Non-equilibrium Dynamics of Tunnel-Coupled Superfluids: Relaxation to a Phase-Locked Equilibrium State in a One-Dimensional Bosonic Josephson Junction PDF
Preview Non-equilibrium Dynamics of Tunnel-Coupled Superfluids: Relaxation to a Phase-Locked Equilibrium State in a One-Dimensional Bosonic Josephson Junction
Springer Theses Recognizing Outstanding Ph.D. Research Marine Pigneur Non-equilibrium Dynamics of Tunnel-Coupled Superfluids Relaxation to a Phase-Locked Equilibrium State in a One-Dimensional Bosonic Josephson Junction Springer Theses Recognizing Outstanding Ph.D. Research Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected foritsscientificexcellenceandthehighimpactofitscontentsforthepertinentfield of research. For greater accessibility to non-specialists, the published versions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explainingthespecialrelevanceoftheworkforthefield.Asawhole,theserieswill provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists. Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria (cid:129) They must be written in good English. (cid:129) ThetopicshouldfallwithintheconfinesofChemistry,Physics,EarthSciences, Engineeringandrelatedinterdisciplinary fields such asMaterials,Nanoscience, Chemical Engineering, Complex Systems and Biophysics. (cid:129) The work reported in the thesis must represent a significant scientific advance. (cid:129) Ifthethesisincludespreviouslypublishedmaterial,permissiontoreproducethis must be gained from the respective copyright holder. (cid:129) They must have been examined and passed during the 12 months prior to nomination. (cid:129) Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. (cid:129) The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field. More information about this series at http://www.springer.com/series/8790 Marine Pigneur Non-equilibrium Dynamics of Tunnel-Coupled fl Super uids Relaxation to a Phase-Locked Equilibrium State in a One-Dimensional Bosonic Josephson Junction Doctoral Thesis accepted by Atominstitut TU Wien, Vienna, Austria 123 Author Supervisor Dr. Marine Pigneur Prof. Hannes-Jörg Schmiedmayer Atominstitut TU Wien Atominstitut TU Wien Vienna,Austria Vienna,Austria ISSN 2190-5053 ISSN 2190-5061 (electronic) SpringerTheses ISBN978-3-030-52843-0 ISBN978-3-030-52844-7 (eBook) https://doi.org/10.1007/978-3-030-52844-7 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2020 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseof illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland ’ Supervisor s Foreword Thequestionifandhowanisolatedmany-bodyquantumsystemrelaxesisacentral problem of modern physics and of high relevance in many diverse fields. It is far from obvious that a system well isolated from its environment can relax at all, as this seems in contradiction with the unitary evolution of quantum mechanics. In recent years, our theoretical understanding has progressed significantly, but experimentalstudiesremainscarce.Itrequirestoovercomeseveralchallengessuch as the realization of truly isolated systems, the highly controlled preparation, and accurate measurement of non-equilibrium dynamics. Ultra-cold atoms thereby are an ideal model system due to the large set of methods to isolate, manipulate, and probe these gases. In this context, the thesis of Marine Pigneur constitutes a landmark as it unambiguously exhibits a relaxation phenomena occurring between two coupled elongated superfluids, known as one-dimensional Bosonic Josephson Junction (1D-BJJ).Theexperimentalrealizationofthissystemreliesonanatomchipdevice, on which micro-fabricated wires allow the precise coherent manipulation of ultra-cold gases using static and radio-frequency magnetic fields. Following a precise preparation protocol, Marine Pigneur initializes various well-controlled quantum states leading to a reproducible non-equilibrium evolution. The resulting dynamics can be investigated in great details through matter-wave interference between the two superfluids. In a first set of experiments, Marine Pigneur prepares the 1D-BJJ with a given phase difference and investigates the subsequent Josephson oscillation dynamics, byprobinginturnthenumberdifferenceandthephasedifferencebetweenthetwo coupled superfluids. She observes a fast relaxation toward an equilibrium state, in whichthetwosuperfluidsarephase-locked.Thisobservationgoesbeyondexisting predictions and challenges our understanding of well-established models for a 1D-BJJ, among which is the sine-Gordon model. Inasecondset,MarinePigneurexploresaregimewherethetwo-tunnel-coupled 1D superfluids differ by their atom number. In this case, she establishes the exis- tence of a relaxation threshold. Below a certain imbalance, still deep inside the v vi Supervisor’sForeword conventionalself-trappingregime,thesystemrelaxestoaphase-lockedequilibrium state. Therefore,herthesisworkestablishestheregimeandconditionsrequired for the relaxation to occur in a 1D-BJJ. Inthebulkofthethesis,MarinePigneurdescribesindetailtheexperimentaland theoretical challenges she had to face. A key issue to unambiguously establish the relaxation was to convincingly distinguish it from dephasing processes. On the theoretical side, the absence of microscopic model reproducing the observation complicated the data analysis. Marine Pigneur therefore developed an analytical model describing the relaxation mechanism in the context of a 1D-BJJ which enabled a much cleaner and robust data analysis. Using the tunability of the experimental setup, Marine Pigneur conducted a broad-ranged study of the relax- ation phenomena according to various parameters, such as the initial energy, the atom number, and the tunnel coupling strength. The dependence of the relaxation time with various experimental conditions is a significant piece of work which initiated an important theoretical effort. The experiments described in this thesis challenge our current theoretical description and constitute an important input to develop an understanding of non-equilibrium dynamics. Vienna, Austria Prof. Hannes-Jörg Schmiedmayer July 2020 Abstract The relaxation of isolated quantum many-body systems is a major unsolved problem of modern physics. It connects to many fundamental questions, ranging from the state of the early universe and heavy-ion collisions to the electron dynamics in condensed matter physics. However, realizations of quantum many-body systems which are both well isolatedfromtheirenvironmentandaccessibletoexperimentalstudyarescarce.In recent years, the field has experienced rapid progress, partly attributed to the unprecedented insights provided by ultra-cold atoms. In this thesis, we present the experimental study of a relaxation phenomenon occurring between two elongated tunnel-coupled superfluids. This system, known asone-dimensionalBosonicJosephsonJunction(1D-BJJ),benefitsfromnumerous advantages. From an experimental point of view, the 1D-BJJ presents the versa- tility, high controllability, and isolability characteristic to ultra-cold atom systems. Thisallowsarigorousandwide-rangingstudyoftherelaxation.Fromatheoretical point of view, the 1D-BJJ benefits from extensive theoretical works provided in particular by the sine-Gordon model. This model has proven successful in describing the equilibrium dynamics of two coupled 1D atomic superfluids up to veryhigh-ordercorrelations.However,itfailstodescribetherelaxationweobserve and it is therefore strongly challenged by this work. In a first set of experiments, a well-defined non-equilibrium state is created by coherent splitting of a single one-dimensional Bose gas into two halves. A precise phase difference between the two halves is introduced while preserving a high phase coherence. The subsequent dynamics exhibit a relaxation to a phase-locked equilibriumstatecontradictingtheoreticalpredictions.Wesupporttheexperimental results with an empirical model that allows quantitative discussions. Various experimental parameters, among which the atom number and the tunnel coupling strength, are varied to investigate their impact on the relaxation mechanism and to help determining its origin. The second experiment investigates the dynamics of a pair of 1D Bose gases differing by their atomic density. In this case, the system presents a more complex distribution of excitations and its dynamics exhibits a threshold above which the vii viii Abstract relaxation is dominated by a dephasing. It provides additional insights into the relaxationmechanismassomeexperimentalparameters,suchasthetrapgeometry, become more relevant in this case compared to the first set of experiments. These observations attest to the existence of a relaxation phenomenon in a 1D-BJJ and illustrate how strongly the non-equilibrium dynamics differ from the equilibriumone,whichiswelldescribedbythermodynamicsandstatisticalphysics. Preface How and to which extent does an isolated quantum many-body system relax? The question is as relevant as it is puzzling. Relevant first, because it is an open problem covering vastly different scales of energy, length, and time. It ranges from the expansion dynamics of the early universe [1–3] and the physics of quark-gluon plasmas [4–6] to the coherence properties of solid-state materials [7–10] and future quantum information devices [11]. Therefore, a thorough understanding could both clarify the origins of our universe and lead to important technological advances. Puzzlingalso,becauseitappearsasacontradiction.Aphenomenonofrelaxation generally implies a dissipation of energy from the system through its interaction withanenvironment.However,inanisolatedquantummany-bodysystem,suchan environment is by definition absent, such that a relaxation seems in contradiction with a unitary evolution. In recent years, both theoretical and experimental works proved that non-integrable systems can reach a thermal equilibrium state resem- bling a Gibbs ensemble [12–21]. A more precise formulation of the question is: how can the unitary non-equilibrium evolution of an isolated quantum many-body system lead to observables which relax to steady, thermal expectation values? To address this question, the experimentalist must face several challenges such astherealizationoftrulyisolatedsystemsandthehighlycontrolledpreparationand accuratemeasurementofnon-equilibrium dynamics.Overthelastyears,ultra-cold gases have been established as ideal model systems in this context [22]. The large set of methods to isolate, manipulate, and probe these gases [23] resulted in unprecedented advances. The most remarkable example illustrating the versatility ofultra-coldgasesmightbetheirtunableinteractions[24,25]andtheirapplication as quantum simulators [26]. To extract information, these systems can be probed with single-atom sensitivity [27–29]. In particular, the experimental realization of one-dimensional (1D) quantum gases enables a detailed study of numerous theoretical models [30, 31], among which are the Luttinger liquids [32, 33] and the sine-Gordon models [34–38]. The 1D Bose gas is an example of integrable systems [39], for which the existence of ix
The list of books you might like
