Nonclassical Effects and Dynamics of Quantum Observables

138 Pages·2022·4.485 MB·English

by  S. Lakshmibala, V. Balakrishnan

SpringerBriefs in Physics
S. Lakshmibala · V. Balakrishnan
Nonclassical Effects and
Dynamics of Quantum
Observables
SpringerBriefs in Physics
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·
S. Lakshmibala V. Balakrishnan
Nonclassical Effects
and Dynamics of Quantum
Observables
S.Lakshmibala V.Balakrishnan
DepartmentofPhysics DepartmentofPhysics
IndianInstituteofTechnologyMadras IndianInstituteofTechnologyMadras
Chennai,India Chennai,India
ISSN 2191-5423 ISSN 2191-5431 (electronic)
SpringerBriefsinPhysics
ISBN 978-3-031-19413-9 ISBN 978-3-031-19414-6 (eBook)
https://doi.org/10.1007/978-3-031-19414-6
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Preface
Ourjobinphysicsistoseethingssimply,tounderstanda
greatmanycomplicatedphenomenainaunifiedway,in
termsofafewsimpleprinciples.
—StevenWeinberg
Thedividebetweenclassicalandquantumphysics,whereandhowthisdivideblurs,
andproposalstoidentifygenuinelyquantumeffectshavebeenaspectsofimmense
interestforresearcherssincetheearlydaysofthediscoveryofquantumlaws.Several
questionsofbothphilosophicalandpracticalimportancehavebeenraisedthrough
differentapproachestounderstandingtheseaspects.Notably,opticsprovidesanideal
platformforexaminingpossibleoverlapsbetweentheclassicalandquantumworlds,
asinterference,coherence,polarization,andevenentanglementcanberecognized,
experimentallytested,andanalyzedwithinboththeclassicalandquantumsettings.
Significantprogressinidentifyinginherentlyquantumeffectshasbeenmadeinrecent
yearsbymeansofnovelexperimentssupportedbytheoreticalarguments.Inmany
situations,however,universallyacceptablequantitiesthatwillunequivocallysignal
theclassicalorquantumnatureofspecificphenomenaarenotavailable.
Notsurprisingly,therefore,diverseapproacheshavebeendevelopedevenwithin
thesettingofoptics,inordertoexaminetheunderlyingnatureofphysicalprocesses
asvariedasphotosynthesis,superradiance,andmanifestationsofentanglement.The
availability of several novel states of light that are nonclassical in the sense that
they depart from ideal coherence, and could exhibit different types of squeezing,
has given tremendous impetus to both theoretical and experimental investigations
aimedatunderstandingtheoverlapbetweentheclassicalandquantumdescriptions.
Theframeworkofspinsystemsandhybridquantumsystemsoflight-matterinterac-
tionsprovidesthepossibilityofexaminingnonclassicaleffectsinrelativelylower-
dimensional Hilbert spaces than those of continuous variables, as exemplified by
theradiationfield.Extensivecurrentresearchusestheseplatformstounderstandthe
natureofgenuinequantumentanglementanditsconnections,ifany,withsqueezing.
Inthiswork,wefocusprimarilyontwoapproachestounderstandingthequantum
regime.Thefirstisbasedontherecognitionthatthebasiclawsofprobabilitytheory
v
vi Preface
governboththeclassicalandquantumdomains.Muchworkisbeingdonetounder-
stand the quantum nature of macroscopic phenomena using tests based on proba-
bilitytheory.Inparticular,werecognizethat,whilequasiprobabilityfunctionssuch
astheWignerdistributionareusedasstandardidentifiersofthenonclassicalityof
quantumstates,thetomogramsfromwhichtheyareconstructedaregenuineproba-
bilitydistributions.Investigationscarriedoutusingonlytomograms(weshallrefer
tothislooselyasthetomographicapproach)couldhelpinunderstandingthelimi-
tations on extracting information about quantum states without undertaking state
reconstruction from tomograms. The second approach is based on the recognition
that the temporal evolution of quantum observables could well be converted into
longtimeseriesofdata,andthetoolsoftimeseriesandnetworkanalysis,whichare
well developed in the treatment of classical dynamical variables, could be applied
tosuchdata.Togetherwiththeunderstandingthatthequantumwavepacketrevival
phenomenonissimilartoPoincarérecurrencesinclassicalphasespace,thisapproach
has the potential to identify the limitations of the classical toolbox in a quantum
setting. Since our focus is primarily on these two approaches, it is inevitable that
thereferencescitedinthisworkcompriseonlyasmallsubsetoftheextensiveand
growingliteratureonnonclassicaleffects,tomograms,andtheanalysisoflargedata
sets.
We acknowledge with pleasure discussions with several former students of
ours over more than two decades, which enhanced our comprehension of several
aspectsofquantumphysics.Inparticular,werecallnumeroushelpfulconversations
withDrs.S.Seshadri,C.Sudheesh,AthreyaShankar,PradipLaha,andB.Sharmila.
Our sincere thanks to Pradip for readily creating and sharing a substantial part of
thecontentsandplotsthatwehaveusedinChaps.3,6,and7.Thisworkwouldnot
havebeenpossiblebutforthepainstakingandtirelesseffortputinbySharmilawho
hasbeenwithusthrougheverystageofthepreparationofthismanuscript,sharing
relevantfilesandformattingthevariouschapters.Ourveryspecialthankstoher.We
alsothankDr.S.Ramananforherinvaluabletechnicalassistanceduringtheprepa-
rationofthemanuscript.Finally,werecordourthankstoDrs.B.Ananthanarayan
(IISc)andLisaScalone(Springer)foreditorialadviceandsupport.
The authors weresupported, inpart,byagrant fromMphasis tothe Center for
QuantumInformation,Communication,andComputing(CQuICC).
We dedicate this work with affectionate gratitude to our respective parents and
grandparents.
Chennai,India S.Lakshmibala
September2022 V.Balakrishnan
Contents
1 Introduction ................................................... 1
References ..................................................... 17
2 Revivals,FractionalRevivalsandTomograms ..................... 21
2.1 Introduction ............................................... 21
2.2 BasicMechanismofWavePacketRevivals ..................... 23
2.3 AnIllustrativeExample ..................................... 24
2.4 SignaturesofRevivalsinExpectationValuesofObservables ...... 26
2.5 EffectofanImperfectlyCoherentInitialState .................. 29
2.6 RevivalsinSingle-ModeSystems:ATomographicApproach ..... 32
2.7 DecoherenceEffects ........................................ 36
2.8 ATomographicApproachtotheDouble-WellBECSystem ....... 37
References ..................................................... 41
3 TomographicApproachtoSqueezing ............................ 43
3.1 Introduction ............................................... 43
3.2 EntropicSqueezingfromOpticalTomograms .................. 45
3.3 Quadrature and Higher-Order Squeezing from Optical
Tomograms ................................................ 48
References ..................................................... 52
4 EntanglementatAvoidedLevelCrossings ........................ 53
4.1 Introduction ............................................... 53
4.2 EntanglementIndicatorsfromOpticalandQubitTomograms ..... 55
4.3 EntanglementIndicatorsandSqueezinginSpinSystems ......... 58
4.4 BipartiteCVModelsandAvoidedLevelCrossings .............. 63
4.5 Avoided Crossings in Multipartite HQ Systems: The
Tavis–CummingsModel ..................................... 66
References ..................................................... 68
vii
viii Contents
5 Dynamics and Entanglement Indicators in Bipartite CV
Systems ....................................................... 71
5.1 Introduction ............................................... 71
5.2 TheBipartiteAtom-FieldInteractionModelRevisited ........... 72
5.2.1 TimeEvolution ...................................... 72
5.2.2 EntanglementDynamics .............................. 75
5.2.3 TomographicEntanglementIndicatorsDuringTime
Evolution ........................................... 77
5.3 TheDouble-WellBECModelRevisited ....................... 79
5.3.1 TimeDevelopment ................................... 79
5.3.2 DecoherenceEffectsintheDouble-WellBECModel ...... 80
References ..................................................... 81
6 DynamicsofEntanglementIndicatorsinHybridQuantum
andSpinSystems ............................................... 83
6.1 Introduction ............................................... 83
6.2 TheDoubleJaynes-CummingsModel ......................... 84
6.2.1 Dynamics ........................................... 84
6.2.2 EquivalentCircuitfortheDJCModelandtheIBMQ
Platform ............................................ 86
6.3 TheDoubleTavis-CummingsModel .......................... 88
6.3.1 TheModel .......................................... 88
6.3.2 EquivalentCircuitandtheIBMQPlatform .............. 88
6.4 BipartiteEntanglementinTripartiteModels .................... 89
6.4.1 TheCavityOptomechanicalSystem .................... 90
6.4.2 (cid:2)-AtomInteractingwithRadiationFields ............... 93
6.5 EntanglementandSqueezinginNMRExperiments .............. 96
6.5.1 NMRExperimentI ................................... 98
6.5.2 BlockadeandFreezinginNuclearSpins ................. 101
6.6 ConcludingRemarks ........................................ 104
References ..................................................... 105
7 Dynamics of the Mean Photon Number: Time Series
andNetworkAnalysis .......................................... 107
7.1 Introduction ............................................... 107
7.2 BriefOverviewofTimeSeriesAnalysis ....................... 108
7.3 TheBipartiteAtom-FieldInteractionModel:TimeSeries
Analysis .................................................. 110
7.3.1 Dynamics ........................................... 110
7.3.2 PowerSpectrumandLyapunovExponent ................ 111
7.3.3 RecurrenceStatistics ................................. 113
7.4 Three-LevelAtomInteractingwithRadiationFields ............. 114
7.5 TheTripartiteHQModelwithIntensity-DependentCouplings .... 116
7.5.1 TheModel .......................................... 116
7.5.2 TimeSeriesAnalysiswithLargeandSmallDataSets ..... 117
7.5.3 ReturnMapsandRecurrenceTimeDistributions ......... 118
Contents ix
7.5.4 RecurrencePlotsandRecurrenceNetwork ............... 119
7.5.5 NetworkAnalysis .................................... 123
7.6 ConcludingRemarks ........................................ 125
References ..................................................... 125
8 ConclusionandOutlook ........................................ 127