Relativistic effects in atom gravimetershust_edu_cn_01.pdf · Post-Newton gravity theory; ... Model...
Transcript of Relativistic effects in atom gravimetershust_edu_cn_01.pdf · Post-Newton gravity theory; ... Model...
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Relativistic effects in atom gravimeters
Yu-Jie Tan
Center for Gravitational Experiment (CGE),
Huazhong University of Science and Technology (HUST),Wuhan, China
2017.09.24 Corfu2017
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Outline
Research motivation
Conclusion
An analytical study method
AG’s Working principle
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1. Research motivation
Applications of gravimeters
Gravimeter: measure the gravitational acceleration g
Geophysics Resources exploration
Gravity navigation Other scientific researches (such as Watt balance)
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1. Research motivation
Classification of gravimeters
CG-5
GWR
FG-5
AG
Relative gravimeters Absolute gravimeters
Accuracy—μGal
1μGal=1×10-8 m/s2
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1. Research motivation
Necessity for establishing a relativistic model of AG
High-precision gravimeter
High-precision tide model;
High-precision geoid;
Post-Newton gravity theory;
……Measured gravity acceleration:
2
2 ......
v vB C D
c c c
Model
measured 0 g g temperature, pressure, Earth’s rotation, gravity gradient….
Newtonian effects
General Relativity
Relativistic effect
Establish a more complete relativistic model for AG,
and improve the precision of AG.
10 μGal 10-7 μGal (∆ϕ/c2)10-8 μGal
Finite speed of light (FSL) effect Second-order Doppler effect
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1. Research motivation
Research status for the AG’s relativistic model
Measured gravity acceleration:
Post-Newton effect of
gravitational field[1]
Relativistic effectsmeasured N PN AGg g g g
AGgRelativistic effects related
to the instruments
Earth
Atoms
[1] S.Wajima et al., Physical Review D, 55 (1997)1964.
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1. Research motivation
FSL effect
GR effects
peters 1 2measured 0
1 2
( )1 2
v Tg g
c
[2-3]
[4] S. Dimopoulos et al., PRD 78 (2008) 042003.
Dimopoulos
measured 0
( )1 3
v Tg g
c
[4]
[2] A. Peters et al., Metrologia 38 (2001) 25-61.
[3] B. Cheng et al., Phys. Rev. A 92 (2015) 063617.
Scalar expression!
Need to explore:
Disagreement for FSL effect;
More complete relativistic model
FSL
GR
Research status for the AG’s relativistic model
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Interference phase gravitational acceleration
2. AG’s Working principleThree-Raman-laser-pulse
atom gravimeter
Rabi oscillation
Split, reflect, recombine
atomic wave packets
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3. An analytical study method
Light: control light1k
2k
upper lower
CB
A A
tt
t t
L dt L dt
tot propagation laser separation
2
20
d x dx dx
d d d
5 intersections
Path integral
Trajectories of atoms and photons
Solve geodesic equation
Phase shift
Gravitational acceleration
Refer the space-time diagram
[4] S. Dimopoulos et al., PRD 78 (2008) 042003.
Conventional calculating method[4]
Light: background light
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m
upper lower upper lower
0
simplify the calculationCB
A A
tt t
t t
L dt L dt L L dt
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3. An analytical study method
An analytical study method
Control light
Coordinate
transformation
Idea: transfer FSL effect into atom’s Lagrangian
After transformation:
Lagrangian of atoms: Motion equation of light :
/dx dt 0 1L L L
Original form
FSL disturbance
1k
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3. An analytical study method
1. Coordinate transformation:
① Solve the motion equations of AG
atom: 21
2L mv mg r
photon:n x
tc
x x
n xt t
c
② Coordinate transformation for
③ Motion equations of AG after transformation
/dx dt
0 1L L L
Original form FSL disturbance
Calculation in Special Relativity frame
1k
Photon ( ) :1k
atom:
Calculating the FSL effect
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3. An analytical study method
2. Total phase shift:
0 1tot propagation separation laser separatio l sern aL L
ABCD Matrix, “Perturbation” approach, Laser phase
Calculating the FSL effect
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3. An analytical study method
3. FSL effect in AG:
Measured gravitational acceleration[5]:
1 2 1 1 2 20
eff 0 eff 0
( ) ( ) 2 ( )1 3 2k kv T e v T e n nv T
g gc c ck g k g
peters 1 2measured 0
1 2
( )1 2
v Tg g
c
Dimopoulos
measured 0
( )1 3
v Tg g
c
missed
[5] Yu-Jie Tan et al.. Finite-speed-of-light perturbation in atom gravimeters. Physical Review A, 2016, 94: 013612.
Calculating the FSL effect
Time delayCoupling of time delay
and frequency chirp frequency chirp
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3. An analytical study method
1 1 2 20 0
eff 0
( ) 2 ( )1 (1 )kv T e n nv T
g g g A Bc c k g
effk
① ② ④③
eff ke k eff ke k eff ke k eff ke k
Calculating the FSL effect
ke : direction of the control light (the light is reflected by the mirror)
: effective wave vector1 2k k
①② or③④ B
①③ or②④ A
①④ or②③ A+B
Experimental
design
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3. An analytical study method
/dx dt
0 1L L L
( )t t f x
x x
L
( )t f x
2 2 2 22 2
2 4 2 2
2 2
2
2 2 2 2 2 2
2
2 2 2 sin1 1 ( )
2 1 2 sin
2 1 ( sin )
r
r
rds cdt
c c c c
r dtdc
dr r d r dc
① Solve the motion equations of AG
atom:
photon:
② Coordinate transformation for
③ Motion equations of AG after
Coordinate transformation
1k
Photon ( ) :1k
atom: 15
calculating the relativistic effects
1. Coordinate transformation:
Calculation in General Relativity frame
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3. An analytical study method
2. Relativistic model for AG:
independent dependent
tot Newtonian relativistic relativistic
Relativistic phase shift[6] :
[6] Yu-Jie Tan et al.. Relativistic effects in atom gravimeters. Physical Review D, 2017, 95: 024002.
calculating the relativistic effects
Keep the sensitivity of gravitational
acceleration within 10^-15 g
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3. An analytical study method
Have been given by others!
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More general expression!
3. An analytical study method
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3. An analytical study method
New results!
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4. Conclusion
Based on the method, we studied FSL effect in atom gravimeters,
and further proposed a preliminary experimental design to test
this effect.
1 2 1 1 2 20
eff 0 eff 0
( ) ( ) 2 ( )1 3 2 ...k kv T e v T e n nv T
g gc c ck g k g
Extending the analysis on FSL effect, we established a more
complete relativistic model for atom gravimeters!
Developed an analytical study method, in which a coordinate
transformation is performed to simplify the calculation!
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Thanks for your attention!