Ultracold atoms, circular waveguides, and cavity QED with millimeter-scale electromagnetic traps

Abstract

The construction of a laser cooling/trapping apparatus with a versatile mm-scale magnetic trap for ultracold atoms is described herein. The design, operation, and performance of this unique trap are presented. The manipulation of this magnetic trapping system facilitated the Bose-condensation of 87Rb atoms in a variety of magnetic traps, most notably a millimeter radius circular magnetic trap for ultracold atoms. The dynamics of the quantum degenerate atom beam in this geometry are explored, as well as future applications with refinements of this system. A new probe of the phase space distribution of a generalized atomic beam is presented, and this probe was employed in the circular magnetic waveguide to characterize the quantum state of the system. Finally, this mm-scale magnetic trap was integrated with a mm-scale high-finesse optical cavity which accesses the strong coupling regime of cavity quantum electrodynamics (QED). Large ensembles of ultracold atoms were delivered to this cavity, and the first experimental results of this new dispersive regime of many-atom cavity QED are described.

Full text

Ultracold Atoms, Circular Waveguides, and Cavity QED with
Millimeter-scale Electromagnetic Traps
by
Kevin Lawrence Moore
B.S. (Harvey Mudd College) 1999
M.A. (University of California, Berkeley) 2005
A dissertation submitted in partial satisfaction of the
requirements for the degree of
Doctor of Philosophy
in
Physics
in the
GRADUATE DIVISION
of the
UNIVERSITY OF CALIFORNIA, BERKELEY
Committee in charge:
Professor Dan M. Stamper-Kurn, Chair
Professor Dmitry Budker
Professor Brigitta Whaley
Spring 2007

The dissertation of Kevin Lawrence Moore is approved:
Chair Date
Date
Date
University of California, Berkeley
Spring 2007

Ultracold Atoms, Circular Waveguides, and Cavity QED with
Millimeter-scale Electromagnetic Traps
Copyright 2007
by
Kevin Lawrence Moore

1
Abstract
Ultracold Atoms, Circular Waveguides, and Cavity QED with Millimeter-scale
Electromagnetic Traps
by
Kevin Lawrence Moore
Doctor of Philosophy in Physics
University of California, Berkeley
Professor Dan M. Stamper-Kurn, Chair
The construction of a laser cooling/trapping apparatus with a versatile mm-scale magnetic
trap for ultracold atoms is described herein. The design, operation, and performance of
this unique trap are presented. The manipulation of this magnetic trapping system facili-
tated the Bose-condensation of 87Rb atoms in a variety of magnetic traps, most notably a
millimeter radius circular magnetic trap for ultracold atoms. The dynamics of the quantum
degenerate atom beam in this geometry are explored, as well as future applications with
refinements of this system. A new probe of the phase space distribution of a generalized
atomic beam is presented, and this probe was employed in the circular magnetic waveg-
uide to characterize the quantum state of the system. Finally, this mm-scale magnetic
trap was integrated with a mm-scale high-finesse optical cavity which accesses the strong
coupling regime of cavity quantum electrodynamics (QED). Large ensembles of ultracold
atoms were delivered to this cavity, and the first experimental results of this new dispersive
regime of many-atom cavity QED are described.
Professor Dan M. Stamper-Kurn
Dissertation Committee Chair

i
To my father,
Maurice Joseph Moore
(1932 - 2007)

ii
Contents
List of Figures v
List of Tables viii
Acknowledgments ix
1 Introduction 1
1.1 ExploringFrontierswithUltracoldAtoms ................... 2
1.2 CavityQuantumElectrodynamics(CQED) .................. 4
1.2.1 Experimental CQED, ca. 2001 ..................... 5
1.3 “E2”-AHistory................................. 6
1.4 Outline ...................................... 9
2 Ultracold Atom Production 11
2.1 TheUHVChamber................................ 12
2.2 OpticalSystem .................................. 13
2.3 TheOven ..................................... 17
2.4 ZeemanSlower .................................. 17
2.5 MagneticTrappingandTransfer ........................ 19
2.5.1 Spherical Quadrupole Trap ....................... 20
2.5.2 QuadrupoleTransferSystem ...................... 21
2.6 Imaging ...................................... 24
2.7 TheFullCoolingApparatus........................... 25
3 The Millitrap 28
3.1 DesignConsiderations .............................. 30
3.2 The Millitrap ................................... 33
3.2.1 CurvatureandAnti-biasCoilConstruction .............. 35
3.2.2 GradientCoilConstruction ....................... 39
3.2.3 Full Mount Assembly .......................... 40
3.2.4 Integration of the Millitrap with the Main Chamber ......... 42
3.3 Operation of Millitrap .............................. 42
3.4 Atom Delivery to Millitrap ........................... 44
3.5 Spectrum of Millitrap Magnetic Trapping Potentials ............. 45

Contents iii
3.5.1 Spherical Quadrupole Trap ....................... 45
3.5.2 Ioffe-PritchardTrap ........................... 46
3.5.3 Time-OrbitingPotentialTrap...................... 48
4 Bose-Einstein Condensation in a Circular Geometry 50
4.1 TheMagneticQuadrupoleRing......................... 50
4.2 CorrectionstotheCylindricallySymmetricQ-ring .............. 51
4.2.1 BiasFields ................................ 52
4.2.2 Gravity .................................. 54
4.2.3 InhomogeneousFields .......................... 54
4.3 Loading Atoms into the Q-Ring ......................... 56
4.4 Majorana Losses in the Q-Ring ......................... 57
4.5 TheTime-OrbitingRingTrap.......................... 59
4.6 ToppingOfftheQ-ring.............................. 60
4.7 BECintheTORT ................................ 61
4.8 MotionintheCircularWaveguide ....................... 62
4.8.1 Azimuthal Oscillatory Motion ...................... 63
4.8.2 UnterminatedMotionintheWaveguide ................ 64
4.8.3 DiagnosingtheAzimuthalPotentialVariations ............ 65
4.8.4 ExpansionoftheAtomicBeam..................... 65
4.9 ProspectsforSagnacInterferometry ...................... 67
4.10 Bi-directional Propagation in the Circular Waveguide ............ 68
4.10.1 CoherentAtomicBeamsplittersviaLightScattering ......... 69
4.10.2 Kapitza-DiracScatteringintheRing.................. 72
5 Diagnosis of a Guided Atom Laser Pulse 75
5.1 InitialConditions................................. 76
5.2 FreeEvolutionintheCircularWaveguide ................... 77
5.3 ANoteonCoordinates.............................. 79
5.4 Phase space Density and the Wigner function ................. 80
5.5 TomographicImagingoftheWignerFunction................. 84
5.6 Superradiance-ASignatureofCoherence ................... 88
5.7 SuperradianceintheRing............................ 89
5.8 SuperradiantPump-ProbeSpectroscopy.................... 91
5.9 BichromaticSuperradiantPump-ProbeSpectroscopy............. 93
5.9.1 Bichromatic SPPS with Two Light Sources .............. 96
5.9.2 Bichromatic SPPS in a rotating frame ................. 96
5.10 Bichromatic SPPS in the Ultracold Atom Storage Ring ...........101
6 Ultracold Ensembles in a Strongly-Coupled Cavity 106
6.1 IntroductiontoCavityQuantumElectrodynamics ..............106
6.1.1 Dissipation-freeCavityQED ......................107
6.1.2 Dissipation-freeCavityQEDwithManyAtoms............108
6.1.3 The Far-Detuned Limit (√Ngo|Δa|) ................112
6.2 Dissipation ....................................114
6.3 TheBEC-CQEDSystem.............................115

Contents iv
6.3.1 TheCavity ................................115
6.3.2 TheCavityMount ............................ 117
6.3.3 Cavity Stabilization ...........................118
6.3.4 CavityProbingandLightDetection ..................123
6.3.5 AtomDeliverytotheCavity ......................124
6.4 Data Processing and Real-Time Detection ...................126
7 First Experiments with the BEC-CQED System 131
7.1 AtomTransits ..................................132
7.2 ProbingtheShiftedCavity ...........................132
7.2.1 Upticks ..................................133
7.2.2 TheStationaryProbe ..........................134
7.2.3 TheChirpedProbe............................135
7.3 FORTintheCavity ...............................136
7.4 SplittingtheCavityShiftwithAtomicPolarization..............141
7.5 HybridTrap....................................143
7.6 CavityFourierTransformSpectroscopy ....................146
7.7 Sub-“Shot Noise” Number Counting ......................147
A Design for the Main Chamber 149
B Designs for the Magnetic Transfer System 151
C Designs for the Millitap 154
D Designs for the Cavity Mounting Structure 159
E Collimated, single-pass atom source from a pulsed alkali metal dispenser
for laser-cooling experiments 163
F Bose-Einstein condensation in a mm-scale Ioffe Pritchard trap 168
G Bose-Einstein Condensation in a Circular Waveguide 176
H Probing the Quantum State of a Guided Atom Laser Pulse 181
Bibliography 186

v
List of Figures
2.1 TheMainChamber ................................. 13
2.2 TheLaser-CoolingSystem.............................. 15
2.3 TheRubidiumOvenandZeemanSlowerSystems................. 18
2.4 Rb-87ZeemanSplitting ............................... 20
2.5 MagneticTransferSystem.............................. 22
2.6 TheFullVacuumChamberLayout......................... 26
2.7 PhotooftheExperiment............................... 27
3.1 High-finesse Optical Fabry-Perot Cavity Mirrors ................. 29
3.2 Placement of the Millitrap Coils .......................... 32
3.3 CurvatureCoilStrip................................. 35
3.4 Curvature Coil Assembly .............................. 37
3.5 AWoundCurvatureCoil .............................. 37
3.6 Mass Grave of Millitrap Coils ............................ 38
3.7 TheFaceplates .................................... 38
3.8 Gradient Coil Assembly ............................... 40
3.9 Central Mount Assembly . . . ........................... 41
3.10 Full Millitrap Assembly ............................... 41
3.11 Millitrap Integration into Vacuum System ..................... 43
3.12ExperimentalSequence ............................... 46
3.13 Phase Space Trajectory in the Millitrap ...................... 47
4.1 QuadrupolarRingDiagram ............................. 51
4.2 Q-ring under Transverse Bias Field ......................... 53
4.3 Gravi-magneticPotentialContourPlot....................... 53
4.4 The Q-ring in the Presence of Inhomogeneous Magnetic Fields ......... 55
4.5 Loading Atoms into the Q-ring ........................... 56
4.6 VariationofMajoranaLossRatewithQ-ringOrientation ............ 59
4.7 Elimination of Majorana Losses in the TORT ................... 61
4.8 AtomicBeamMotionintheWaveguide ...................... 64
4.9 FlatteningtheCircularWaveguide ......................... 66
4.10Mean-fieldDrivenExpansionintotheWaveguide................. 67
4.11SagnacInterferometryinaCircularWaveguide .................. 69
4.12Kapitza-DiracScatteringintheRing........................ 71

List of Figures vi
4.13 Bidirectional Propagation in the Ring via Kapitza-Dirac Scattering ....... 73
4.14ResonantKapitza-DiracScatteringintoSpecificMomentumModes....... 74
5.1 ExpandingGuidedAtomLaserBeam ....................... 76
5.2 ObservedTransverseWidthDecay ......................... 78
5.3 CoordinateAxesfortheRotatingAtomBeam .................. 79
5.4 HypothesizedPhaseSpaceEvolution........................ 82
5.5 TheProjection-sliceTheorem............................ 86
5.6 SkewedPhaseSpaceProbe ............................. 87
5.7 SuperradianceintheRing.............................. 90
5.8 AngularDependenceofSuperradiance....................... 91
5.9 BichromaticSuperradiancePump-ProbeSpectroscopy .............. 93
5.10 Bichromatic SPPS in a Circular Waveguide .................... 98
5.11CoherenceTimesvs.AngularPosition.......................103
5.12InferredPhaseSpaceDistribution .........................104
5.13CoherenceTimesforMultipleOrbits........................105
6.1 Relevant Clebsch-Gordon Spectrum for |F=1,m
F=−1Atoms........111
6.2 EnergyLevelAvoidedCrossingintheMany-AtomCavitySystem .......113
6.3 DispersiveEnergyLevelStructure .........................114
6.4 TheRetractableCavity ...............................118
6.5 TheCavityMountingStructure...........................120
6.6 TheCavity-PZTSystem...............................121
6.7 TheCavityLaserFeedbackSystem.........................122
6.8 Many-AtomCavityQEDinPractice........................125
6.9 BECintheTOPTrap(OutsidetheCavity)....................126
6.10CRVCTimingDiagram ...............................129
6.11CRVCCircuitDiagram. ...............................130
7.1 ObservationofControlledAtomTransits. .....................132
7.2 UptickTimes.....................................133
7.3 CavityLineTransitswithStationaryProbe ....................134
7.4 CavityLineShiftasaNumberMeasurement ...................136
7.5 SweepingtheProbeOvertheShiftedCavityResonance .............137
7.6 Loading Atoms into the Cavity FORT .......................140
7.7 TransverseModeTrapping .............................141
7.8 IndexedVariationofCavityCoupling .......................142
7.9 LineSplittingwithaLinearlyPolarizedProbe. .................. 143
7.10TheHybridTrap...................................144
7.11FourierTransformPowerSpectrumofHybridLine................146
A.1 TheMainChamber .................................150
B.1 ReentrantBucket...................................152
B.2 TheMagneticTransferCoils ............................ 153
C.1 Millitrap Faceplate ..................................155

List of Figures vii
C.2 Millitrap Mount (Bottom Piece) ..........................156
C.3 Millitrap Mount (Center Piece) ...........................157
C.4 Millitrap Mount (Top Bracket) ........................... 158
D.1 Cavitymount(mainplatform) ...........................160
D.2 Cavity mount (mating piece) ............................161
D.3 Cavity pendulum mount ...............................162

viii
List of Tables
2.1 Final Experimental Pressures .......................... 14
2.2 SlowerParameters ................................ 19
2.3 MagneticTransferCoilParameters....................... 23
2.4 Position/GradientMatrixfortheMagneticTransfersystem ......... 24
2.5 NumericalAperturesfortheImagingSystem ................. 25
3.1 Parameters for Millitrap Coil Windings .................... 45
5.1 GuidedAtomLaserBeamParameters ..................... 77
5.2 GuidedAtomLaserBeamCoordinateDefinitions............... 80
6.1 CavityQEDParameters............................. 116
7.1 OpticalLatticeParameters ...........................139

ix
Acknowledgments
‘Ndanka, ndanka’ mo jappa golo. - Wolof proverb
‘Slowly, slowly’ catches the monkey. I’m quite certain that this phrase, frequently
invoked during my time in Africa, did not have graduate school in mind when it was first
uttered. Nevertheless, the counsel of patience and thoughtfulness could hardly have been
better advice for six years of trying to build and operate the complicated apparatus that
resulted in the work presented in this thesis. These are, unfortunately, not virtues to
which I naturally tend, but perhaps on my best days I approached this ideal. Rather,
these virtues (and many others) may certainly be applied to those who knew me during
this time, and it is my great privilege in these opening pages to thank those who helped
me along this path.
First and foremost, I am grateful beyond words to my advisor, Dan Stamper-Kurn,
with whom my working relationship began 20,000 miles away in the wilds of West Africa
before he was a professor and before I was Berkeley student. I contacted him in November
of 2000 through the nascent technique of internet stalking, as I saw his name on the
Berkeley Physics website as a professor who was looking for graduate students. Since we
started working together in June 2001, my appraisal of his scientific acumen has morphed
continuously and monotonically along the spectrum from “impressed by” to “in utter awe
of.” He’s been an amazing advisor, a good friend, and I will miss our conversations a great
deal.
This thesis would be a much thinner without the help of Kater Murch and Deep
Gupta, the two of whom I cannot thank enough for all of the years of fun we had together
down in the lab. I am not naturally a superstitious person, but some lucky turn of fate

Acknowledgments x
brought these two incredible individuals into my graduate life at nearly the same time.
Deep, who is probably the most pleasant person to work with on the planet, brought his
immense good nature and some desperately needed maturity to the effort, as well as a
much-needed Lebowski enthusiast to properly appreciate my oft-repeated quotes. Kater,
who is a few years younger than I yet somehow vastly wiser, brought his incredible spirit
and astounding variety of talents (“Oh, you play the cello and the guitar? Hmm, you can
paint? Oh, you’ve renovated your entire house? Oh look, you’re our best soccer player.
What’s that, you organically farm, too? Hey, how’s that pre-iPod Apple stock doing for
you?”). Of everything that’s changing as I complete my time at Berkeley, seeing this
team of three come to an end is the saddest. I look forward to their company in different
contexts in the coming years, preferably in the daytime now that we don’t have to pull the
all-nighters together anymore.
Another individual to whom this work is largely indebted is Tom Purdy, who joined
the millitrap effort at precisely the right time (i.e. when I was about to torch 75 LeConte in
frustration). With his deft hands added to the project, we were finally able to put together
a workable millitrap which became the workhorse of this these. Beyond his intelligence,
skill, and affability, Tom also wins hands down for the most creative birthday cake I’ve ever
seen in my entire life. Complete with an army of gummy bears storming the frosting hill
in coordinated assault on the unsuspecting Peeps barracks, his “Comment on the Human
Condition” cake is still making me laugh even as I write this many years later.
Mukund Vengalattore, affectionately referred to as “Butters,” has been my officemate
for the last year, and a better companion with whom to finish my doctoral work I truly
cannot imagine. That said, I will give warning to any future co-workers that they should
not be fooled by his calm demeanor and gentle spirit. This act belies his intense competitive
and sporadically malevolent nature, as evidenced by his intentional crippling of my ankle
because I was beating him at racquetball. You’ll pay for that, Butters. . . one of these days,
you’ll pay.
And way back to the beginning, of course, there were three. James Higbie, Lorraine
Sadler, and I were Dan’s first graduate students, and a surely a motley crew we made back
in 2001 before we knew what we were getting into. The sense of shared history with these

Acknowledgments xi
founding members is strong, and while our scientific experiences remained mostly parallel
in space and time (except for my haphazard constructions which are probably still slowing
down E1), they have been wonderful coworkers from Day 1 and I wish them very well as
they respectively embark on their next adventures.
I would imagine it poor form to allow one’s Acknowledgements to exceed the length
of the thesis itself, so quite reluctantly I must issue a most sincere blanket thank you to
everyone who’s passed through the Stamper-Kurn fellowship these past six years. It was
a privilege to play soccer, get coffee, eat birthday cakes, solve anagrams, and occasionally
do some science with you all.
Similarly, as I am technically finishing 22nd grade, I have a laundry list of former
teachers who deserve my unqualified thanks for their contributions to my intellectual de-
velopment. While space ever constrains me, I would be woefully remiss if I did not recognize
three individuals to whom I am especially grateful.
For the generally ungraceful years I endured junior high school, Joel Narva sparked my
interest in a myriad of subjects ranging from logic to computer programming to feedback
to prime numbers, and of course the subject of algebra which was his charge. Far more
than just learning about math, his classes positively buzzed with enthusiasm about the
subject matter and no opportunity was missed to bring in interesting tangents. I’ve yet to
lose the excitement for such intellectual digressions, and outside of my immediate family
no teacher is more responsible than Joel Narva for my since-discovered penchant to seek
out my own tangents.
On into high school, where my lazy academic philosophy hit a very significant road-
block in Kevin Connell’s English class. It was here that I first discovered what really makes
the written word worth reading, and haven’t viewed it the same since. All of a sudden
Stephen King seemed like a hack and I found myself turning to the likes of Orwell, Hem-
ingway, Vonnegut, and Heller to satisfy my newfound requirement that books boast not
just a plot but artistry, depth, and humanity. That said, I still think The Scarlet Letter
is horrible.
Halfway into my tenure at Harvey Mudd College, I had the great fortune of working
closely with Tom Donnelly, then a brand new professor. In addition to teaching me quan-

Acknowledgments xii
tum mechanics, guiding my haphazard calculations on non-equilibrium electron systems,
and shipping me off to face the fire at the 1999 American Physical Society meeting in
Atlanta, Tom became one of my closest friends from the college years (and has remained
so). Both then and now, I have been continually envious of his ability to lead a full life as
an exceptional scientist, teacher, and human being.
As for my role models at Berkeley, one need look no further than the amazing cadre
of individuals I’ve had the fortune of calling my friends in the last six years: Mike Grobis,
who never missed an opportunity to organize and manage memorable events such as the
physics holiday party, the physics softball team, or the daily insertion of his foot into
his own mouth. In addition to being a great roommate, friend, and co-discoverer of the
croc-o-duck, Ryan “Bonesaw” Lindberg has proven that the reports of the death of plasma
physics have probably been somewhat exaggerated (maybe). Michael Boylan-Kolchin, as
a savvy poker player, softball all-star, and cosmologist extraordinaire, has proven that
Delaware actually has more to offer than that joke in Wayne’s World. Nadir Jeevanjee,
who I first encountered dancing in my living room in a hot orange dress, has proven to the
world the astonishing fact that there is actually a career out there which pays less than
graduate school. And, filed under the heading of “unparalleled patience,” Jess Walter
endured my flakiness as a friend and band member, yet was always ready for the next
round of cheap sushi. At longer distances, I must briefly and profusely thank the Peace
Corps crowd, Jeff Johannes, the Eugene crew, and my many second families amidst the
Gherty clan. Finally, Liz Powell deserves more thanks than anyone for keeping me sane
during the actual writing of this thesis. (I can assure the reader it was no small task.)
I remain further indebted to the following people, places, and/or things which all pro-
vided considerable aid and comfort to me during my time at Berkeley: the Cal Triathlon
team, my former band Five Little Words/The Infidels/(all the other unmentionable names
we embraced for brief periods of time), the Psi Stars, the Berkeley physics poker guys, The
Daily Show/Colbert Report, my Cannondale R-1000, the SF music scene, the iPod, Rhap-
sody (which I’ve somehow been using for free for the last two years), The Big Lebowski,
Kingpin Donuts, Cafe Strada, the 21st Amendment to the Constitution and its logical
progeny, the Bud Light Fan Club.

Acknowledgments xiii
I’ve been blessed with wonderful home fires burning in the Northwest, and a special
note of thanks must go to my family, Dave, Amy, and little Wyatt. The most special note
of gratitude and love must go to my mother, who has been the most wonderful support to
me from the day I was born right up to the submission day when she checked the document
for spelling, typographical, and grammatical errors1.
Underneath the undeniably happy occasion of completing my Ph.D. is a deep sadness
that my father, Maurice Joseph Moore, did not live to see me become the second Dr.
Moore. I know how much he would have loved seeing this day come, and it is to him that
I dedicate this work.
1Their was plennty.