Electromagnetically Induced Transparency and Slow Light

1. Electromagnetically Induced Transparency and Slow Light Joyce Poon Oct. 29, 2003

2. Outline • What is EIT? • Overview of light-atom interaction • EIT physics: derivation, experimental results • Dispersive properties and slow light • Other interesting effects

3. 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)

4. |2 |1 Quick Review of Light-Matter Interaction 2 level atom, semiclassical picture Hamiltonian: Unperturbed part: Perturbation: Rabi Frequency:

5. 2 Level Atom, Semiclassical Picture Solve the system of equations using TDPT. Ansatz: “interaction picture” After RWA: Solution: (no detuning) sine and cosine Probability amplitudes: and

6. |3 c |2 p |1 Physics of EIT Consider lambda system (3 level atom): coupling probe Nominally, medium absorbs the probe (resonant transition). 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

7. Some Math Unperturbed Hamiltonian: Perturbation: Wavevector: Solution: 2 Rabi frequencies corresponding to the probe and coupling Neglected damping, decay, broadening

8. Transparency Solutions Consider various initial conditions: (i) atom is not absorbing for all t. More typical EIT situation: (ii) for all t “un-coupled/dark state” population trapped in lower states A coherent superposition is required (phase is very important): (iii) for all t “coupled state”

9. Adiabatic Preparation How to prepare coherent state? • Assume initially, the population is in the ground state |1 . • Turn on coupling (probe off, p=0), this is an eigenstate! • The population is all in the ground state |1 . • Then increase both the control and probe slowly (adiabatically) and the atom will remain in the eigenstate. Condition for adiabatic preparation:

10. Experimental Results Transmission vs. Probe Detuning First demonstration by K.J. Boller, A. Imamoglu, and S.E. Harris in Strontium (Sr) vapour (1991) Energy Diagram Transmission at resonance changed from exp(-20) to exp(-1) ! Transmission of probe laser. Top: No coupling laser, Bottom: With coupling

11. Dispersion and Slow Light Refractive index changes rapidly with frequency near resonance slow group velocity Normally, this is an absorbing region of the spectrum, but with EIT, the medium is transparent to the pulse. To find group velocity, calculate susceptibility:

12. 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 at 40nK, vg= 17m/s!!! c/vg~107

13. 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

14. 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 …

15. References • 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.