Physics of Ultra-Cold Matter: Atomic Clouds, Bose-Einstein Condensates and Rydberg Plasmas

410 Pages·2013·4.301 MB·English

by  J.T. Mendonça, Hugo Terças (auth.)

SpringerSerieson
atomic, optical, and plasma physics 70
SpringerSerieson
atomic, optical, and plasma physics
TheSpringerSeriesonAtomic,Optical,andPlasmaPhysicscoversinacompre-
hensivemannertheoryandexperimentintheentirefieldofatomsandmolecules
andtheirinteractionwithelectromagneticradiation.Booksintheseriesprovide
arichsourceofnewideasandtechniqueswithwideapplicationsinfieldssuchas
chemistry,materialsscience,astrophysics,surfacescience,plasmatechnology,ad-
vancedoptics,aeronomy,andengineering.Laserphysicsisaparticularconnecting
themethathas providedmuchofthecontinuing impetusfor newdevelopments
inthefield.Thepurposeoftheseriesistocoverthegapbetweenstandardunder-
graduatetextbooksandtheresearchliteraturewithemphasisonthefundamental
ideas,methods,techniques,andresultsinthefield.
Forfurthervolumes:
http://www.springer.com/series/411
J.T. Mendonc¸a (cid:129) Hugo Terc¸as
Physics of Ultra-Cold Matter
Atomic Clouds, Bose Einstein Condensates
and Rydberg Plasmas
123
J.T.Mendonc¸a HugoTerc¸as
InstitutoSuperiorTecnico Universite´BlaisePascal
Av.RoviscoPais1 Aubie`reCedex,France
Lisbon,Portugal
ISSN1615-5653
ISBN978-1-4614-5412-0 ISBN978-1-4614-5413-7(eBook)
DOI10.1007/978-1-4614-5413-7
SpringerNewYorkHeidelbergDordrechtLondon
LibraryofCongressControlNumber:2012947410
©SpringerScience+BusinessMedia,LLC2013
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof
thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,
broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology
nowknownorhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnection
with reviews or scholarly analysis or material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of
this publication or parts thereof is permitted only under the provisions of the Copyright Law of the
Publisher’slocation,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.
PermissionsforusemaybeobtainedthroughRightsLinkattheCopyrightClearanceCenter.Violations
areliabletoprosecutionundertherespectiveCopyrightLaw.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
While the advice and information in this book are believed to be true and accurate at the date of
publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor
anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with
respecttothematerialcontainedherein.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Preface
This book aims to present an unified view of three different areas of ultra cold
matter, stressing its differences and similarities. We have also tried to reconcile
our two complementary and sometimes conflicting attitudes, related with the
research motivation and the pedagogical purpose. Most of the book is written
with a pedagogical intent, where priority is given to analytical derivations of the
main physicalconceptsand results, over detailed informationaboutthe published
research literature. Every chapter contains, nevertheless a short discussion on
selected experiments and theoretical work. A large number of books have been
publishedonBoseEinsteincondensates,butwehaveapproachedthissubjectfrom
adifferentandsomewhatunconventionalperspective.Ouraimistosuggestanew
approachtotheproblemsinvolvedwiththeproductionofultra-coldatoms,Rydberg
plasmasandBosecondensates.
Weweresurprised,duringthepreparationofthiswork,withthestrongsimilari-
tiesthatcanbefoundinthecollectiveprocessesthatcantakeplaceinbothclassical
andquantumgases,inneutralgasatomswaswellasinplasmas.Wehavetherefore
explored the problems of collective modes in condensed and non-condensedcold
matter. By covering such different fields and such large areas of knowledge, we
couldnotbeexhaustiveandcomplete.Wehaveneverthelessgiven,foreachsubject,
andwheneverpossible,referencestorecentreviewarticleswherethereadercanfind
amoredetailedaccountoftheliterature.
We would like to thank our co-authors in this area, and the stimulating dis-
cussions we had with many researchers, with both theoretical an experimental
backgrounds.We specially want thank Robin Kaiser who gaveus guidancein the
field of atom cooling and confinement, Robert Bingham and Charles Wang for
their fresh and innovativeapproachto quantum coherence,and Padma Shukla for
hisinspirationin the approachofnovelaspects ofultra-coldandstronglycoupled
plasmas.WealsowouldliketothankThomasPohlforveryhelpfuldiscussionson
Rydbergatoms,andJorgeLoureiroforhispreciouscontributionsintheexploration
of new aspects of collective processes. We also thank Gert Brodin and Mattias
Marklund for their support on quantum vacuum problems, and Antonio Serbeto
andGordonRobbfortheiroccasionalcollaborationoncondensates.Researchbeing
v
vi Preface
a collective process itself, our work results from the contributions of several and
sometimesanonymouspeople.Wethankthemall.
Lisbon,Portugal J.T.Mendonc¸a
AubiereCedex,France HugoTerc¸as
Numaincertahorafria
pergunteiaofantasma
queforc¸anosprendia
Perguntas,CarlosDrummonddeAndrade
Contents
1 Introduction................................................................. 1
1.1 ThreePhasesofUltra-coldMatter................................... 1
1.2 HistoricalPerspective................................................ 3
1.3 BookOverview....................................................... 4
References.................................................................... 6
PartI AtomicClouds
2 LaserCooling ............................................................... 9
2.1 AtomintheLaserField.............................................. 9
2.2 LaserCoolingForce.................................................. 14
2.3 DopplerLimit ........................................................ 17
2.4 MagneticTraps....................................................... 18
2.4.1 MultipolarFieldConfiguration ............................ 19
2.4.2 HelmholtzConfiguration................................... 20
2.4.3 IoffeConfiguration ......................................... 20
2.4.4 Anti-HelmholtzConfiguration............................. 21
2.5 SisyphusCooling..................................................... 23
2.6 EvaporativeCooling.................................................. 25
2.7 SympatheticCooling................................................. 29
References.................................................................... 33
3 WaveKineticApproach.................................................... 35
3.1 Wigner-MoyalProcedure............................................ 35
3.1.1 Quasi-distributions ......................................... 36
3.1.2 WeylTransformation....................................... 39
3.1.3 WaveKineticEquation..................................... 41
3.1.4 TheQuasi-classicalLimit.................................. 43
3.2 Center-of-MassEquation ............................................ 44
3.3 WaveKineticDescriptionoftheLaser-AtomInteraction.......... 47
3.4 Two-LevelAtom ..................................................... 48
vii
viii Contents
3.5 LinkswithDynamicsandStatistics................................. 50
3.5.1 Quasi-classicalLimit....................................... 50
3.5.2 MomentumDiffusionandtheDopplerLimit............. 51
3.6 LambdaConfiguration............................................... 53
3.7 TwoCoupledRadiativeTransitions................................. 55
3.8 InfluenceofaBlue-DetunedPump.................................. 58
References.................................................................... 60
4 AtomicClouds .............................................................. 63
4.1 Atom-AtomCollisions............................................... 64
4.2 FeshbachResonances................................................ 69
4.3 CollectiveForces..................................................... 74
4.4 EquilibriumProfiles.................................................. 79
4.4.1 QualitativeDiscussion...................................... 80
4.4.2 QuantitativeModel......................................... 82
4.5 CoulombExpansion.................................................. 84
References.................................................................... 88
5 WavesandOscillationsinClouds......................................... 89
5.1 HybridSound......................................................... 89
5.1.1 FluidDescription........................................... 89
5.1.2 KineticApproach........................................... 91
5.2 Tonks-DattnerModes................................................ 96
5.3 LargeScaleOscillations ............................................. 99
5.3.1 TheCentre-of-MassOscillation ........................... 99
5.3.2 NormalModes.............................................. 100
5.4 NonlinearModeCoupling........................................... 103
5.5 Quasi-linearDiffusion ............................................... 107
5.6 Phaser,thePhononLaser ............................................ 110
References.................................................................... 114
6 PhotonsintheUltra-coldGas............................................. 115
6.1 OpticalProperties .................................................... 116
6.2 ModulationalInstability ............................................. 118
6.3 PhotonBubbles....................................................... 120
6.4 RotonInstability...................................................... 125
6.5 DensityFluctuations ................................................. 131
6.6 CollectiveLaserScattering .......................................... 135
References.................................................................... 138
PartII ThePhysicsofBose-EinsteinCondensates
7 BoseEinsteinCondensates ................................................ 143
7.1 UniformGas.......................................................... 144
7.2 TrappedGas .......................................................... 145
7.3 AtomCorrelations.................................................... 149
Contents ix
7.4 MeanFieldApproximation.......................................... 153
7.5 Thomas-FermiApproximation ...................................... 155
7.6 FluidandKineticFormulations...................................... 158
7.6.1 QuantumFluidEquations.................................. 158
7.6.2 WaveKineticEquation..................................... 160
References.................................................................... 161
8 ElementaryExcitationsinBECs.......................................... 163
8.1 SoundWaves ......................................................... 163
8.2 GlobalOscillations................................................... 165
8.3 KineticProcesses..................................................... 168
8.4 LandauDamping..................................................... 169
8.5 DynamicalInstabilities............................................... 171
8.6 WakefieldsinBose-EinsteinCondensates .......................... 174
References.................................................................... 180
9 Solitons....................................................................... 181
9.1 EffectiveOne-DimensionalGross-PitaevskiiEquation ............ 182
9.2 One-DimensionalDarkandGreySolitons.......................... 184
9.2.1 EnergyoftheSoliton....................................... 187
9.3 TheInverseScatteringTransform................................... 188
9.4 InteractionBetweenTwoDarkSolitons ............................ 189
9.5 BrightSolitons ....................................................... 193
9.6 DarkSolitonsinHarmonicTraps.................................... 194
9.7 TheSolitonGas ...................................................... 197
9.8 SolitonsinTwoDimensions......................................... 200
References.................................................................... 202
10 QuantumFieldTheoryofBECs.......................................... 205
10.1 BogoliubovTheory................................................... 205
10.2 BECDepletion ....................................................... 209
10.3 PhononPairCreation................................................. 211
10.3.1 TimeRefraction............................................. 211
10.3.2 DynamicalCasimirEffect.................................. 215
10.4 AcousticBlackHoles................................................ 217
10.4.1 HawkingRadiation......................................... 218
10.4.2 EffectiveMetricinaCondensate .......................... 219
10.4.3 AcousticHawking(Unruh)Radiation..................... 220
References.................................................................... 222
11 Superfluidity ................................................................ 225
11.1 PhononKinetics...................................................... 225
11.2 PhononFluidEquations.............................................. 228
11.3 SlowPerturbationsintheSuperfluid................................ 230
11.4 SuperfluidCurrents................................................... 232
11.5 PhononLandauDamping............................................ 234
x Contents
11.6 RotonExcitation ..................................................... 235
11.6.1 WaveKineticEquationwithDipolarInteractions ........ 236
11.6.2 DispersionRelation......................................... 237
11.6.3 RotonInstability............................................ 238
References.................................................................... 240
12 RotatingBECs .............................................................. 241
12.1 QuantumVortices .................................................... 241
12.2 VortexNucleation.................................................... 244
12.3 TkachenkoModes.................................................... 245
12.4 RossbyWaves ........................................................ 246
12.5 Rossby-TkatchenkoModes.......................................... 252
12.6 CouplingwithPhotonOAMStates.................................. 254
References.................................................................... 256
13 QuantumCoherence ....................................................... 257
13.1 AtomInterferometry................................................. 257
13.2 TimeInterferometry.................................................. 259
13.3 DecoherenceProcesses .............................................. 262
13.4 GravitationalDecoherence........................................... 265
13.5 JosephsonTunnelingofaCondensate .............................. 269
References.................................................................... 274
PartIII ThePhysicsofUltracoldPlasmas
14 Ultra-coldPlasmas ......................................................... 277
14.1 DifferentPlasmaRegimes ........................................... 278
14.2 BasicPlasmaProperties.............................................. 280
14.3 IonizationProcesses.................................................. 283
14.4 SingleParticleMotion ............................................... 285
14.5 AdiabaticInvariants.................................................. 289
14.6 PlasmaEquations..................................................... 293
14.6.1 KlimontovitchEquation.................................... 294
14.6.2 VlasovEquation............................................ 296
14.6.3 KineticEquationswithCollisions ......................... 298
14.7 FluidEquations....................................................... 299
References.................................................................... 302
15 PhysicsofRydbergPlasmas............................................... 305
15.1 PlasmaExpansionintheCollisionalRegime....................... 306
15.1.1 FreeDiffusion .............................................. 306
15.1.2 AmbipolarDiffusionRegime.............................. 308
15.1.3 RecombinationinVolume.................................. 309
15.2 CollisionlessPlasmaExpansion..................................... 310
15.3 StronglyCoupledIons ............................................... 313
15.3.1 Ion-NeutralCoupling....................................... 313