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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 InterferometryUsing 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
L. A. P. T.
L. A. P. T.
L. A. P. T.
L. A. P. T.
GR-Relevant Terrestrial Experiments
SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light InterferometryUsing 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
L. A. P. T.
L. A. P. T.
L. A. P. T.
L. A. P. T.
GR-Relevant Terrestrial Experiments
SAGNAC EFFECT FOR SENSING OF LENSE-THIRRING ROTATION Using Fast-Light InterferometryUsing 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 themotion 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 convenientthan water bucketsare torque-free gyroscopes...
Dragging = precessionof 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 23 3
SRG Mc R R
ω= ≡
Ω
M = mass of the sphereR = 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
23
G M Rc R r
ω = − Ω
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:
( )xω ω≡ur ur r
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• Dragging of the orbital plane:
Newtonian gravity General relativity
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• Magnitude of the effect:
dd = 0.13 cm ( = 0.886 cm)
Circular orbit of radius r :
2
2
45
SE
Sat
R Rdr
π Ω=
Ω
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 theLense-Thirring effect with two Earch satellitesScience, 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 effectNature, 431, 958 (21 October 2004)Confirmation of the orbital effect to 6% accuracy, using satellite data
• Gravity Probe B, 2005Expected 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
1ε = 2ε =
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
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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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:
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Terrestrial Tests Using Precision Gyroscopes
VCO1
AOM1 AOM
2 VCO2
diff.
Laser
?V1
beatdet
? f
diff.
? V2
?VCO1VCO1
AOM1 AOM
2 VCO2VCO2
diff.diff.
LaserLaser
?V1 ?V1V1
beatdet
? f
diff.
diff.
? V2? V2V2
?
Ring Laser Gyroscope Atom-Interferometric Gyroscope
Center for Photonic Communication and Computing Laboratory for Atomic and Photonic Technology
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Quick Look at Atom-Interferometry
ATOM INTERFEROMETRY: BASIC IDEA
ATOM AS A dE Broglie WAVE
vv
λ = (h / m v)
Rb at 300o C:
λ = 0.0153 nm
2θλ Λ = λ / 2Sinθ
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+hk >
|E>
|A, p>
TRAVELLING WAVES
LASER-CONTROLLED SPIN EXCITATION
NB
Time
|E>
EASY TO LOCALIZEMUCH STRONGER
OFF-RESONANT
DECOHERENCE FREESTRONG RECOIL
|A, p>
|B, p+2hk >
LASER-CONTROLLED SPIN EXCITATION RECOIL
|E>
|A>
|B>
|E>
|A>
|B>
hk
|E>
|A>
|B>
hk
|E>
|A>
|B>2hk
PUSHING TO THE RIGHT |E>
|A>
|B, 2hk>
PUSHING TO THE LEFT
|E>
|A, p>
|B, -2hk>
SPLITTING ATOMIC WAVES USING LCSE
|A>
|B>
|A>
|B, 2hk>
|B,- 2hk >
|A, 4hk>
INTERFEROMETER IN ONE DIMENSION
±100 hk 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
Ω
π/2
ω1 ω1 ω1
ω2 ω2ω2
ω1
ω2
φ
φ
BCI
CI
Ω
|a>
|b>
x
z
|a>
|b>
L L
d
vx
π/2 π
Ω
π/2
ω1ω1 ω1ω1 ω1ω1
ω2ω2 ω2ω2ω2ω2
ω1ω1
ω2ω2
φ
φ
BCI
CI
Ω
|a>
|b>
x
z
3035 MHz
121 MHz
F=3
F=2
DOP
R1
R2
F’=4F’=3
1517.5 MHz
OP GALVOSCANNER
D
PMT
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
PMT
R1
R2
OP GALVOSCANNER
D
PMT
R1
R2AA
BB
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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
DetΩ
CW
CCW
Det
Wave-Source
Ω
CW
CCW
DetΩ
CW
CCW
Det
Wave-SourceWave-Source
Ω
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 π ±±± = RVLT /
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BS1 BS2
R
CW(+)
CCW(-)
2/1 oP
PR CvV
vVV±
±=± ±± ±= vTRL π ±±± = RVLT /
General View of the Sagnac Effect
)1/(/2)1(
2 222 <<≡∆≡Ω≈
−Ω
=−≡∆ −+ooo
o
CvfortCAC
ATTt ββ
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 ±TA : 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 <<≡∆≡Ω≈
−Ω
=−≡∆ −+ooo
o
CvfortCAC
ATTt ββ
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 ±TA : 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 acousticwaves 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 <<≡∆≡Ω≈
−Ω
=−≡∆ −+ooo
o
CvfortCAC
ATTt ββ
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 ±TA : Area normal to
)(/4 2 shiftphaseSagnacgenericCfAt oΩ=∆=∆ πωφ
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General View of the Sagnac Effect
A
B
A
B
A
B
A
B
A
B
Ω
A
B
A
B
A
BA
B
Ω
1
1
4
3
2
1
2
3
4
A
B
A
B
A
B
A
B
A
B
Ω
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
ΩΩ
A
B
A
B
A
BA
B
ΩA
B
A
B
A
B
A
B
A
B
A
BA
B
A
B
ΩΩ
1
1
4
3
2
1
2
3
4
Result is independent of Axis of Rotation
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General View of the Sagnac Effect
)(/4 2 shiftphaseSagnacgenericCfAt oΩ=∆=∆ πωφ
)/(4 CA ooo φλπφ ∆≡Ω=∆
OPTICAL SAGNAC PHASE SHIFT:
MATTER-WAVE SAGNAC PHASE SHIFT:
f=Co/o
( ) )1/1/1(;/ 22oGoGo CVforCVhmCf <<≈−== γγ
Relevant Frequency is the Compton Frequency:
/4 hmAΩ=∆ πφ
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 π ±±± = 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 ±TA : Area normal to
oPR CVV ==±
2/2 oCATTt Ω=−≡∆ −+ )/(4 ooCA λπφ Ω=∆
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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 π ±±± = 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 ±TA : Area normal to
COMPR VVV ==±
2/2 COMVATTt Ω=−≡∆ −+
However, fundamentally wrong! VCOM does not influence the result
h2/2COMmV=ω hmA /2 Ω=∆ πφ
