high precision absolute gravity gradiometry with atom interferometry

183 Pages·2001·2.3 MB·English

HIGH PRECISION ABSOLUTE GRAVITY
GRADIOMETRY WITH ATOM INTERFEROMETRY
a dissertation
submitted to the department of physics
and the committee on graduate studies
of stanford university
in partial fulfillment of the requirements
for the degree of
doctor of philosophy
By
Jeffrey Michael McGuirk
September 2001
(cid:1)c Copyright 2001 by Jeffrey Michael McGuirk
All Rights Reserved
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I certify that I have read this dissertation and that in
my opinion it is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Mark Kasevich
(Principal Adviser)
I certify that I have read this dissertation and that in
my opinion it is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
Steven Chu
(Department of Physics and Applied Physics)
I certify that I have read this dissertation and that in
my opinion it is fully adequate, in scope and quality, as
a dissertation for the degree of Doctor of Philosophy.
John Turneaure
(Department of Physics)
Approved for the University Committee on Graduate
Studies:
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Abstract
An absolute gravity gradiometer was demonstrated using atom interference tech-
niques. This is the first realization of an gradiometer which uses an absolute standard
for its calibration. A gravity gradiometer measures spatial changes in the gravita-
tional field over a fixed baseline by making simultaneous acceleration measurements
with two spatially separate accelerometers. The gradiometer has a differential sen-
sitivity of 4 × 10−9g in 1 s and a differential accuracy of 10−9g. This is the best
gradiometer accuracy reported to date and the sensitivity competes favorably with
existing state-of-the-art instruments. A proof-of-principle measurement of the grav-
ity gradient of a small test mass was made leading towards a precision measurement
of the gravitational constant. The performance was characterized on a vibrationally
noisy reference platform, testing the ability of the gradiometer to reject common-
mode accelerations. Techniques for extracting gradient information were explored.
Applications of sensitive and accurate gravity gradiometers include tests of general
relativity, studies of the gravitational constant, navigation, and geophysical studies.
The principle behind the measurement is as follows: proof masses for the two ac-
celerometers consist of two ensembles of laser-cooled cesium atoms whose acceleration
is measured by an interferometer sequence. The interferometer is comprised of light
pulses in a π/2−π−π/2 pulse sequence which acts to divide, deflect, and recombine
each atomic wavepacket. The final state of the atom depends on the inertial forces
experienced by the atom during its trajectory through the interferometer. The two
simultaneous acceleration measurements are subtracted to produce a gravity gradi-
ent. This technique is advantageous because it offers intrinsic absolute calibration,
robust operation, and uniformity of proof masses.
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Acknowledgements
I am deeply grateful to my advisor Mark Kasevich. In addition to being a gifted
physicist who taught me an amazing amount of physics, Mark has both the vision
to pursue interesting ideas and the experimental ability to carry them out. On top
of physics, it has just been fun to work with Mark. I cannot forget the opportunity
he allowed me to live on both coasts. Along the way, I have been fortunate to work
with a number of talented people. Dean Haritos and Philippe Bouyer helped build
the experiment at Stanford. During his post-doc, Mike Snadden assisted with the
proof-of-principle work at Stanford, helped during the move to Yale in 1997, and was
instrumental in the steps leading to the current device performance. Also, in his spare
time, Mike wrote 25,000 lines of computer code to control the timing and data acqui-
sition. Greg Foster and Jeff Fixler helped develop the data extraction routines and
demonstrate the performance of the gradiometer, and they have smoothly assumed
the running of the experiment for the measurement of G. Post-doc Kai Bongs and
students Romain Launay and Neelima Sehgal developed the details of the interfer-
ometer theory and enlightened me with many discussions. I am also thankful for the
general laboratory expertise of my colleagues Brian Anderson and Todd Gustavson,
and for many useful discussions with Kurt Gibble. The work in this dissertation was
funded by ONR, NASA, and NRO. My time in Stanford and New Haven was made
more enjoyable and my sanity was maintained with the help of Dean, Mike, Todd,
Brian, Jamie Kerman, and the Saeco Magic de Luxe. Finally I wish to thank my
family for their support.
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Contents
Abstract v
Acknowledgements vi
1 Introduction 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Gradiometry and the equivalence principle . . . . . . . . . . . . . . . 2
1.3 Laser manipulation of atoms . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Atom interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Gravity Gradiometry 6
2.1 Gradient tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Gradient units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Gradiometer applications . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 Inertial navigation . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.2 Subsurface mass anomalies . . . . . . . . . . . . . . . . . . . . 9
2.3.3 Gravitational constant . . . . . . . . . . . . . . . . . . . . . . 11
2.3.4 Tests of General Relativity . . . . . . . . . . . . . . . . . . . . 14
2.3.5 Fifth force experiments . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Alternate gradiometer technologies . . . . . . . . . . . . . . . . . . . 15
2.4.1 Mass-spring gradiometers . . . . . . . . . . . . . . . . . . . . 15
2.4.2 Superconducting instruments . . . . . . . . . . . . . . . . . . 16
2.4.3 Falling cornercube gradiometer . . . . . . . . . . . . . . . . . 16
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2.4.4 Absolute gradiometry . . . . . . . . . . . . . . . . . . . . . . . 17
3 Laser Cooling and Trapping 18
3.1 Atomic structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2 Two-level atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Optical forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.1 Scattering force . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.2 Dipole force . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4 Magnetic forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5 Laser cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.5.1 Doppler cooling . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.5.2 Polarization gradient cooling . . . . . . . . . . . . . . . . . . . 26
3.6 Magneto-optical trapping . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.6.1 Trap loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.6.2 Atomic fountains . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.7 Two-photon stimulated Raman transitions . . . . . . . . . . . . . . . 31
3.8 Atom detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.9 Experiment synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 Atom Interferometry 39
4.1 Intuitive analogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2 Interferometer description . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Wavepacket overlap phase . . . . . . . . . . . . . . . . . . . . . . . . 43
4.4 Laser phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.4.1 Frequency term . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4.2 Initial phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.5 Free propagation phase . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.5.1 Path integral formalism . . . . . . . . . . . . . . . . . . . . . 47
4.5.2 Perturbative approach . . . . . . . . . . . . . . . . . . . . . . 49
4.6 Nonuniform acceleration fields . . . . . . . . . . . . . . . . . . . . . . 50
4.6.1 Exact solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.6.2 Gravity gradients . . . . . . . . . . . . . . . . . . . . . . . . . 51
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4.6.3 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.7 Limitations to the theory . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.8 Application to gradiometry . . . . . . . . . . . . . . . . . . . . . . . . 55
5 Experimental Apparatus 57
5.1 Apparatus overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 Vacuum system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2.1 Motivation for vacuum . . . . . . . . . . . . . . . . . . . . . . 57
5.2.2 Vacuum chamber design and preparation . . . . . . . . . . . . 59
5.2.3 Chamber evacuation . . . . . . . . . . . . . . . . . . . . . . . 62
5.3 Laser system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3.1 Master laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3.2 Laser amplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.3.3 Optical fiber system . . . . . . . . . . . . . . . . . . . . . . . 68
5.4 Laser cooled atomic sources . . . . . . . . . . . . . . . . . . . . . . . 69
5.5 State preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.5.1 Optical pumping . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.5.2 Composite pulse techniques . . . . . . . . . . . . . . . . . . . 74
5.6 Atom interferometer . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.6.1 Raman lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.6.2 Beam delivery . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.6.3 Propagation reversal . . . . . . . . . . . . . . . . . . . . . . . 82
5.6.4 Raman beam parameters . . . . . . . . . . . . . . . . . . . . . 83
5.6.5 Interferometer operation . . . . . . . . . . . . . . . . . . . . . 85
5.7 Detection system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.7.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.7.2 Detection apparatus . . . . . . . . . . . . . . . . . . . . . . . 87
5.7.3 Detection system performance . . . . . . . . . . . . . . . . . . 91
5.7.4 Noise analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
5.8 Vibration isolation subsystem . . . . . . . . . . . . . . . . . . . . . . 94
5.8.1 Mechanical design . . . . . . . . . . . . . . . . . . . . . . . . . 95
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5.8.2 DSP servo system . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.9 Microwave generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6 Results 99
6.1 Proof-of-principle results . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2 Signal extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2.1 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2.2 Interference fringe fitting . . . . . . . . . . . . . . . . . . . . . 102
6.2.3 Magnetic phase shifting . . . . . . . . . . . . . . . . . . . . . 104
6.2.4 Gaussian elimination reduction . . . . . . . . . . . . . . . . . 106
6.2.5 Circle fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.2.6 Ellipse fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2.7 Summary of data extraction methods . . . . . . . . . . . . . . 115
6.3 Sensitivity characterization . . . . . . . . . . . . . . . . . . . . . . . . 116
6.3.1 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.3.2 Proof-of-principle mass detection . . . . . . . . . . . . . . . . 118
6.4 Accuracy estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.1 Tidal measurement . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.2 Allan variance . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6.4.3 Gravitational constant measurement . . . . . . . . . . . . . . 122
6.5 Immunity to environmental noise . . . . . . . . . . . . . . . . . . . . 124
6.5.1 Linear acceleration . . . . . . . . . . . . . . . . . . . . . . . . 124
6.5.2 Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7 Discussion 130
7.1 Performance Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.1.1 SNR limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.1.2 Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.2 Related methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.2.1 Large area interferometers . . . . . . . . . . . . . . . . . . . . 133
7.2.2 Interferometer comparisons . . . . . . . . . . . . . . . . . . . 139
7.2.3 Multi-loop interferometers . . . . . . . . . . . . . . . . . . . . 142
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