Transcript Slide 1

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Manifestation of General Relativity in
Practical Experiments
Selim M. Shahriar
Laboratory for Atomic and Photonic Technology
Northwestern University
Evanston, IL
[http://lapt.ece.northwestern.edu]
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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
...
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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
...
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Quick Review of Lense-Thirring Effect
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• Rotation with respect to absolute space gives rise to
centrifugal forces, as illustrated by the “bucket experiment“:
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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“).
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The rotation of the earth should “drag“ (local) inertial frames.
very small
frequency
very
small
effect
w will later be called Thirring-Lense frequency.
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More convenient
than water buckets
are torque-free
gyroscopes...
Dragging = precession
of gyroscope axes
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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:
M=
R =



mass of the sphere
radius of the sphere
4GM
2
3 c R

2 RS
3 R
(valid in the weak field
approximation =
linearized theory)
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• Dragging effects outside the shell:
T.
In the equatorial plane:


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 
2GM R
 
2
3 c R  r 
3
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• Dragging effects near a massive rotating sphere:
   (x)
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• Dragging of the orbital plane:
Newtonian gravity
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General relativity
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• Magnitude of the effect:
Circular orbit of radius r :
d 
4
 E RS R
5  Sat
r
2
2
Earth satellite with close orbits:
d = 0.13 cm ( R S = 0.886 cm)
d
Angular frequency of the orbital plane:
0.26 arc-seconds/year
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• Useful analogy that applies for stationary (weak) gravitational
fields:
“Newtonian“ part of the gravitational field
“electric“ behaviour:
1/r² attractive force
Rotating
body:
Both
behaviours
apply!
“Machian“ part of the gravitational field
(sometimes called “gravimagnetism“):
“magnetic“ behaviour
matter flow
Lense-Thirring frequency
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Rotating charge distribution <-> rotating matter
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Sattelite-based Tests:
•
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. PerezMercader: Test of general relativity and measurement of the LenseThirring 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
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LAGEOS Project:
•
•
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2 satellites LAGEOS (NASA, launched 1976) and
LAGEOS 2 (NASA + ASI, launched 1992)
Original goal: precise determination
of the Earth‘s gravitational field
Major semi-axes:
a1 
•
12270 km,
a2 
LAGEOS
LAGEOS
22
12210 km
Excentricities:
0.004 km,  2  0.014
Diameter: 60 cm, Mass: 406 kg
1 
•
•
•
Position measurement by reflection
of laser pulses
(accurate up to some mm!)
Main difficulty: deviations from
spherical symmetry of the Earth‘s
gravity field
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LAGEOS
LAGEOS
Laboratory for Atomic and Photonic Technology
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•
•
Improved model of the Earth‘s
gravitational field:
EIGEN-GRACE02S
Evaluation of 11 years position data
Improved choice of observables
(combination of the nodes of both
satellites)
Observed value =
99%  5% of the predicted value
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LAGEOS 2
LAGEOS
Laboratory for Atomic and Photonic Technology
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Gravity Probe B:
•
•
•
•
•
•
Satellite based experiment, NASA und Stanford University
Goal: direct measurement of the dragging
(precession) of gyroscopes‘ axes
by the Lense-Thirring effect
(Thirring-Schiff-effect)
4 gyroscopes with quartz rotors: the
roundest 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%
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Terrestrial Tests Using Precision Gyroscopes
d iff.
?
Laser
d iff.
V1
?
VCO1
AOM2
AOM1
?f
beat
det
VCO2
?
Ring Laser Gyroscope
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V2
Atom-Interferometric Gyroscope
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Quick Look at Atom-Interferometry
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ATOM INTERFEROMETRY: BASIC IDEA
ATOM AS A dE Broglie WAVE
v
l = (h / m v)
v
Rb at 300o C:
l = 0.0153 nm
ATOMIC INTERFERENCE FRINGES
L  l / 2Sinq
l
2q
METHOD FOR ACHIEVING LARGE ANGLE:
LASER-CONTROLLED SPIN EXCITATION
OFF-RESONANT
|E>
1.2
NB
1
|B>
0.8
0.6
0.4
|A>
0.2
0
Time
RF EXCITATION OF ATOMS
TRAVELLING WAVES
|E>
1.2
NB
1
|B, p+k >
0.8
0.6
0.4
|A, p>
0.2
0
Time
LASER-CONTROLLED SPIN EXCITATION
OFF-RESONANT
|E>
1.2
NB
1
|B, p+2k >
0.8
0.6
0.4
|A, p>
0.2
0
Time
MUCH STRONGER
EASY TO LOCALIZE
DECOHERENCE FREE
STRONG RECOIL
LASER-CONTROLLED SPIN EXCITATION
|E>
RECOIL
|E>
2k
|B>
|B>
|A>
|A>
k
k
|E>
|E>
|B>
|B>
|A>
|A>
PUSHING TO THE RIGHT
|E>
|B, 2k>
|A>
PUSHING TO THE LEFT
|E>
|B, -2k>
|A, p>
SPLITTING ATOMIC WAVES USING LCSE
|B>
|A>
|B, 2k>
|A>
|B,- 2k >
|A, 4k>
INTERFEROMETER IN ONE DIMENSION
SYSTEM:
87RB
100 k SPLITTING POSSIBLE
FRINGE SPACING: ~ 4 NM
Atomic Sagnac Interferometer
2
L
A
R2
z
L
T.
PM T
2
2
BCI
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A.
x
|a >
π /2
d
|b >
π
|b >

R1
vx

1
|a >
1
D
OP
π/2
1
G ALVO
SCANNER
F ’= 4
121 M H z
B
F ’= 3
1517.5 M H z
CI
2
D
OP

R2
R1
3035 M H z

1
Center for Photonic Communication and Computing
F=3
F=2
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Quick Look at Sagnac Effect
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General View of the Sagnac Effect
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Det
W
CW
Wave
-Source
CCW
WAVE SOURCES:
Optical Waves
Matter Waves
Acoustic Waves
???
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General View of the Sagnac Effect
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CW(+)

D et
CW
W a ve
-S o u rce
BS2
BS1
R
CCW
CCW(-)
DEFINE:
VP : Phase Velocity in Absence of Rotation

V R : Relativistic Phase Velocities Seen in an Inertial Frame

T : time for the Phase Fronts to travel from BS1 t BS2
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General View of the Sagnac Effect
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CW(+)
VP : Phase Velocity in Absence of Rotation
BS2
BS1
R

V R : Relativistic Phase Velocities Seen in an Inertial Frame
T

: time for the Phase Fronts to travel from BS1 t BS2
CCW(-)
V

R

VP  v
1  VPv / C

2
o
Center for Photonic Communication and Computing
L   R  vT

T



 L / VR
Laboratory for Atomic and Photonic Technology
General View of the Sagnac Effect
CW(+)
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VP : Phase Velocity in Absence of Rotation

V R : Relativistic Phase Velocities Seen in an Inertial Frame
BS2
BS1
T
R

: time for the Phase Fronts to travel from BS1 t BS2
A : Area normal to
CCW(-)
VP  v

VR 
1  VPv / C
t  T

T


L
2
o
2 A
Center for Photonic Communication and Computing
  R  vT
 2 A  / C o   to
2
C (1   )
2
o

2

( for
T



 L / VR
  v / C o  1)
Laboratory for Atomic and Photonic Technology
General View of the Sagnac Effect
CW(+)
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VP : Phase Velocity in Absence of Rotation

V R : Relativistic Phase Velocities Seen in an Inertial Frame
BS2
BS1
T
R

: time for the Phase Fronts to travel from BS1 t BS2
A : Area normal to
CCW(-)
t  T

T


2 A
 2 A  / C o   to
2
C (1   )
2
o
2
( for
  v / C o  1)
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
General View of the Sagnac Effect
CW(+)
L.
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A.
T.
VP : Phase Velocity in Absence of Rotation

V R : Relativistic Phase Velocities Seen in an Inertial Frame
BS2
BS1
T
R

: time for the Phase Fronts to travel from BS1 t BS2
A : Area normal to
CCW(-)
t  T

T


2 A
 2 A  / C o   to
2
C (1   )
2
o
2
     t  4 fA  / C o
2
Center for Photonic Communication and Computing
  v / C o  1)
( for
( generic Sagnac
phase shift )
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General View of the Sagnac Effect
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Result is independent of Axis of Rotation
A
1
A
B
1
A

2
B
B
B
2
A

A
B
3
A
B
B
4
A
4
A
B
1
B
3
A
Center for Photonic Communication and Computing
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General View of the Sagnac Effect
     t  4 fA  / C o
2
( generic Sagnac
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phase shift )
OPTICAL SAGNAC PHASE SHIFT:
f=Co/
   4 A  /( l o C o )    o
o
( optical
MATTER-WAVE SAGNAC PHASE SHIFT:
Relevant Frequency is the Compton Frequency:
(  1 / 1  V G / C o   1
f   mC o / h ;
2
2
   4 mA  / h
Center for Photonic Communication and Computing
for V G  C o )
( matter
Laboratory for Atomic and Photonic Technology
Wrong View of the Sagnac Effect
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Laboratory for Atomic and Photonic Technology
Wrong View of the Sagnac Effect
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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.
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“Wrong” View of the Optical Sagnac Effect
CW(+)
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VP : Phase Velocity in Absence of Rotation

V R : Phase Velocities Seen in an Inertial Frame
BS2
BS1
R
T

: time for the Phase Fronts to travel from BS1 t BS2
A : Area normal to
CCW(-)

VR  VP  Co
t  T

T

L

 2 A / C o
2
  R  vT

T



 L / VR
   4 A  /( l o C o )
This happens to be correct only when the index is unity
This line of reasoning gives the wrong result when n 1
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“Wrong” View of the Atomic Sagnac Effect
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Laboratory for Atomic and Photonic Technology
“Wrong” View of the Atomic Sagnac Effect
CW(+)
L.
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T.
VP : Phase Velocity in Absence of Rotation

V R : Phase Velocities Seen in an Inertial Frame
BS2
BS1
R
T

: time for the Phase Fronts to travel from BS1 t BS2
A : Area normal to
CCW(-)
V
t  T


R
T
 V P  V COM

L
 2 A  / V COM
2

  R  vT
  mV COM / 2 
2

T



 L / VR
   2 mA  / h
Off by a factor of 2, but pretty close!
However, fundamentally wrong! VCOM does not influence the result
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Quick Look at Slow and Fast Light
Center for Photonic Communication and Computing
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Concept of Phase Velocity of a Monochromatic Wave
z 1= (c/n) t1
z
z
2
Phase front
Monochromatic plane wave
Ez, t   E o e
i k z   t 
 c.c.
t
Phase
  k z  t
Dispersion relation
k
n
c
Constant phase front
t
1
t
t
2
moves a distance
z in time
k z    t
Phase velocity
vp 
z
t


k

c
n
vp > c does not contradict special theory of relativity
t
Group Velocity: Non-monochromatic Signal
Superposition of two single frequency plane waves
E  E o cos k1z  1 t   cos k 2 z  2 t 
1
 2E o cosk z   t cosk z   t 
2
Rapidly oscillating
term
envelope
vp
Vg
Group velocity
vg 

vp 
k
  1  2  2 , k  k1  k 2  2
For non-dispersive medium v g 
Wave group
Phase velocity
c
n

k

c
n
  1  2  2 ,
k  k1  k 2 
2 , ki 
n i
c
, i  1, 2
Pulse in a Dispersive Medium
Pulse
In a dispersive medium, n( ), for no pulse distortion,
frequency components add in phase at pulse peak
   k z  t , k  
d
d
0

d n z
d c
Group Velocity

nz
c
n  
c
 t  0, z  v g t
c
vg 
n
Group Index
ng  n  
Phase Index
dn

d
dk
d
dn
t
d
Dispersion
dn
Slow & fast light effects make use of large dn/d
d
in the vicinity of material resonance
dn
d
 0 normal dispersion

 0 anomalous dispersion


Slow Light

Fast Light
Dispersion and Slow Light using EIT in a -System
Susceptibility to first order in probe field amplitude
1
|2>
1
|2>
g s,
gp,
probe field strong field
|3>
 2  0
--
g p  gs
2
2

31
2
 i   
i   i    g
31
2
21
31
2
s
|->
|+>
|1>
-type atomic system
1.0005
Dressed State Basis
normal
dispersion
1
0.9995
-3-1.5

2
i      
0
g
2
s
31
, ng 
ng can be as large as O(107)
vg (< c) O(102) m/s
20 N  21
g
2
s
2
-1
-0.5
0
0.5
1
1.5
7
x 10
2

1.5
1
g2s /
0.5
-4-1.5
mag. of group index

i 4 N  21
1=0
absorp. coeff.
x 10
For large amplitude of strong field and
4
is decoherence rate for ground states
Dark State
index
2
=

 i N  21
x 10
-1
-0.5
0
0.5
1
1.5
7
x 10
positive
group index
3
2
1
0
-1
-1.5
-1
-0.5
0
0.5
detuning (1)
1
1.5
2
7
x 10
Slow Light in Pr:YSO
5/2
3/2
1/2
4.6
4.8
Coupling
=605.977 nm
(Site 1)
Repump
Probe
1/2
3/2
10.2
17.3
5/2
Energy Diagram
Experimental Setup
-- 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
Coupling beam switched on at –200
0.2 msec
s
1 msec
10 msec
P
70
Input probe
beam
s
C
No coupling
beam (x0.25)
Pulse sequence
5/2
3/2
1/2
4.6
4.8
Coupling
Probe transmission (%)
R
Incomplete
Probe absorption
Repump
Probe
1/2
3/2
Slowed
light
Group delay
Measured group delay ~
10.2
17.3
100
s = 33 m/sec
5/2
Energy Diagram
Turukhin et. al. Phys. Rev. Lett. 88 (2002) 023601
Fast Light Using Anomalous Dispersion
L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000).
Fast Light Using Anomalous Dispersion
Inside pulse delayed by:
T=L/Vg-L/C=(ng-1)L/C
Inside pulse advanced by:
- T=(1-ng)L/C
L.J. Wang, A. Kuzmich, and A. Dogariu, Nature, 406, 277 (2000).
Role of Fresnel Drag in Sagnac Effect
CW(+)
L.
P.
A.
T.
VP : Phase Velocity in Absence of Rotation

V R : Relativistic Phase Velocities Seen in an Inertial Frame
BS2
BS1
R
T

: time for the Phase Fronts to travel from BS1 t BS2
A : Area normal to
CCW(-)
VP  v

VR 
1  VPv / C
same
V

R

2
o
Co
n
Center for Photonic Communication and Computing
L

  R  vT
 v F ;

 F  (1 
T
1
n
2
)



 L / VR
Fresnel
Drag
Coefficient
Laboratory for Atomic and Photonic Technology
Role of Fresnel Drag in Sagnac Effect
VP  v

VR 
L
1  VPv / Co
same
2
V

R

Co

  R  vT
 v F ;
n

 F  (1 
L.
T
1
n
2
)


P.
A.
T.

 L / VR
Fresnel
Drag
Coefficient
 t  n (1   F )   t o   t o
2
   n (1   F )    o    o
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
Doppler Shift and Laub Drag in Sagnac Effect
L.
P.
A.
T.
Det
W
VM
CW
VM
Frame & source stationary; medium rotating
VM
B.
VM
Laser
Flexible
Fiber
Clamp
stationary
CCW
A.
Frame & source rotating; medium stationary
C.
No Doppler Effect if the Laser is stationery, but the stage rotates,
with the no relative motion between the mirrors and the medium
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Doppler Shift and Laub Drag in Sagnac Effect
L.
P.
A.
T.
Laser and MZI frame are stationery, and the medium moves with a relative Velocity of VM.
Det
W
VM
VM
CW
Frame & source stationary; medium rotating
VM
B.
VM
Laser
Flexible
Fiber
stationary
CCW
Clamp
A.
Frame & source rotating; medium stationary
C.
CW(+) and CCW(-) beams are Doppler shifted by equal and opposite amounts, given by:


  VM / C o
The relativistic velocities are then given by:
V

R

Co
no
(1 

no

n

)  v F 
Center for Photonic Communication and Computing
Co
no
 VM
 n
n o 
2
 v F 
Co
no
 VM
n
g
no 
2
no
 v F ;
Laboratory for Atomic and Photonic Technology
Doppler Shift and Laub Drag in Sagnac Effect
L.
P.
A.
T.
Laser and MZI frame are stationery, and the medium remains stationery (or vice versa)
Det
W
VM
CW
VM
Frame & source stationary; medium rotating
VM
B.
VM
Laser
Flexible
Fiber
Clamp
stationary
CCW
A.
Frame & source rotating; medium stationary
C.
Here VM=(-v)=- R, so that the relativistic velocities are then given by:

VR 
Co
no
 v L ;
L
n g  n o  

1
 1  2 

2
n
n
o
o


The Laub
Drag 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
Doppler Shift and Laub Drag in Sagnac Effect
L.
P.
A.
T.
Laser and MZI frame are stationery, and the medium remains stationery (or vice versa)

La
D et
r
t
se
De

VM
VM
CW
B.
F ra m e & so u rce sta tio n a ry; m e d iu m ro ta tin g
VM


VM
Laser
La
CCW
V
t
r
s ta tio n a ry
C la m p
A.

R
se
De
F le xib le
F ib e r

Co
no
 v L ;
 t  n (1   L )   t o ;
2
F ra m e & so u rce ro ta tin g ; m e d iu m sta tio n a ry
L
n g  n o  

1
 1  2 

2
n
n
o
o


   n (1   L )    o
2
(For ng>>no)
 t  n g  to ;
Center for Photonic Communication and Computing
C.
Enhancement
Factor
  ng o
Laboratory for Atomic and Photonic Technology
Optical Sagnac Effect in a Passive Ring Cavity
L.
P.
A.
T.
diff.
f
beat
det
Laser
diff.
V1
VCO1
AOM2
AOM1
VCO2
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
Optical Sagnac Effect in a Passive Ring Cavity
L.
P.
A.
T.
d iff.
Laser
d iff.

V1

VCO1
AOM2
AOM1
VCO2

V2
C o 2 N
o 
No Rotation:
f
beat
det
no
P
With Rotation:



 VE 
2 N
P
 o 
o
2
Center for Photonic Communication and Computing
;


V E  V R  v;
o 
2 R o
C o no

o
C o no

A
P
Laboratory for Atomic and Photonic Technology
Enhancement of Sagnac Effect in a PRC using
Fast-Light
L.
P.
A.
T.
d iff.
Laser
d iff.

V1

VCO1
AOM2
AOM1
VCO2


  o 
In general:
V
(here

E
V

R
f
beat
det

2

 VE 
V2
2 N
P


v
v 
 1 

 
n ( ) 
C o n ( ) 
Co
is considered a parameter whose amplitude is to be determined)
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Enhancement of Sagnac Effect in a PRC using
Fast Light
L.
P.
A.
T.
d iff.

V1

Laser
d iff.

VE  VR


v
v 
 1 

 
n ( ) 
C o n ( ) 
Co

VCO1
AOM2
AOM1
VCO2

V

E

Co 
v
 
~

 1 
n
;
no 
C o no
2 
  o 

2

 VE 
f
beat
det
V2
n~  [  n /   ] / n o
2 N
P
Self-Consistent Solution:
Center for Photonic Communication and Computing
 
o
no
 o 
~
1  on
ng
Laboratory for Atomic and Photonic Technology
Enhancement of Sagnac Effect in a PRC using
Fast Light
L.
P.
A.
T.
d iff.

Laser

VCO1
AOM2
AOM1
 
d iff.
V1
f
beat
det
 o
no




  o  
o
~
1  on
ng
VCO2

Constraint:
   o  ;
V2
 n  n o n~    1
1    C o n o / v ;
v  R;
 n /      n o /  o [1  
1
]
Critically Anomalous Dispersion (CAD):
 n /     n o /  o 
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Enhancement of Sagnac Effect in a PRC using
Fast Light
L.
P.
A.
T.
d iff.

Laser

VCO1
AOM2
AOM1
 
d iff.
V1
f
beat
det
 o
no




  o  
o
~
1  on
ng
VCO2

V2
Numerical Example for the Constraint:
   o  ;
1    C o n o / v ;
v  R;
 n /      n o /  o [1  
1
]
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
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Enhancement of General Purpose Interferometric
Sensing Using Fast Light
L.
P.
A.
T.
diff.
f
beat
det
V1
Laser
Reference
Chamber
diff.
VCO1
Test
Chamber
AOM1
AOM2
VCO2
Center for Photonic Communication and Computing
V2
Laboratory for Atomic and Photonic Technology
Enhancement of General Purpose Interferometric
Sensing Using Using Fast Light
L.
P.
A.
T.
d iff.
f
beat
det

V1
Laser
R e fe re n c e
C ham ber
d iff.
VCO1
T est
C ham ber
AOM1
AOM2

VCO2
Model:
ref region : n ( )  n o    
n
;
{  n /      n o /  o [1  

n
n
test region : n ( )  n o    
 S 
;

S
With no dispersion:
   o 

no
1
];
 
no
V2
 1}
ng
{  n /  S   , independen t of  }
 S   o
With anomalous dispersion:
   o   ;
Center for Photonic Communication and Computing
{ 
n
 1;
the CAD
condition }
ng
Laboratory for Atomic and Photonic Technology
Slow-Light Enhanced Rotation Sensing: Experiment
L.
P.
A.
T.
Dye
Laser
Probe
PBS
HWP
S-polarized
Pump
PBS
Pump
Spinning
Sodium Vapor
Cell
AOM
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Slow-Light Enhanced Rotation Sensing: Experiment
L.
P.
A.
T.
5P1/2
Saturated pump absorption
Probe absorption in EIT cell
6
Magnitude (a.u.)
5
Probe
4
Pump
3
2
~ 1.772 GHz
0
F=2
5S3/2
1
-3
-2
-1
0
Frequency (GHz)
1.772 GHz
1
2
3
F=1
ph o t odio de o u t pu t
lo ck -in - de t e ctio n
0.4
0. 3 5
M a g nitude (a .u.)
0.3
0. 2 5
0.2
0. 1 5
0.1
0. 0 5
0
-5
-4
-3
-2
-1
0
1
2
3
4
5
F r e que nc y (M H z)
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Anomalous Dispersion Enhanced Rotation Sensing: Experiment
L.
P.
A.
T.
R o ta tio n
S ta g e
T i-S a p h
Laser
F le x ib le
F ib e r
d iff.
AOM 1
beat
det
f

C la m p
B F -P u m p
R b va p o r
C e ll
hw p
d iff.
BFPG
PBS
PBS
|2 >
AOM 2
AOM 1
AOM 2
B F -P u m p
(B P F G : B i-fre q u e n c y
p u m p g e n e ra to r)
(P B S : p o la riz in g
b e a m s p litte r)
p ro b e
B i-fre q u e n c y
pum p
|3 >
|1 >
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Anomalous Dispersion Enhanced Rotation Sensing: Experiment
L.
P.
A.
T.
Experimental Set-Up: vapor-cells
Off-resonant
Raman pump
Optical
pump
Raman
cell
PBS
PBS
Probe
(or seed)
Fabry-Perot
filter
WP
Absorption
cell
PBS
Single photon
detector
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Anomalous Dispersion Enhanced Rotation Sensing: Experiment
L.
P.
A.
T.
Experimental Set-Up: Trapped Atoms
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
L.
P.
A.
T.
Artificial Black-Hole Using Slow Light
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Analogy Between
Charged Particles in a Magnetic Field
And
Photons in a Rotating Medium (Gravimagentism)
Beff
B (magnetic field)
Aeff
A (vector potential)
T.
(effective magnetic field)
(effective vector potential)
Rotating
Medium
(Vortex)
B
B
B
Beff
Beff
Beff
Force
v
Force
B
L.
P.
A.
charged
particle
Center for Photonic Communication and Computing
Beff
v
photons
Laboratory for Atomic and Photonic Technology
Artificial Blackhole with Slow-Light
in a Rotating Medium
Beff
Aeff
L.
P.
A.
T.
(effective magnetic field)
(effective vector potential)
Rotating
Medium
(Vortex)
Beff
Beff
Beff
Force
Beff
Center for Photonic Communication and Computing
v
Slow-photons
(1 cm/sec)
Laboratory for Atomic and Photonic Technology
Artificial Blackhole with Slow-Light
in a Rotating Medium
L.
P.
A.
T.
U. Leonhardt and P. Piwnicki Physical Review A, December 1999 Volume 60, Number 6
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
Artificial Blackhole with Slow-Light
in a Rotating Medium
L.
P.
A.
T.
Optical
Schwarzschild
Radius
U. Leonhardt and P. Piwnicki Physical Review A, December 1999 Volume 60, Number 6
Center for Photonic Communication and Computing
Laboratory for Atomic and Photonic Technology
L.
P.
A.
T.
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