Precision measurements of spin interactions with high density atomic vapors

351 Pages·2011·7.46 MB·English

by  Georgios Vasilakis

Precision measurements of spin
interactions with high density atomic
vapors
Georgios Vasilakis
A Dissertation
Presented to the Faculty
of Princeton University
in Candidacy for the Degree
of Doctor of Philosophy
Recommended for Acceptance
by the Department of
Physics
Adviser: Michael V. Romalis
September 2011
c Copyright by Georgios Vasilakis, 2011.
(cid:13)
All rights reserved.
Abstract
Polarized atomic vapors can be used to detect fields interacting with a spin. Recent
advances have extended the sensitivity of atomic magnetometers to a level favorable
for fundamental physics research, and in many cases the sensitivity approaches quan-
tum metrology limits.
In this thesis, we present a high density atomic K-3He comagnetometer, which
features suppressed sensitivity to magnetic fields, but retains sensitivity to anomalous
fields that couple differently than a magnetic field to electron and nuclear spins. The
comagnetometer was used to measure interactions with a separate optically pumped
3He nuclear spin source. The 3He spin precession frequency in the comagnetometer
was measured with aresolutionof 18pHzover thecourseof approximately onemonth,
enabling us to constrain the anomalous spin-spin interaction between neutrons to be
less than 2.5 10 8 of their magnetic or less than 2 10 3 of their gravitational
− −
× ×
interaction at a length scale of 50 cm. We set new laboratory bounds on the coupling
strength of light pseudoscalar, vector and pseudovector particles to neutrons, and
we consider the implications of our measurement to recently proposed models for
unparticles and Goldstone bosons from spontaneous breaking of Lorentz symmetry.
We also describe theoretically and experimentally a quantum non-demolition
(QND) measurement of atomic spin in the context of radio frequency magnetometer
with hot alkali-metal vapors. Using stroboscopic probe light we demonstrate sup-
pression of the probe back-action on the measured observable, which depends on
the probe duty cycle and on the detuning of the probe modulation frequency from
twice the alkali Larmor frequency. We study the dependence of spin-projection noise
on the polarization for atoms with spin greater than 1/2 and develop a theoretical
model that agrees well with the data. Finally, it is shown theoretically that QND
measurements can improve the long-term sensitivity of atomic magnetometers with
non-linear relaxation.
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Acknowledgements
I would first like to thank my adviser Michael Romalis for his continuous assis-
tance throughout all these years. Mike has always been eagerly available to answer
questions, provide ingenious solutions to problems and explain the physics. His en-
thusiasm, drive and motivation have been a source of inspiration for me, not only as
a scientist but also as a person in general who sets high goals and pushes himself to
realize them. I am grateful to him for giving me the opportunity to work in a great
environment, on such exciting projects and complete a work that I feel proud of. I
appreciate how he encouraged my development as a physicist, and the understanding
that he showed with my visits to Greece. I would also like to thank Will Happer
for elucidating many points on optical pumping and serving as a second writer on a
short notice. I want to extend a warm thanks to the committee of my final public
oral examination: Michael Romalis, William Jones and David Huse.
Working in the Romalis lab gave me the opportunity to make good friends and
interact with very promising physicists. Justin Brown has been a close friend through-
out all these years, who helped immensely with the science and the struggles of life
at Princeton. I am particularly grateful to him for all the trouble that he took to
prepare the required documents so that I can put the thesis on deposit. Scott Seltzer
(aka “The Great Scott”) has been a good friend and an invaluable help to understand
the atomic magnetometer; he also set the standard of a great thesis, which served as a
model for mine. Tom Kornack laid the groundwork for the anomalous spin-dependent
measurement and guided my first steps in the K-3He comagnetometer. Vishal Shah
helped me significantly to develop an understanding of quantum noise. I also enjoyed
and learned a lot from the numerous discussions with Katia Mehner and Rajat Ghosh
about the pleasures of life. Many more colleagues in the atomic physics group made
the time more pleasant and productive: Hoan Dang, Lawrence Cheuk, Ben Olsen,
Bart McGuyer, Sylvia Smullin, Pranjal Vachaspati, Nezih Dural, Dan Hoffman, Hui
iv
Xia, Kiwoong Kim, Natalie Konstinski, Ivana Dimitrova, Oleg Polyakov and all the
students who spent their summers with us.
The university and particularly the physics department is fortunate to have very
competent staff. Claudin Champagne, Barbara Grunwerg, and Mary Santay made
sure that all purchasing requests were carried through efficiently and promptly. Mike
Peloso and Ted Lewis were very helpful with mechanical constructions, while Mike
Souza made glass cells that met our highstandards. Iamalso very thankful toJessica
Heslin and Laurel Lerner who were very helpful with the administrative tasks.
Besides my colleagues, during my time at Princeton I was privileged to meet very
nice people and develop solid friendships. Ilias Tagkopoulos and his wife Eli Berici
have provided in Princeton the love and support that normally one finds only in
family. Eli was also responsible for my healthy and tasty diet. Chrysanthos Gounaris,
my roommate for a year, has been consistently, from the first days of graduate school
till now (and hopefully for the years to come), a friend that I can trust and rely on.
Alexandros Ntelekos (aka ”The Hero”) brought the Greek spirit in Princeton and
supported me with his example to go all the way through the end. I cannot miss to
mention all the excitement that Alex and I have shared for Olympiacos. Emmanouil
Koukoumidis has turned out to be much more than just a great friend, for which I feel
very fortunate. Ioannis Papadogiannakis and his wife Anastassia Papavassiliou were
instrumental in helping me find a balance in the beginning of the Ph.D., and provided
afeeling ofhomeduringmyfirsttwoyearsatPrinceton. KaterinaTsolakidou, Joanna
Papayannis, Ioannis Poulakakis, Megan Foreman, Eleni Pavlopoulou, Aakash Pushp,
NataliaPetrenko, Catherine Abou-Nemeh, andBarbaraHiltonhavemademebreathe
easier and I thank all of them from my heart.
I am indebted to Manolis Charitakis (aka “Megalos”), Thanassis Lamprakis and
Theo Drakakis, my friends in Greece who have been extremely supportive throughout
all these years. Manolis, Thanassis and Theo made me feel always that I was an
v
integral part of their lives despite the distance, and would put a lot of effort to cheer
me up whenever they sensed that something was bothering me. I would also like to
thank George Fillipidis, simply for being who he is and inspiring me to explore new
paths of life.
The journey for the Ph.D. wouldn’t have started and wouldn’t have been com-
pleted without the help of Vassilis Papakonstantinou. Vassilis has been a steady
companion for more than 14 years, a friend who always manages to uplift me, and
constantly encourages me to become a better person.
I don’t have words to express my affection and gratitude to Penelope Karadaki.
It has been three years since Penelope entered my life, and for every single day since
then she has been the source of my happiness, the sun that brightens my life, the
rose that intoxicates the air that I breathe. Among other things, Penelope provided
the solid emotional support and the continuous encouragement that were necessary
to complete this work. I wish that I can provide to Penelope a fraction of what she
has given to me.
I would finally like to thank my family for the support andlove all these years. My
sister Maria Vasilaki and my brother Ioannis Vasilakis have always been considerate
to me and ready to take actions to protect me from any difficult situation. Our
parents, Emmanouil and Hariklia Vasilaki, have selflessly devoted themselves to us
andhave never stopped nurturing the best in us. For all their limitless love andthings
that have done for me I dedicate this thesis to them.
vi
To my parents
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Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
1 Introduction 1
2 Theoretical Background 6
2.1 Atomic Energy levels . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 The density matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Evolution in the magnetic field . . . . . . . . . . . . . . . . . . . . . 10
2.4 Interaction of alkali atoms with light . . . . . . . . . . . . . . . . . . 11
2.4.1 Polarizability Hamiltonian . . . . . . . . . . . . . . . . . . . . 12
2.4.2 Light Shift and Absorption Operator . . . . . . . . . . . . . . 15
2.4.3 Polarizability tensor . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.4 Polarizability at high-pressures/large detunings . . . . . . . . 19
2.4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4.6 Effective Magnetic-like field from light . . . . . . . . . . . . . 22
2.5 Repopulation Pumping . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.6 Total Optical Pumping . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.7 Radiation Trapping and Quenching . . . . . . . . . . . . . . . . . . . 26
viii
2.8 Light propagation in an atomic ensemble . . . . . . . . . . . . . . . . 27
2.8.1 Faraday Rotation . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.8.2 Optical Absorption . . . . . . . . . . . . . . . . . . . . . . . . 30
2.9 Usefulness of Spherical Tensor Representation of ρ . . . . . . . . . . . 31
2.10 Relaxation of Polarized Atoms . . . . . . . . . . . . . . . . . . . . . . 31
2.10.1 Collisional Relaxation . . . . . . . . . . . . . . . . . . . . . . 32
2.10.2 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.11 Relaxation of Polarized Noble Gas Atoms . . . . . . . . . . . . . . . . 42
2.12 Spin-Exchange Collisions between Alkali-Metal Atoms and Noble Gas
Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.13 Spin-Exchange Collisions between Pairs of Alkali Metal Atoms . . . . 45
2.14 Spin Temperature Distribution . . . . . . . . . . . . . . . . . . . . . 47
2.15 Density Matrix Evolution . . . . . . . . . . . . . . . . . . . . . . . . 50
2.16 Bloch equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.16.1 Steady state solution of the Bloch equation . . . . . . . . . . . 51
2.16.2 Estimation of T and T . . . . . . . . . . . . . . . . . . . . . 54
1 2
2.16.3 Effective Gyromagnetic Ratio: . . . . . . . . . . . . . . . . . . 59
2.16.4 Two species spin-exchange collisions . . . . . . . . . . . . . . . 60
2.17 Quantum Optical States and Operators . . . . . . . . . . . . . . . . . 61
2.17.1 Electric field operator . . . . . . . . . . . . . . . . . . . . . . . 61
2.17.2 Polarization Basis . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.17.3 Stokes Representation . . . . . . . . . . . . . . . . . . . . . . 63
2.17.4 Coherent states . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3 Comagnetometer Theory 65
3.1 Description of the Comagnetometer . . . . . . . . . . . . . . . . . . . 65
3.1.1 Dynamics of Overlapping Spin Ensembles . . . . . . . . . . . 66
3.2 Steady State Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
ix
3.2.1 Refinements in steady state signal . . . . . . . . . . . . . . . . 73
3.2.2 Sensitivity of the comagnetometer . . . . . . . . . . . . . . . . 75
3.2.3 An intuitive model . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3 Dynamic Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.4 AC Response to Transverse Magnetic Fields . . . . . . . . . . . . . . 83
3.5 Fundamental Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
3.5.1 Atomic Spin Noise . . . . . . . . . . . . . . . . . . . . . . . . 85
3.5.2 Photon Shot Noise . . . . . . . . . . . . . . . . . . . . . . . . 90
3.6 Response To Transients . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4 Comagnetometer Implementation 99
4.1 Comagnetometer Experimental Setup . . . . . . . . . . . . . . . . . . 99
4.1.1 Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.1.2 Oven . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.1.3 Magnetic Fields and Shields . . . . . . . . . . . . . . . . . . . 107
4.1.4 Vacuum tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.1.5 Comagnetometer Optical Setup . . . . . . . . . . . . . . . . . 109
4.2 Comagnetometer Field and Light-shift adjustment . . . . . . . . . . . 124
4.2.1 Zeroing of δB . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
z
4.2.2 Zeroing of the transverse fields. . . . . . . . . . . . . . . . . . 127
4.2.3 Zeroing of the Light-shifts . . . . . . . . . . . . . . . . . . . . 130
4.2.4 Zeroing of pump-probe nonorthogonality . . . . . . . . . . . . 132
4.2.5 Field angular misalignment . . . . . . . . . . . . . . . . . . . 134
4.3 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.4 Pump power optimization . . . . . . . . . . . . . . . . . . . . . . . . 139
4.5 Effect of comagnetometer noise in the tuning routines . . . . . . . . . 140
4.6 Comagnetometer Characterization . . . . . . . . . . . . . . . . . . . . 142
4.6.1 Optical Absorption . . . . . . . . . . . . . . . . . . . . . . . . 142
x