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

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

Inertial navigation ? ax Wx az Wy Wz ay 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. ax ? Wx az Wy Start Wz ay 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!

Sagnac effect L+- L- = 4πR2Ω/c W R = 0.1 m et Ω = 0.01 °/h CCW Wave CW Wave O O’ L+- L- = 4πR2Ω/c W R = 0.1 m et Ω = 0.01 °/h Δφ < 1 nanoradian

Principle of the ring laser gyro CCW Modes W Dn n CCW Wave CW Modes c/L Gain medium CW Wave

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

Cavity filled with a dispersive medium Cavity resonance condition: Sagnac effect: with W with Dispersive medium If , Sensitivity

Ring laser gyro The fundamental noise is given by the Schawlow-Townes linewidth of the laser: Lifetime of photons in the cavity

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

Sensitivity? Lifetime driven by phase velocity: But Scale factor increased and noise unchanged gain on sensitivity But Lifetime driven by group velocity Scale factor increased so is the noise no gain on sensitivity Scale factor: Linewidth: How does the cavity photons lifetime tcav depend on dispersion ?

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

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

One optical transition Λ system One optical transition Electromagnetically Induced Transparency (EIT) Width of transparency window

EIT and Slow Light Strong positive dispersion Kramers-Kronig Kash & al, PRL, 1999: 90 m.s-1 in Rb Hau & al, Nature, 1999: 17 m.s-1 in cold Na

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

Metastable 4He m = -1 1 d 3P1 wp Wp wc Wc 3S1 1S0 Lifetime ~8000s d 3P1 s+ wp Wp wc s- Wc 3S1 RF discharge 1S0 Lifetime ~8000s polarization selected Λ system

Room temperature 4He* Spin conservation through collisions with He M. Pinard and F. Laloë, J. Physique 41 799 (1980) Almost no Penning ionization (thanks to optical pumping) Shlyapnikov & al, PRL 73 3247 (1994) No loss of coherence time

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

EIT and optical detuning Fano profile B. Lounis and C. Cohen-Tannoudji, J. Phys. II (France) 2, 579 (1992)

Doppler broadening Sum of all profiles over the Doppler width ~1 GHz dR ~ Coupling Wc Probe Wp 3S1 Where WD is the half linewidth of the Doppler profile

Experimental set-up

Experimental results Group velocity around 8 km.s-1 ! Im(χ) (a.u.) Raman detuning (kHz) Coupling intensity (W.m-2) Width at half maximum (kHz) Group delay (µs) Coupling intensity (W.m-2) Group velocity around 8 km.s-1 ! Goldfarb, F. & al., EPL (Europhysics Letters), 2008, 82, 54002 Ghosh, J. & al., Phys.Rev.A, 2009

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

EIT inside a cavity: set-up λ/2 AO1 AO2 PBS ωP , ΩP ωC , ΩC Laser & Beam Shaping PD Telescope 4He* cell PZ Shutter T=2%

Experiment

Global results Measured decay time ~ a few µs 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 !

Cavity decay rate Non monochromatic field Group velocity 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 Non monochromatic field Group velocity

Cavity decay rate Consequences on the fundamental noise of laser cavity based sensors? Increase of Δν

Negative dispersion in cavity Lifetime ? Δt Vg>0

Negative dispersion in cavity Lifetime ? Δt Vg<0

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

Narrow absorption peak of small amplitude Negative dispersion Optical detuning : asymmetry of the absorption profile 3P1 Doppler width ~1 GHz dR ~ Coupling Wc Probe Wp 3S1 Δ Narrow absorption peak of small amplitude Negative dispersion

Negative group velocity Doppler width ~1 GHz dR ~ Coupling Wc Probe Wp 3S1 Δ Raman detuning (kHz) Raman detuning (kHz) Group delay (µs)

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

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*

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