Cavity decay rate in presence of a Slow-Light medium

Transcription

1 Cavity decay rate in presence of a Slow-Light medium Laboratoire Aimé Cotton, Orsay, France Thomas Lauprêtre Fabienne Goldfarb Fabien Bretenaker School of Physical Sciences, Jawaharlal Nehru University, Delhi, India Rupamanjari Ghosh Santosh Kumar Thales R&T, Palaiseau, France Sylvain Schwartz 1

2 Outline Issues: the ring laser gyro EIT and dispersion Experimental set-up Cavity decay rate Negative dispersion in He* 2

3 Inertial navigation Problem: allow a vehicle to know its attitude and position at any moment by knowing only the coordinates of its starting point and using internal measurements only.? a x Ω x Start Ω y Ω z a z a y Solution: continuously measure three linear accelerations and three angular velocities. Error smaller than 1 nautical mile per hour: Drift of the gyros < 0.01 /hour (Earth rotation 15 / hour) Till the 1960 s: undisputed reign of mechanical gyros! 3

4 Sagnac effect CCW Wave CW Wave O O Ω L + - L - = 4πR 2 Ω/c R = 0.1 m et Ω = 0.01 /h Δφ < 1 nanoradian 4

5 Principle of the ring laser gyro CCW Modes Ω Gain medium CCW Wave CW Modes ν c/l ν CW Wave ν = 4A λ L Ω 5

6 Dispersion in cavity Positive dispersion reduces the linewidth of a resonator Could dispersion enhance sensitivity of cavity based sensors? 6

7 Cavity filled with a dispersive medium Ω Cavity resonance condition: ν = Sagnac effect: δl δν L = δn δ ν n L δν = ν n ng δl L with with δn = c p n( ν )L dn δν dν dn n g = n + ν d ν Dispersive medium If ng + 0, Sensitivity 7

8 Ring laser gyro The fundamental noise is given by the Schawlow-Townes linewidth of the laser: ν = h ν π P out τ cav τ cav = round trip duration Losses per round trip Lifetime of photons in the cavity 8

9 Lifetime of photons 2 different points of view Δt 1) Phase velocity Resonant cavity: monochromatic field 2) Group velocity Gaussian pulse Δt? 9

10 Sensitivity? Lifetime driven by phase velocity: Scale factor increased and noise unchanged gain on sensitivity But Lifetime driven by group velocity Scale factor increased so is the noise ν = Scale factor: δν = ν h ν π n ng Linewidth: δl L P out τ cav no gain on sensitivity How does the cavity photons lifetime τ cav depend on dispersion? 10

11 Outline Issues: the ring laser gyro EIT and dispersion Experimental set-up Cavity decay rate Negative dispersion in He* 11

12 Electromagnetically Induced Transparency? Fact: Optical transition is made transparent for a resonant field (otherwise opaque medium) How it happens: A quantum interference effect, induced by a control field applied on a second transition 12

13 One optical Λ system transition δ δ R a Ω c γ ab Ω Ω p p << Ω c c Γ R b Width Electromagnetically of transparency window Induced 2ΓR Transparency (EIT) ρ b t c relax = Γ R ρ b c + Ω 2γ 2 c ab 13

14 EIT and Slow Light Kramers-Kronig c v g ω d Re( χ ) n + 2 dω = Slow Light! Strong positive dispersion Kash & al, PRL, 1999: 90 m.s -1 in Rb Hau & al, Nature, 1999: 17 m.s -1 in cold Na 14

15 Outline Issues: the ring laser gyro EIT and dispersion Experimental set-up Cavity decay rate Negative dispersion in He* 15

16 Metastable 4 He = m 2-1 ω p σ + Ω p 0 0 δ ω c σ Ωc 1 1 RF discharge 3 P 1 3 S 1 1 S 0 Lifetime ~8000s polarization selected Λ system 16

17 Room temperature 4 He* Spin conservation through collisions with He M. Pinard and F. Laloë, J. Physique (1980) Almost no Penning ionization (thanks to optical pumping) Shlyapnikov & al, PRL (1994) No loss of coherence time 17

18 Benefits of collisions Possibility to pump over the entire Doppler width through Velocity Changing Collisions (VCCs) Atoms are confined into the laser beam (diffusive transit instead of ballistic transit) - Increase of coherence time - Co-propagating beams 18

19 EIT and optical detuning δ R C a Ω c γ ab Ωp << Ω c c δ C R Γ R = ω ω ca = ω P C ω C b Fano profile B. Lounis and C. Cohen-Tannoudji, J. Phys. II (France) 2, 579 (1992) 19

20 Doppler broadening Sum of all profiles over the Doppler width Doppler width ~1 GHz δ R 3 P 1 Coupling Ω c ~ ~ Probe Ω p 3 S 1 2Γ R + Ω 2γ 2 c ab 2Γ R + Ω 2W Where W D is the half linewidth of the Doppler profile 2 c D 20

21 Experimental set-up 21

22 Experimental results Im(χ) (a.u.) Group delay (µs) Raman detuning (khz) Coupling intensity (W.m -2 ) Width at half maximum (khz) Coupling intensity (W.m -2 ) 2Γ R + Ω 2W Group velocity around 8 km.s -1! Goldfarb, F. & al., EPL (Europhysics Letters), 2008, 82, c D Ghosh, J. & al., Phys.Rev.A,

23 Outline Issues: the ring laser gyro EIT and dispersion Experimental set-up Cavity decay rate Negative dispersion in He* 23

24 EIT inside a cavity: set-up Laser & Beam Shaping λ/2 PBS AO 1 ω P, Ω P AO 2 Shutter PZ ω C, Ω C Telescope PD T=2% PBS 4 He* cell PBS T=2% 24

25 Experiment 25

26 Global results Decay time of the cavity Group delay introduced by the cell (open cavity) Measured decay time ~ a few µs ~150 ns with phase velocity Group velocity! 26

27 Cavity decay rate τ = cav τ group losses τ cav T. Lauprêtre, C. Proux, R. Ghosh, S. Schwartz, F. Goldfarb, and F. Bretenaker «Photon lifetime in a cavity containing a slow-light medium» Accepted by OL 1 πτ cav Non monochromatic field Group velocity 27

28 Cavity decay rate Consequences on the fundamental noise of laser cavity based sensors? δν = ν n ng δl L ν = h ν π P out τ cav n g + 0 τ cav + 0 Increase of Δν 28

29 Negative dispersion in cavity Lifetime? Δt Vg>0 29

30 Negative dispersion in cavity Lifetime? τ group < 0 for 1 round trip Δt Vg<0 30

31 Outline Issues: the ring laser gyro EIT and dispersion Experimental set-up Cavity decay rate Negative dispersion in He* 31

32 Negative dispersion Optical detuning : asymmetry of the absorption profile Doppler width ~1 GHz Δ δ R 3 P 1 Coupling Ω c ~ ~ Probe Ω p 3 S 1 Narrow absorption peak of small amplitude Negative dispersion 32

33 Negative group velocity Doppler width ~1 GHz Δ δ R 3 P 1 Coupling Ω c ~ ~ Probe Ω p 3 S 1 Group delay (µs) Raman detuning (khz) Raman detuning (khz) 33

34 Conclusion Decay rate of a cavity filled with a strong positive dispersion medium is governed by the group velocity Negative group velocity? 34

35 Advertisment Poster session: Tu-P15 S. Kumar, T. Lauprêtre, F. Bretenaker, R. Ghosh, and F. Goldfarb Interacting dark resonances in a tripod system of room temperature 4He* 35

36 Thank you! 36