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

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

3. 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!

4. 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

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

6. 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?

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

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

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

10. 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 ?

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

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

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

14. 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

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

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

17. Room temperature 4He* 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

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

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

20. 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

21. Experimental set-up

22. 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

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

24. 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%

25. Experiment

26. 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 !

27. 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

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

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

30. Negative dispersion in cavity
Lifetime ? Δt
Vg<0

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

32. 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

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

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

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*

36. Thank you!