Normally, this is an absorbing region of the spectrum, with but EIT, the medium is transparent to the pulse. To find group velocity, calculate susceptibility:
Experimental Demonstration
Harris et al. (1992): Pb vapour, c/vg = 250 Hau et al. (1999): Bose-Einstein condensate of Na, T<435nK
small Doppler broadening narrow linewidth more delay
More Recent Developments
Hot Gas: Scully et al. (1999): 360K Rb, vg=90m/s
Rabi frequency of coupling field must be much larger than the Doppler linewidth and homogeneous broadening of probe and coupling transitions
Room Temp.: Budker et al. (1999): Rb vapour, vg ~ 8m/s In solids: Turukhin et al. (2002): Pr doped Y2SiO5, 5K, vg=45m/s
Praseodymium (59): rare earth Very intense beams required: coupling=77W/cm2, probe=5.5W/cm2
Delays for various probe detunings in Pr doped Y2 SiO5
Other Applications of EIT
Lasers without inversion
No absorption into |3 , no need for stimulated emission to counteract stimulated absorption Get amplification at probe frequency
Nonlinear optics
Optical nonlinearity strongest at resonance Now resonant wavelength is not attenuated Enhanced Kerr nonlinearity, nonlinear frequency conversion
EIT in semiconductors (LWI)
Engineer transition energy levels (band engineering) in quantum wells/wires/dots
...
References
1. 2. 3. 4. 5. 6. 7. 8. 9. S. Alam. Lasers without Inversion and Electromagnetically Induced Transparency. Washington: SPIE, 1999. S.E. Harris. Electromagnetically Induced Transparency. Physics Today. July 1997. 36-42. K.J. Boller, A. Imamgolu, and S.E. Harris. Observation of Electromagnetically Induced Transparency. PRL. 66(20): 2593-2596,1991. S.E. Harris, J.E. Field, and A. Kasapi. Dispersive Properties of Electromagnetically Induced Transparency. PRA. 46(1): r29-r32, 1992. J.R. Kuklinski, U. Gaubatz, F.T. Hioe, and K. Bergmann. Adiabatic Population Transfer in a Three-Level System Driven by Delayed Laser Pulses. PRA. 40(11): 6741-6744, 1989. S.E. Harris, J.E. Field, and A. Imamoglu. Nonlinear Optical Processes using Electromagnetically Induced Transparency. PRL. 64(10): 1107-1110, 1990. L.V. Hau, S.E. Harris, Z. Dutton, and C.H. Behroozi. Light Speed Reduction to 17 Meters per Second in an Ultracold Atomic Gas. Nature. 397, 594-598, 1999. M. Kash et al. Ultraslow Group Velocity and Enhanced Optical Effects in a Coherently Driven Hot Atomic Gas. PRL. 82(26):5229-5232, 1999. D. Budker, D.F. Kimball, S.M. Rochester, and V.V. Yashchuk. Nonlinear Magneto-optics and Reduced Group Velocity of Light in Atomic Vapor with Slow Ground State Relaxatoin. PRL. 83(9):1767-1770, 1999. A.V. Turukhin et al. Observation of Ultraslow and Stored Light Pulses in a Solid. PRL. 88(2):23602, 2002.
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