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
Outline
•
•
•
•
•
Issues: the ring laser gyro
EIT and dispersion
Experimental set-up
Cavity decay rate
Negative dispersion in He*
2
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
ax
measurements only.
?
Start
Wx
Wy
Wz
az
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!
3
Sagnac effect
CCW Wave
CW Wave
O
O’
W
R = 0.1 m et Ω = 0.01 °/h
L+- L- = 4πR2Ω/c
Δφ < 1 nanoradian
4
Principle of the ring laser gyro
CCW Modes
W
Dn
n
CCW Wave
CW Modes
Gain medium
c/L
CW Wave
Dn 
4A
L
W
5
Dispersion in cavity
Positive dispersion reduces the linewidth of a
resonator
Could dispersion enhance sensitivity of cavity
based sensors?
6
Cavity filled with a dispersive medium
Cavity resonance condition: n  p
Sagnac effect:  L
W
n
n

n
n
n
Dispersive medium
n


L
L
n L
ng L
with
n 
c
n n  L
dn
dn
with n g  n  n
n
dn
dn
If n g  0  , Sensitivity  
7
Ring laser gyro
The fundamental noise is given by the
Schawlow-Townes linewidth of the laser:
Dn 
 cav 
round  trip duration
Losses per round  trip
hn
1
4  Pout  cav
2
Lifetime of photons in the cavity
8
Lifetime of photons
• 2 different points of view
Δt
1) Phase velocity
Resonant cavity:
monochromatic field
2) Group velocity
Gaussian pulse
Δt ∞ ?
9
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
Scale factor:
n
n

n L
ng L
Linewidth:
Dn 
hn
1
4  Pout  cav
no gain on sensitivity
How does the cavity photons lifetime cav depend on dispersion ?
10
2
Outline
•
•
•
•
•
Issues: the ring laser gyro
EIT and dispersion
Experimental set-up
Cavity decay rate
Negative dispersion in He*
11
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
One optical
transition
Λ system
R
Wc
c
a
 ab
W p p  W c
W
b
R
Induced
WidthElectromagnetically
of transparency window
2 R 
Transparency
(EIT)
 




b
t
c

  R 

 relax
Wc
2
2  ab
b c
13
EIT and Slow Light
• Kramers-Kronig
c
vg 
 d Re(  )
Slow Light !
Strong
2
d  positive dispersion
n
Kash & al, PRL, 1999: 90 m.s-1 in Rb
Hau & al, Nature, 1999: 17 m.s-1 in cold Na
14
Outline
•
•
•
•
•
Issues: the ring laser gyro
EIT and dispersion
Experimental set-up
Cavity decay rate
Negative dispersion in He*
15
Metastable 4He
m=
-1
p
0
s
Wp
1
0

s
3P
1
c
Wc
2
1
3S
1
RF discharge
1S
0
• Lifetime ~8000s
 polarization selected Λ system
16
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
17
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
EIT and optical detuning
R
a
DC
Wc
c
 ab
W
p
R
 W c
b
D C   ca   C
 R   P  C
Fano profile
B. Lounis and C. Cohen-Tannoudji, J. Phys. II (France) 2, 579 (1992)
19
Doppler broadening
• Sum of all profiles over the Doppler width
Doppler width
R
3P
1
~1 GHz
Coupling
Wc
2 R 
W
2
c
2  ab
~
~ Probe
Wp
3S
1
Wc
2
2R 
2W D
Where WD is the half linewidth of the Doppler profile
20
Experimental set-up
21
Im(χ) (a.u.)
Width at half maximum (kHz)
Experimental results
Raman detuning (kHz)
Coupling intensity (W.m-2)
Wc
2
Group delay (µs)
2R 
2W D
 Group velocity around 8 km.s-1 !
Goldfarb, F. & al.,
EPL (Europhysics Letters),
2008, 82, 54002
Ghosh, J. & al.,
Phys.Rev.A, 2009
22
Coupling intensity (W.m-2)
Outline
•
•
•
•
•
Issues: the ring laser gyro
EIT and dispersion
Experimental set-up
Cavity decay rate
Negative dispersion in He*
23
EIT inside a cavity: set-up
Laser & Beam
Shaping
λ/2
PBS
AO2
PZ
ωP , ΩP
ωC , ΩC
Telescope
Shutter
PBS
PD
T=2%
AO1
4He*
cell
PBS
T=2%
24
Experiment
25
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
Cavity decay rate
 cav 
 group
losses
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
 cav
1
 cav
• Non monochromatic field
Group velocity
27
Cavity decay rate
• Consequences on the fundamental noise
of laser cavity based sensors?
n
n

n L
Dn 
ng L
ng  0

hn
1
4  Pout  cav
 cav  0
2

Increase of Δν
28
Negative dispersion in cavity
• Lifetime ?
Δt
Vg>0
29
Negative dispersion in cavity
• Lifetime ?
 group  0 for 1 round  trip
Δt
Vg<0
30
Outline
•
•
•
•
•
Issues: the ring laser gyro
EIT and dispersion
Experimental set-up
Cavity decay rate
Negative dispersion in He*
31
Negative dispersion
• Optical detuning : asymmetry of the
absorption profile Doppler width
~1 GHz
Coupling
Wc
Δ
~
R
3P
1
~ Probe
Wp
3S
1
Narrow absorption peak of
small amplitude
 Negative dispersion
32
Negative group velocity
Doppler width
R
~1 GHz
~
3P
1
~ Probe
W
p
3S
1
Group delay (µs)
Coupling
Wc
Δ
Raman detuning (kHz)
Raman detuning (kHz)
33
Conclusion
• Decay rate of a cavity filled with a
strong positive dispersion medium is
governed by the group velocity
• Negative group velocity?
34
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
Thank you!
36