EIT and Slow Light in Nonlinear Magneto Optic Rotation
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1 EIT and Slow Light in Nonlinear Magneto Optic Rotation George R. Welch Marlan O. Scully Irina Novikova Eugeniy Mikhailov Andrey Matsko Yuri Rostovtsev Alexey Belyanin Edward Fry Phil Hemmer Olga Kocharovskaya Vitaly Kocharovsky Alexey Sokolov Suhail Zubairy Office of Naval Research Texas A&M University Institute for Quantum Studies Texas Advanced Research Program Outline: Atomic Coherence Three-level coherence Modified susceptibility Electromagnetically Induced Transparency Index of refraction: Enhanced Index, Slow light Applications! Ultra-sensitive magnetometry Non-linear magneto-optic rotation Sensitivity Limitations (ac Stark, radiation trapping) Vacuum Squeezing Slow Light Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 1
2 Statistical Mixture of States: Only two relevant energy levels a b c d ψ = a or ψ = b or! Ordinary Absorption, Refraction, and Amplification Coherent Superposition of States: Three or more levels! a b c New effects d ψ = α c + β d Susceptibility: Two Atomic Energy Levels a b Vg = c/60 in sodium Tom Mossberg, 1977 unpublished absorption index of refraction n=1 Anomolous dispersion dn 0 dω Normal Normal dispersion dn 0 dω < g > g v > c v < c Strong Strong Absorption v g =?? Superluminal speeds (e.g., tunnelling) Chiao et al. (Berkeley) (ω-ω 0 )/γ Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 2
3 Atomic Coherence Effects Three (or more) Atomic Energy Levels a Natural decay γ The combined action of the drive and probe lasers produces a quantum superposition of the two lower states: c Coupling Laser Drive Laser Coherence Decay γ bc b Probe Laser: frequency ω ψ = α b + β c Then, the probe field interacts with this superposition state. Three Level System a Ω c γ bc γ Ω p b For: Low density (single atom response) Monochromatic probe Weak probe Ω > Ωp Calculate susceptibility of homogeneously broadened 3-level system. See for example, Scully and Zubairy, Quantum Optics, Cambridge University Press, where Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 3
4 Three Atomic Energy Levels Electromagnetically Induced Transparency c a b Transmission through 10,000 absorption lengths, Harris et al., absorption index of refraction n=1 Non- Non- Anomolous dispersion dn dω > 0 v g << c Ultra slow light Transparency Vg = 1 m/s (c/300,000,000) Ketterly et al., (ω-ω 0 )/γ Effect of Coherence on Interaction Two Levels: a Three Levels: a b c b Index of refraction: Steep normal dispersion Absorption: Induced transparency Ultra-Slow Light Enhanced Index of Refraction Lasing Without Inversion Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 4
5 Slow Light?!? What gives? Refraction v red < c dispersion v blue < v red v = c/n Air Water Quartz Diamond Some semiconductors Phase and Group Velocities Superposition of travelling waves v p Phase velocity v p v p v g Group velocity wave groups Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 5
6 Superposition of Travelling Waves Phase and Group velocity Optical Group Velocity in a Medium Dispersion Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 6
7 Spatial Dispersion: The effect of moving atoms. Intensity Energy propagates at the group velocity (usually.) Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 7
8 Equal Phase velocities: No dispersion Short wavelength: Long wavelength: Equal Phase velocities: No dispersion Short wavelength: Long wavelength: Group Velocity = Phase Velocity Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 8
9 Unequal Phase velocities: N ormal dispersion Short wavelength: Long wavelength: Unequal Phase velocities: N ormal dispersion Short wavelength: Long wavelength: Group Velocity < Phase Velocity Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 9
10 Unequal Phase velocities: Anomolous dispersion Short wavelength: Long wavelength: Group Velocity > Phase Velocity Where can we find very steep dispersion? Answer: Atoms in coherent quantum mechanical superposition states! Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 10
11 EIT Slow light history: c/13, Xiao et al., PRL 74, 666 (1995). c/165, Kasapi, Jain, Yin, and Harris, PRL 74, 2447, (1995). c/3000, Schmidt, Wynands, Hussein, Meschede PRA 53, R27, (1996). (Inferred from dn/dω) c/10 5 Lukin, Fleischhauer, Zibrov, Robinson, Velichansky, Hollberg, Scully, PRL 79, 2959 (1997). (Inferred from probe phase shift.) c/2x10 7 Hau, Harris, Dutton, and Behroozi, Nature 397, 594 (1999). (BEC) c/3x10 6 TAMU, PRL 82, 5229 (1999). (Hot vapor) c/4x10 7 Budker, Kimball, Rochester, and Yashchuk, PRL 83, 1757 (1999). (NMOR) c/6x10 6 Turukhin, Musser, Sudarshanam, Shahriar, and Hemmer, PRL 88, (2002). (Solid) Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 11
12 Science Fiction: Light of Other Days, Bob Shaw ( ), in Analog Science Fiction, John W. Campbell, Jr., Ed. August, (Hugo and Nebula award winner.) The most important effect, in the eyes of the average individual, was that light took a long time to pass through a sheet of slow glass. A new piece was always jet black because nothing had yet come through, but one could stand the glass beside, say, a woodland lake until the scene emerged, perhaps a year later. If the glass was then removed and installed in a dismal city flat, the flat would for that year appear to overlook the woodland lake. During the year it wouldn' t be merely a very realistic but still picture the water would ripple in sunlight, silent animals would come to drink, birds would cross the sky, night would follow day, season would follow season. Until one day, a year later, the beauty held in the subatomic pipelines would be exhausted and the familiar gray cityscape would reappear.... Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 12
13 New Applications - TAMU IQS Ultra-Sensitive Optical Magnetometry (Novikova/Welch) Quantum Information Storage (Lukin et al., Hau et al., Zibrov et al.) Resonant Four-Wave Mixing (Mikhailov/Welch) New IR Detectors (Scully/Boyd) New FIR (1-100µ) Lasers (Kocharovsky/Belyanin, Capasso) Sub-femtosecond Sub-cycle Laser Pulses (Sokolov, Harris) Quantum Nucleonics / g-ray Lasers (Kocharovskaya) Quantum Computing (Hemmer/Scully/Zubairy) Anthrax Spore Detection (Scully) Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 13
14 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 14
15 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 15
16 Compensate Power Broadening by Increasing Density transmission 100% ω trans frequency γ a transmission 100% frequency x1 x2 x5 x10 x25 0% Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 16
17 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 17
18 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 18
19 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 19
20 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 20
21 Measurements S 1, arb.units Tran sm ission, arb.u nits S 2, arb.units M a gne tic field, m G Recorded signals Magn etic field, m G R ota tion angle φ, ra d Rotation angle M agn etic field, mg Transmission S 1 +S M a gne tic field, m G 1 S1 S φ = arcsin 2 S1 + S 2 2 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 21
22 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 22
23 High Optical Density: Large rotation angle Photodetector signals Magnetic field, mg Scaling to high density and laser power gives multiple oscillations as polarization rotation passes 2π Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 23
24 Corresponding Verde constant: V~ min oersted-1 cm-1 Magnetic TGG crystal: V ~0.4 min oersted-1 cm-1 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 24
25 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 25
26 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 26
27 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 27
28 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 28
29 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 29
30 Radiation trapping: model a Iout κl γ = 1 R R ( ) ( γ + ) 2 0 R I Ω 0 Ω + δ γ 0 b + Ω b in dφ db B 0 = = 2µ B I ln out ( γ ) 0 + R Iin Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 30
31 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 31
32 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 32
33 Radiation trapping R o tation rate dφ/d B, rad/g Transmission I out /I in Theoretical Prediction dφ db B 0 2µ = γ B 0 I ln I out in Something is causing the deterioration of ground-state coherence with atomic density. We believe it is the reabsorption of spontaneously emitted photons (radiation trapping). Matsko, Novikova, Scully, Welch, PRL, 87, (2001) Matsko, Novikova, Scully, Welch, JMO, 49, 367 (2002). Effective repumping rate R/ γ Experimental confirmation Atomic density N, cm -3 beam diameter 2mm beam diameter 5mm Radiation trapping becomes important on the scale of the: Cell (diameter 25mm) - N~ cm -3 Laser beam (diameter 2mm) - N~ cm -3 Laser beam (diameter 5mm) - N~ cm -3 Effective repumping rate R/γ Scale for onset of radiation trapping: 3 2 γ Nλ d r 8π W Atomic density N, cm -3 D > 1 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 33
34 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 34
35 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 35
36 Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 36
37 Application to Magnetometry Status: Width: Γ=100 mg Rotation: dφ/db = 100 rad/g Power: P = 3mW Sensitivity: B min = f min /(dφ/db) Shot-noise limit: dφ min = (hω/pt) 1/2 B min <~ G/Hz Outlook: Higher Power: P = 100 mw Higher Density N = cm -3 Buffer Gas, Squeezed Vacuum B min <~ G/Hz Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 37
38 Conclusion: Slow Light for Fun and Profit? Dr. George Welch, Texas A&M (KITP Quantum Optics Miniprogram 7/26/02) 38
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