1 Cavity decay rate in presence of a Slow-Light medium Thomas Lauprêtre Fabienne Goldfarb Fabien...

1

Cavity decay rate in presence of a Slow-Light

mediumThomas LauprêtreFabienne GoldfarbFabien Bretenaker

Laboratoire Aimé Cotton, Orsay, France

School of Physical Sciences, Jawaharlal Nehru University, Delhi, India

Rupamanjari GhoshSantosh 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

Start

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.

Solution: continuously measure three linear accelerations and three angular velocities.

?ax

ay

az

x

y z

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

O

L+- L- = 4πR2Ω/c

O’

R = 0.1 m et Ω = 0.01

°/h

Δφ < 1

nanoradian

CW WaveCCW Wave

5

Principle of the ring laser gyro

Gain mediumCW Modes

CCW Modes

c/L

L

A

4

CCW Wave

CW Wave

6

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

Dispersive medium

Ln

cp

L

L

n

n

L

d

dnn

d

dnnng

L

L

n

n

g

Cavity resonance condition:

Sagnac effect:

with

with

If , Sensitivity 0gn

8

The fundamental noise is given by the

Schawlow-Townes linewidth of the

laser:2

1

4 cavoutP

h

triproundper Losses

duration tripround

cav

Ring laser gyro

Lifetime of photons in the cavity

9

Lifetime of photons

• 2 different points of view

1) Phase velocity Resonant cavity:monochromatic field

2) Group velocityGaussian pulseΔt ∞ ?

Δt

10

• 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

no gain on sensitivity

2

1

4 cavoutP

h

Sensitivity?

L

L

n

n

g

Scale factor:

Linewidth:

How does the cavity photons lifetime How does the cavity photons lifetime cavcav depend on depend on

dispersion ?dispersion ?

11

Outline


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

cp c

One optical transitionΛ system

ab

cR 2

22

p

Rc b

a

ab

Electromagnetically Induced Transparency (EIT)

Width of transparency window

R

cbR

relax

cb

t

14

EIT and Slow Light

• Kramers-Kronig

Strong positive dispersion

d

dn

cvg )Re(

2

Slow Light !

Kash & al, PRL, 1999: 90 m.s-1 in RbHau & al, Nature, 1999: 17 m.s-1 in cold

Na

15

Outline


16

Metastable 4He

1S0

3P1

3S1

m = -1 10

RF discharge

p p

0

12

c

c

• Lifetime ~8000s

polarization selected Λ system

17

• 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)

Room temperature 4He*

No loss of coherence time

18

• 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)

Benefits of collisions

- Increase of coherence time

- Co-propagating beams

19

CcaC

EIT and optical detuning

R

ccp

c b

a

ab

RC

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

CPR

20

Doppler broadening• Sum of all profiles over the Doppler width

ab

cR 2

22

D

cR W2

22

Where WD is the half linewidth of the Doppler profile

3P1

Doppler width

~1 GHzR

~ ~Couplingc

Probep

3S1

21

Experimental set-up

22

Experimental results

D

cR W2

22

Coupling intensity (W.m-2)

Wid

th a

t h

alf

ma

xim

um

(k

Hz)

Gro

up

de

lay

(µ

s)

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

Im(χ

) (a

.u.)

Raman detuning (kHz)

23

Outline


24

EIT inside a cavity: set-up

λ/2 AO1

AO2

PBS

ωP , ΩP

ωC , ΩC

Laser & Beam

Shaping

PD

Telescope

4He* cell

PBS

PZ

Shutter

PBS

T=2% T=2%

25

Experiment

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 !

27

Cavity decay rate

cav1

cav

lossesgroup

cav

• 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

28

Cavity decay rate

• Consequences on the fundamental noise of laser cavity based sensors?

Increase of Δν

L

L

n

n

g

0gn

2

1

4 cavoutP

h

0cav

29

• Lifetime ?

Negative dispersion in cavity

Δt

Vg>0

30

• Lifetime ?

Negative dispersion in cavity

Δt

Vg<0

tripround 1 f or 0group

31

Outline


32

Negative dispersion

• Optical detuning : asymmetry of the absorption profile

Narrow absorption peak of small amplitude

Negative dispersion

3P1

Doppler width

~1 GHzR

~ ~Couplingc

Probep

3S1

Δ

33


Negative group velocity


Gro

up

del

ay (

µs)

3P1

Doppler width

~1 GHz

R

~ ~Coupling

c

Probep

3S1

Δ

34

Conclusion

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

• Negative group velocity?

35

Poster session: Tu-P15 S. Kumar, T. Lauprêtre, F. Bretenaker, R. Ghosh, and F.

GoldfarbInteracting dark resonances in a tripod system of room

temperature 4He*

Advertisment

36

Thank you!

1 Cavity decay rate in presence of a Slow-Light medium Thomas Lauprêtre Fabienne Goldfarb Fabien...

Documents

Transcript of 1 Cavity decay rate in presence of a Slow-Light medium Thomas Lauprêtre Fabienne Goldfarb Fabien...