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Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Manifestation of General Relativity in Practical Experiments
Selim M. Shahriar
Laboratory for Atomic and Photonic TechnologyNorthwestern University
Evanston, IL
[http://lapt.ece.northwestern.edu]
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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GR-Relevant Terrestrial Experiments
SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light Interferometry Using Atomic Interferometry
ARTIFICAL BLACKHOLE USING SLOW LIGHT
GPS AND QUANTUM CLOCK-SYNCHRONIZATION
EQUIVALENCE PRINCIPLE AND SLOW-LIGHT
LIGO PROJECT FOR DETECTING GRAV. WAVES
FAST-LIGHT AND ATOMIC INTER. FOR DET. GRAV. WAVES
...
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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GR-Relevant Terrestrial Experiments
SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light Interferometry Using Atomic Interferometry
ARTIFICAL BLACKHOLE USING SLOW LIGHT
GPS AND QUANTUM CLOCK-SYNCHRONIZATION
EQUIVALENCE PRINCIPLE AND SLOW-LIGHT
LIGO PROJECT FOR DETECTING GRAV. WAVES
FAST-LIGHT AND ATOMIC INTER. FOR DET. GRAV. WAVES
...
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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GR-Relevant Terrestrial Experiments
SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light Interferometry Using Atomic Interferometry
ARTIFICAL BLACKHOLE USING SLOW LIGHT
GPS AND QUANTUM CLOCK-SYNCHRONIZATION
EQUIVALENCE PRINCIPLE AND SLOW-LIGHT
LIGO PROJECT FOR DETECTING GRAV. WAVES
FAST-LIGHT AND ATOMIC INTER. FOR DET. GRAV. WAVES
...
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Quick Review of Lense-Thirring Effect
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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• Rotation with respect to absolute space gives rise to centrifugal forces, as illustrated by the “bucket experiment“:
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Inertia is a phenomenon that relates the motion of bodies to the
motion of all matter in the universe (“Mach‘s Principle“).
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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w will later be called Thirring-Lense frequency.
The rotation of the earth should “drag“ (local) inertial frames.
verysmalleffect
very smallfrequency
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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More convenient
than water buckets
are torque-free
gyroscopes...
Dragging = precession
of gyroscope axes
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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• The interior of a rotating spherical matter shell is (approximately) an inertial frame that is dragged, i.e. rotates with respect to the exterior region:
(valid in the weak field approximation =linearized theory)
2
4 2
3 3SRG M
c R R
M = mass of the sphere
R = radius of the sphere
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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• Dragging effects outside the shell:3
2
2
3
G M R
c R r
In the equatorial plane:
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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• Dragging effects near a massive rotating sphere:
( )x ������������������������������������������
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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• Dragging of the orbital plane:
Newtonian gravity General relativity
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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• Magnitude of the effect:
dd = 0.13 cm ( = 0.886 cm)
Circular orbit of radius r :
2
2
4
5SE
Sat
R Rd
r
Earth satellite with close orbits:
0.26 arc-seconds/year
Angular frequency of the orbital plane:
SR
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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• Useful analogy that applies for stationary (weak) gravitational fields:
“Newtonian“ part of the gravitational field “electric“ behaviour:
“Machian“ part of the gravitational field “magnetic“ behaviour
(sometimes called “gravimagnetism“):
1/r² attractive force
matter flow
Lense-Thirring frequency
Rotatingbody:Bothbehavioursapply!
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Rotating charge distribution <-> rotating matter
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• George Pugh (1959), Leonard Schiff (1960)
Suggestion of a precision experiment using a gyroscope in a satellite
• I. Ciufolini, E. Pavlis, F. Chieppa, E. Fernandes-Vieira and J. Perez-Mercader: Test of general relativity and measurement of the Lense-Thirring effect with two Earch satellites
Science, 279, 2100 (27 March 1998)
Measurement of the orbital effect to 30% accuracy, using satellite data (preliminary confirmation)
• I. Ciufolini and E. C. Pavlis: A confirmation of the general relativistic prediction of the Lense-Thirring effect
Nature, 431, 958 (21 October 2004)
Confirmation of the orbital effect to 6% accuracy, using satellite data
• Gravity Probe B, 2005
Expected confirmation of gyroscope dragging to 1% accuracy
Sattelite-based Tests:
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• 2 satellites LAGEOS (NASA, launched 1976) andLAGEOS 2 (NASA + ASI, launched 1992)
• Original goal: precise determinationof the Earth‘s gravitational field
• Major semi-axes: 12270 km, 12210 km
• Excentricities: 0.004 km, 0.014
• Diameter: 60 cm, Mass: 406 kg• Position measurement by reflection
of laser pulses(accurate up to some mm!)
• Main difficulty: deviations from spherical symmetry of the Earth‘s gravity field
1a 2a
LAGEOS
LAGEOS 2
1 2
LAGEOS
LAGEOS 2
LAGEOS Project:
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• Improved model of the Earth‘sgravitational field:EIGEN-GRACE02S
• Evaluation of 11 years position data
• Improved choice of observables(combination of the nodes of bothsatellites)
Observed value = 99% 5% of the predicted value LAGEOS
LAGEOS 2
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• Satellite based experiment, NASA und Stanford University
• Goal: direct measurement of the dragging(precession) of gyroscopes‘ axesby the Lense-Thirring effect(Thirring-Schiff-effect)
• 4 gyroscopes with quartz rotors: theroundest objects ever made!
• Launch: 20 April 2004
• Orbital plane: Earth‘s center + north pole + IM Pegasi (guide star) Launch window: 1 Second!
• Expectation for 2005: Measurement of the Thirring-Lense frequency with an accuracy of 1%
Gravity Probe B:
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Terrestrial Tests Using Precision Gyroscopes
VCO1
AOM1 AO
M2 VCO2
diff.
Las
er
?V1
beatdet
? f
diff
.
? V2
?VCO1VCO1
AOM1 AO
M2 VCO2VCO2
diff.diff.
Las
er
Las
er
?V1 ?V1V1
beatdet
? f
diff
.d
iff.
? V2? V2V2
?
Ring Laser Gyroscope Atom-Interferometric Gyroscope
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Quick Look at Atom-Interferometry
ATOM INTERFEROMETRY: BASIC IDEA
ATOM AS A dE Broglie WAVE
vv
= (h / m v)
Rb at 300o C:
= 0.0153 nm
2 Sin
ATOMIC INTERFERENCE FRINGES
LASER-CONTROLLED SPIN EXCITATION
NB
Time
OFF-RESONANT
|B>
|E>
|A>
METHOD FOR ACHIEVING LARGE ANGLE:
RF EXCITATION OF ATOMS
NB
Time
|B, p+k >
|E>
|A, p>
TRAVELLING WAVES
LASER-CONTROLLED SPIN EXCITATION
NB
Time
|E>
EASY TO LOCALIZE
MUCH STRONGER
OFF-RESONANT
DECOHERENCE FREESTRONG RECOIL
|A, p>
|B, p+2k >
LASER-CONTROLLED SPIN EXCITATION RECOIL
|E>
|A>
|B>
|E>
|A>
|B>
k
|E>
|A>
|B>
k
|E>
|A>
|B>
2k
PUSHING TO THE RIGHT |E>
|A>
|B, 2k>
PUSHING TO THE LEFT
|E>
|A, p>
|B, -2k>
SPLITTING ATOMIC WAVES USING LCSE
|A>
|B>
|A>
|B, 2k>
|B,- 2k >
|A, 4k>
INTERFEROMETER IN ONE DIMENSION
100 k SPLITTING POSSIBLE
SYSTEM: 87RB
FRINGE SPACING: ~ 4 NM
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Atomic Sagnac Interferometer
|a>
|b>
L L
d
vx
π/2 π
π/2
1 1 1
2 22
1
2
BCI
CI
|a>
|b>
x
z
|a>
|b>
L L
d
vx
π/2 π
π/2
11 11 11
22 2222
11
22
BCI
CI
|a>
|b>
x
z
3035 MHz
121 MHz
F=3
F=2
DOP
R1
R2
F’=4F’=3
1517.5 MHz
OP GALVOSCANNER
D
PM
T
R1
R2A
B
3035 MHz
121 MHz
F=3
F=2
DOP
R1
R2
F’=4F’=3
1517.5 MHz
3035 MHz
121 MHz
F=3
F=2
DOP
R1
R2
F’=4F’=3
1517.5 MHz
OP GALVOSCANNER
D
PM
T
R1
R2
OP GALVOSCANNER
D
PM
T
R1
R2AA
BB
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Quick Look at Sagnac Effect
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General View of the Sagnac Effect
DetW
CW
CCW
Det
Wave-Source
W
CW
CCW
WAVE SOURCES:
Optical Waves
Matter Waves
Acoustic Waves
???
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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General View of the Sagnac Effect
Det
CW
CCW
Det
Wave-Source
CW
CCW
Det
CW
CCW
Det
Wave-SourceWave-Source
CW
CCW
BS1 BS2
R
DEFINE:
CW(+)
CCW(-)
VP : Phase Velocity in Absence of Rotation
RV: Relativistic Phase Velocities Seen in an Inertial Frame
: time for the Phase Fronts to travel from BS1 t BS2 T
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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General View of the Sagnac Effect
BS1 BS2
R
CW(+)
CCW(-)
VP : Phase Velocity in Absence of Rotation
RV: Relativistic Phase Velocities Seen in an Inertial Frame
: time for the Phase Fronts to travel from BS1 t BS2 T
2/1 oP
PR CvV
vVV
vTRL RVLT /
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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BS1 BS2
R
CW(+)
CCW(-)
2/1 oP
PR CvV
vVV
vTRL RVLT /
General View of the Sagnac Effect
)1/(/2)1(
2 222
ooo
o
CvfortCAC
ATTt
VP : Phase Velocity in Absence of Rotation
RV: Relativistic Phase Velocities Seen in an Inertial Frame
: time for the Phase Fronts to travel from BS1 t BS2 T
A : Area normal to
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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BS1 BS2
R
CW(+)
CCW(-)
General View of the Sagnac Effect
)1/(/2)1(
2 222
ooo
o
CvfortCAC
ATTt
VP : Phase Velocity in Absence of Rotation
RV: Relativistic Phase Velocities Seen in an Inertial Frame
: time for the Phase Fronts to travel from BS1 t BS2 T
A : Area normal to
NOTE:
This expression does not depend at all on the velocity of the wave It involves the free space velocity of light only, even if acoustic waves or matter waves are used
For optical waves, this results is independent of the refractive index
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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BS1 BS2
R
CW(+)
CCW(-)
General View of the Sagnac Effect
)1/(/2)1(
2 222
ooo
o
CvfortCAC
ATTt
VP : Phase Velocity in Absence of Rotation
RV: Relativistic Phase Velocities Seen in an Inertial Frame
: time for the Phase Fronts to travel from BS1 t BS2 T
A : Area normal to
)(/4 2 shiftphaseSagnacgenericCfAt o
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General View of the Sagnac Effect
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
BA
B
1
1
4
3
2
1
2
3
4
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
BA
B
A
B
A
B
A
B
A
B
A
B
A
BA
B
A
B
1
1
4
3
2
1
2
3
4
Result is independent of Axis of Rotation
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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General View of the Sagnac Effect
)(/4 2 shiftphaseSagnacgenericCfAt o
OPTICAL SAGNAC PHASE SHIFT:
MATTER-WAVE SAGNAC PHASE SHIFT:
f=Co/o
)1/1/1(;/ 22oGoGo CVforCVhmCf
Relevant Frequency is the Compton Frequency:
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Wrong View of the Sagnac Effect
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Wrong View of the Sagnac Effect
Now a team led by Wolfgang Schleich at the University of Ulm in Germany have suggested a way to adapt the ring-laser gyros currently used to track rotation in aircraft and satellites…..
These devices fire laser beams in opposite directions around a fibre-optic ring. If a plane is turning, the laser beam travelling with the rotation has to travel further to catch up with its starting point, so it arrives later than the beam travelling against the rotation. When the beams meet, they create an interference pattern from which it is possible to work out the difference in the arrival times of the two beams, and hence the rate of rotation…..
Shleich points out that the same principle also works with cold atom beams, and because atoms move more slowly than light, the shift is more obvious. This should allow far slower rates of rotation to be measured.
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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“Wrong” View of the Optical Sagnac Effect
This happens to be correct only when the index is unityThis line of reasoning gives the wrong result when n1
BS1 BS2
R
CW(+)
CCW(-)
vTRL RVLT /
VP : Phase Velocity in Absence of Rotation
RV: Phase Velocities Seen in an Inertial Frame
: time for the Phase Fronts to travel from BS1 t BS2 T
A : Area normal to
oPR CVV
2/2 oCATTt )/(4 ooCA
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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“Wrong” View of the Atomic Sagnac Effect
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“Wrong” View of the Atomic Sagnac Effect
Off by a factor of 2, but pretty close!
BS1 BS2
R
CW(+)
CCW(-)
vTRL RVLT /
VP : Phase Velocity in Absence of Rotation
RV: Phase Velocities Seen in an Inertial Frame
: time for the Phase Fronts to travel from BS1 t BS2 T
A : Area normal to
COMPR VVV
2/2 COMVATTt
However, fundamentally wrong! VCOM does not influence the result
2/2COMmV hmA /2
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Quick Look at Slow and Fast Light
Concept of Phase Velocity of a Monochromatic Wave
Monochromatic plane wave
Constant phase front moves a distance z in time t
tzk
Phase velocity n
c
kt
zvp
t
t 1 t 2
Phase front
t
z z 1= (c/n) t
1 z 2
vp > c does not contradict special theory of relativity
Dispersion relation
.c.ceEt,zE tzkio
Phase tzk
c
nk
Superposition of two single frequency plane waves
Group Velocity: Non-monochromatic Signal
tzkcostzkcosE2
tzkcostzkcosEE
o
2211o
envelope Rapidly oscillating term
2kkk,2
kv
2121
g
2,1i,c
nk,2kkk
,2
n
c
kv
ii21
21
p
Group velocity
Phase velocity
Vg
vp
Wave group
1
2
For non-dispersive mediumn
cvg
Pulse in a Dispersive MediumPulse
t
In a dispersive medium, n(), for no pulse distortion, frequency components add in phase at pulse peak
d
ndnnIndexGroup
kd
d
dnd
n
cvVelocityGroup
tvz,0tc
zn
c
z
d
nd0
d
d
c
nk,tzk
g
g
g
DispersionPhase Index
Slow & fast light effects make use of large dn/d
in the vicinity of material resonance
LightFastdispersionanomalous0d
nd
LightSlowdispersionnormal0d
nd
Dispersion and Slow Light using EIT in a -System
|+> |->
|2>
Dressed State Basis
2s
2p gg
Dark State
gp, probe field
gs, strong field
1
|1>
|3>
|2>
-type atomic system
2
= 021
4gii
iNi2s13122
132
21
Susceptibility to first order in probe field amplitude
For large amplitude of strong field and 1=0
2s
2210
g2s
1302
21
g
N2n,
g
iN4i
ng can be as large as O(107)
vg (< c) O(102) m/s
-- 31 is decoherence rate for ground states
-1.5 -1 -0.5 0 0.5 1 1.5
x 107
0.9995
1
1.0005
inde
x-1.5 -1 -0.5 0 0.5 1 1.5
x 107
0.5
1
1.5
2
x 10-3
abso
rp.
coef
f.
-1.5 -1 -0.5 0 0.5 1 1.5 2
x 107
-1
0
1
2
3
x 10-4
detuning (1)
mag
. of
gro
up in
dex
gs2/
normal dispersion
positive group index
Slow Light in Pr:YSO
Coupling
Probe
Repump
4.64.8
10.2
17.3 5/2
3/2
1/2
1/2
3/2 5/2
Energy Diagram
Experimental Setup
=605.977 nm(Site 1)
-- Repump refills the spectral holes burned by pump and probe fields or prevents persistent SHB due to long population life time of ground state sublevels (100s @ 5K)
-- Appropriate pulse sequences for the beams are generated using AOM switching
Observation of Slow Light in Pr:YSO
Measured group delay ~
100 s = 33 m/sec
Coupling beam switched on at –200 s
Input probebeam
No couplingbeam (x0.25)
Slowedlight
IncompleteProbe absorption
Pro
be tr
ansm
issi
on (
%)
Group delay
70 s
10 msec
R
C
P
1 msec
0.2 msec
Pulse sequence
Turukhin et. al. Phys. Rev. Lett. 88 (2002) 023601
Coupling
Probe
Repump
4.64.8
10.2
17.3 5/2
3/2
1/2
1/2
3/2 5/2
Energy Diagram
Fast Light Using Anomalous Dispersion
L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000).
Fast Light Using Anomalous Dispersion
L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000).
Inside pulse delayed by:
T=L/Vg-L/C=(ng-1)L/C
Inside pulse advanced by:
-T=(1-ng)L/C
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Role of Fresnel Drag in Sagnac Effect
BS1 BS2
R
CW(+)
CCW(-)
2/1 oP
PR CvV
vVV
vTRL RVLT /
VP : Phase Velocity in Absence of Rotation
RV: Relativistic Phase Velocities Seen in an Inertial Frame
: time for the Phase Fronts to travel from BS1 t BS2 T
A : Area normal to
)1
1(;2n
vn
CV FF
oR same
FresnelDragCoefficient
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Role of Fresnel Drag in Sagnac Effect
2/1 oP
PR CvV
vVV
vTRL RVLT /
)1
1(;2n
vn
CV FF
oR same
FresnelDragCoefficient
ooF ttnt )1(2
ooFn )1(2
Fresnel Drag Effect is Included in the Proper Description of the Sagnac Effect
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Doppler Shift and Laub Drag in Sagnac Effect
No Doppler Effect if the Laser is stationery, but the stage rotates,with the no relative motion between the mirrors and the medium
Laser
Det
DetW DetDetW
CW
CCW
VM
VM
VM
VM
Clamp
FlexibleFiber
Laser
Det
DetLaser
stationary
C.
B.
A.
Frame & source stationary; medium rotating
Frame & source rotating; medium stationary
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Doppler Shift and Laub Drag in Sagnac Effect
Laser and MZI frame are stationery, and the medium moves with a relative Velocity of VM.
Laser
Det
DetW DetDetW
CW
CCW
VM
VM
VM
VM
Clamp
FlexibleFiber
Laser
Det
DetLaser
stationary
C.
B.
A.
Frame & source stationary; medium rotating
Frame & source rotating; medium stationary
CW(+) and CCW(-) beams are Doppler shifted by equal and opposite amounts, given by:
oM CV /
The relativistic velocities are then given by:
;)1(
22 Fo
ogM
o
oF
oM
o
oF
oo
oR v
n
nnV
n
Cv
n
nV
n
Cv
n
nn
CV
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Doppler Shift and Laub Drag in Sagnac Effect
Laser and MZI frame are stationery, and the medium remains stationery (or vice versa)
Laser
Det
DetW DetDetW
CW
CCW
VM
VM
VM
VM
Clamp
FlexibleFiber
Laser
Det
DetLaser
stationary
C.
B.
A.
Frame & source stationary; medium rotating
Frame & source rotating; medium stationary
Here VM=(-v)=-R, so that the relativistic velocities are then given by:
22
11;
o
og
oLL
o
oR n
nn
nv
n
CV
The LaubDrag Coefficient
G.A. Sanders and S. Ezekiel J. Opt. Soc. Am. B, 5, 674 (1988)
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Doppler Shift and Laub Drag in Sagnac Effect
Laser and MZI frame are stationery, and the medium remains stationery (or vice versa)
22
11;
o
og
oLL
o
oR n
nn
nv
n
CV
Laser
Det
Det DetDet
CW
CCW
VM
VM
VM
VM
Clamp
FlexibleFiber
Laser
Det
DetLaser
stationary
C.
B.
A.
Frame & source stationary; medium rotating
Frame & source rotating; medium stationary
LaserLaser
Det
Det
Det
Det DetDet
CW
CCW
VM
VM
VM
VM
Clamp
FlexibleFiber
Laser
DetDetDetDet
CW
CCW
VM
VM
VM
VM
Clamp
FlexibleFiber
LaserLaser
Det
DetLaser
Det
DetLaser
Det
Det
Det
DetLaser
Laser
stationary
C.C.
B.B.
A.A.
Frame & source stationary; medium rotating
Frame & source rotating; medium stationary
;)1(2oL tnt oLn )1(2
;og tnt ogn
(For ng>>no)
EnhancementFactor
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Optical Sagnac Effect in a Passive Ring Cavity
VCO1
AOM1 AO
M2 VCO2
diff.
Laser
V1
beatdet
f
diff
.
V2
S. R. Balsamo and S. Ezekiel, Applied Physics Letters, 30, 478 (1977)
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Optical Sagnac Effect in a Passive Ring Cavity
VCO1
AOM1 AO
M2 VCO2
diff.
Las
er
V1
beatdet
f
diff
.
V2
VCO1VCO1
AOM1 AO
M2 VCO2VCO2
diff.diff.
Las
erL
aser
V1 V1V1
beatdet
f
diff
.di
ff.
V2 V2V2
P
N
n
C
o
oo
2No Rotation:
P
A
nCnC
RvVV
P
NV
oo
o
oo
ooRE
ooE
2
;;2
2
With Rotation:
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. T.Enhancement of Sagnac Effect in a PRC using
Fast-Light
VCO1
AOM1 AO
M2 VCO2
diff.
Las
er
V1
beatdet
f
diff
.
V2
VCO1VCO1
AOM1 AO
M2 VCO2VCO2
diff.diff.
Las
erL
aser
V1 V1V1
beatdet
f
diff
.di
ff.
V2 V2V2
In general:P
NVEo
2
2
(here is considered a parameter whose amplitude is to be determined)
)(1
)( nC
v
n
CvVV
o
oRE
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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L. A. P
. T.Enhancement of Sagnac Effect in a PRC using
Fast Light
VCO1
AOM1 AO
M2 VCO2
diff.
Las
er
V1
beatdet
f
diff
.
V2
VCO1VCO1
AOM1 AO
M2 VCO2VCO2
diff.diff.
Las
erL
aser
V1 V1V1
beatdet
f
diff
.d
iff.
V2 V2V2
)(1
)( nC
v
n
CvVV
o
oRE
oooo
oE nnnn
nC
v
n
CV /]/[~;
2~1
P
NVEo
2
2
Self-Consistent Solution:g
oo
o
o
n
n
n
~1
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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L. A. P
. T.Enhancement of Sagnac Effect in a PRC using
Fast Light
VCO1
AOM1 AO
M2 VCO2
diff.
Las
er
V1
beatdet
f
diff
. V2
VCO1VCO1
AOM1 AO
M2 VCO2VCO2
diff.diff.
Las
erL
aser
V1 V1V1
beatdet
f
diff
.d
iff.
V2 V2V2
Constraint: 1~ nnn o
]1[//;;/1; 1 ooooo nnRvvnC
Critically Anomalous Dispersion (CAD):
oonn //
og
oo
o
o
n
n
n~1
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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. T.
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L. A. P
. T.Enhancement of Sagnac Effect in a PRC using
Fast Light
VCO1
AOM1 AO
M2 VCO2
diff.
Las
er
V1
beatdet
f
diff
.
V2
VCO1VCO1
AOM1 AO
M2 VCO2VCO2
diff.diff.
Las
erL
aser
V1 V1V1
beatdet
f
diff
.d
iff.
V2 V2V2
Numerical Example for the Constraint:
]1[//;;/1; 1 ooooo nnRvvnC
Consider a ring cavity with R=1 meter, a rotation rate of ~73 micro-radian per second (earth rate), and no=1.5:
The enhancement factor can be as high as 1012 while still satisfying the constraints
og
oo
o
o
n
n
n~1
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. T.Enhancement of General Purpose Interferometric
Sensing Using Fast Light
VCO1
diff.
Laser
V1
beatdet
f
V2
diff
.
AOM1
AOM2
VCO2
TestChamber
ReferenceChamber
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L. A. P
. T.Enhancement of General Purpose Interferometric
Sensing Using Using Fast Light
VCO1
diff.
Las
er
V1
beatdet
f
V2
diff
.
AOM1
AOM2
VCO2
TestChamber
ReferenceChamber
VCO1VCO1
diff.
Las
erL
aser
V1 V1V1
beatdet
fbeatdet
f
V2 V2V2
diff
.d
iff.
diff
.d
iff.
AOM1
AOM2
VCO2VCO2
TestChamber
ReferenceChamber
}1];1[//{;)(: 1
g
oooo n
nnn
nnnregionref
},/{;)(:
oftindependenSnS
nS
nnnregiontest o
Model:
With no dispersion: oo
o Sn
With anomalous dispersion:
};1{; conditionCADthen
n
go
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Slow-Light Enhanced Rotation Sensing: Experiment
DetDetD
yeL
aser
AOM
PBS
Pu
mp
Pro
be
SpinningSodium Vapor Cell
HW
P
S-p
olarized
PBS
Pump
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Slow-Light Enhanced Rotation Sensing: Experiment
F=2
F=1
5S3/2
Probe
1.772 GHz
Pump
5P1/2
-5 -4 -3 -2 -1 0 1 2 3 4 50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Frequency (MHz)
Mag
nit
ude
(a.u
.)
photodiode outputlock-in-detection
-3 -2 -1 0 1 2 30
1
2
3
4
5
6
Frequency (GHz)
Mag
nitu
de (
a.u.
)
Saturated pump absorptionProbe absorption in EIT cell
~ 1.772 GHz
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Anomalous Dispersion Enhanced Rotation Sensing: Experiment
AOM1 AO
M2
diff.
beatdet
f
diff
.
Rotation Stage
Clamp
PBS
PB
S
BF-Pump
BF-Pump
hwp
BFPG
Ti-
Sap
hL
aser
FlexibleFiber
Rb vapor Cell
(BPFG: Bi-frequencypump generator)
(PBS: polarizingbeam splitter)
AOM1
AOM2
AOM1 AO
M2
diff.diff.
beatdet
f
diff
.d
iff.
Rotation Stage
Clamp
PBS
PB
S
BF-Pump
BF-Pump
hwp
BFPG
Ti-
Sap
hL
aser
FlexibleFiber
Ti-
Sap
hL
aser
Ti-
Sap
hL
aser
FlexibleFiber
Rb vapor Cell
(BPFG: Bi-frequencypump generator)
(PBS: polarizingbeam splitter)
AOM1
AOM2
Bi-frequencypump
probe
|1>
|2>
|3>
Bi-frequencypump
probe
|1>
|2>
|3>
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Anomalous Dispersion Enhanced Rotation Sensing: Experiment
Raman cell
Absorption cell
Off-resonantRaman pump
Probe (or seed)
Opticalpump
Single photondetector
Fabry-Perotfilter
PBS
PBS
WP
PBS
Experimental Set-Up: vapor-cells
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Anomalous Dispersion Enhanced Rotation Sensing: Experiment
Experimental Set-Up: Trapped Atoms
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Artificial Black-Hole Using Slow Light
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Analogy Between Charged Particles in a Magnetic Field
AndPhotons in a Rotating Medium (Gravimagentism)
A (vector potential)
B
BB
B
(magnetic field)
chargedparticle
vForce
(effective magnetic field)
B
Aeff (effective vector potential)
Beff
photons
vForce
RotatingMedium (Vortex)
Beff
Beff
Beff
Beff
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Artificial Blackhole with Slow-Lightin a Rotating Medium
(effective magnetic field)
Aeff (effective vector potential)
Beff
Slow-photons(1 cm/sec)
vForce
RotatingMedium (Vortex)
Beff
Beff
Beff
Beff
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Artificial Blackhole with Slow-Lightin a Rotating Medium
U. Leonhardt and P. Piwnicki Physical Review A, December 1999 Volume 60, Number 6
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Artificial Blackhole with Slow-Lightin a Rotating Medium
OpticalSchwarzschildRadius
U. Leonhardt and P. Piwnicki Physical Review A, December 1999 Volume 60, Number 6
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GR-Relevant Terrestrial Experiments
SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light Interferometry Using Atomic Interferometry
ARTIFICAL BLACKHOLE USING SLOW LIGHT
GPS AND QUANTUM CLOCK-SYNCHRONIZATION
EQUIVALENCE PRINCIPLE AND SLOW-LIGHT
LIGO PROJECT FOR DETECTING GRAV. WAVES
FAST-LIGHT AND ATOMIC INTER. FOR DET. GRAV. WAVES
...