[en] We demonstrate how the initial state of ultracold atoms in an optical lattice controls the emergence of ergodic dynamics as the underlying spectral structure is tuned into the quantum chaotic regime. Distinct initial states' chaos threshold values in terms of tunneling as compared to interaction strength are identified, as well as dynamical signatures of the chaos transition, on the level of experimentally accessible observables and time scales.
Disciplines :
Physics
Author, co-author :
Pausch, Lukas ; Université de Liège - ULiège > Département de physique > Optique quantique
Carnio, Edoardo G ; Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany ; EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
Buchleitner, Andreas; Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany ; EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
Rodríguez, Alberto ; Departamento de Física Fundamental, Universidad de Salamanca, E-37008 Salamanca, Spain ; Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca, E-37008 Salamanca, Spain
Language :
English
Title :
How to seed ergodic dynamics of interacting bosons under conditions of many-body quantum chaos.
Publication date :
2025
Journal title :
Reports on Progress in Physics
ISSN :
0034-4885
eISSN :
1361-6633
Publisher :
Institute of Physics Publishing (IOP), England
Volume :
88
Issue :
5
Pages :
057602
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
AEI - Agencia Estatal de Investigación DFG - Deutsche Forschungsgemeinschaft ERDF - European Regional Development Fund FWO - Fonds Wetenschappelijk Onderzoek Vlaanderen
Funding text :
A R thanks Marcos Rigol for helpful discussions. The authors acknowledge support by the state of Baden-W\u00FCrttemberg through bwHPC and the German Research Foundation (DFG) through Grants No. INST 40/467-1 FUGG (JUSTUS cluster), No. INST 40/575-1 FUGG (JUSTUS 2 cluster), and No. 402552777, and by Ministerio de Ciencia e Innovaci\u00F3n/Agencia Estatal de Investigaci\u00F3n (Spain) through Grant No. PID2020-114830GB-I00. E.G.C. acknowledges support from the Georg H Endress foundation. This project (EOS 40007526) has received funding from the FWO and F.R.S-FNRS under the Excellence of Science (EOS) programme. This research has made use of the high performance computing resources of the Castilla y Le\u00F3n Supercomputing Center (SCAYLE, www.scayle.es), financed by the European Regional Development Fund (ERDF), and of the CSUC (Consorci de Serveis Universitaris de Catalunya) supercomputing resources. We thankfully acknowledge RES resources provided by the Galician Supercomputing Center (CESGA) in FinisTerrae III to activity FI-2024-2-0027. The supercomputer FinisTerrae III and its permanent data storage system have been funded by the Spanish Ministry of Science and Innovation, the Galician Government and the European Regional Development Fund (ERDF).
Hittmair O 1972 Lehrbuch der Quantentheorie Verlag Karl Thiemig
Geisel T Radons G Rubner J 1986 Kolmogorov-Arnol’d-Moser barriers in the quantum dynamics of chaotic systems Phys. Rev. Lett. 57 2883 10.1103/PhysRevLett.57.2883
Du M L Delos J B 1987 Effect of closed classical orbits on quantum spectra: Ionization of atoms in a magnetic field Phys. Rev. Lett. 58 1731 10.1103/PhysRevLett.58.1731
Brunner E Pausch L Carnio E G Dufour G Rodríguez A Buchleitner A 2023 Many-Body Interference at the Onset of Chaos Phys. Rev. Lett. 130 080401 10.1103/PhysRevLett.130.080401
1989 Chaos and Quantum Physics École d’été de Physique théorique des Houches, Session LII Giannoni M-J Voros A Zinn-Justin J North Holland
Buchleitner A Delande D 1993 Quantum dynamics of a circular rydberg state in a microwave field Phys. Rev. Lett. 71 3633 10.1103/PhysRevLett.71.3633
Carvalho A R R Buchleitner A 2004 Web-assisted tunneling in the kicked harmonic oscillator Phys. Rev. Lett. 93 204101 10.1103/PhysRevLett.93.204101
Brünner T Dufour G Rodríguez A Buchleitner A 2018 Signatures of indistinguishability in Bosonic Many-Body Dynamics Phys. Rev. Lett. 120 210401 10.1103/PhysRevLett.120.210401
Evrard B Pizzi A Mistakidis S I Dag C B 2024 Quantum many-body scars from unstable periodic orbits Phys. Rev. B 110 144302 10.1103/PhysRevB.110.144302
Berry M V 1977 Regular and irregular semiclassical wavefunctions J. Phys. A: Gen. Phys. 10 2083 10.1088/0305-4470/10/12/016
Tanner G Richter K Rost J-M 2000 The theory of two-electron atoms: between ground state and complete fragmentation Rev. Mod. Phys. 72 497 10.1103/RevModPhys.72.497
Gutzwiller M C 1990 Chaos in Classical and Quantum Mechanics Springer
Laskar J 1993 Frequency analysis for multi-dimensional systems. global dynamics and diffusion Physica D 67 257 10.1016/0167-2789(93)90210-R
von Milczewski J Diercksen G H F Uzer T 1996 Computation of the arnol’d web for the hydrogen atom in crossed electric and magnetic fields Phys. Rev. Lett. 76 2890 10.1103/PhysRevLett.76.2890
Schlagheck P Buchleitner A 1999 Stable classical configurations in strongly driven helium Physica D 131 110 10.1016/S0167-2789(98)00223-1
Stöber J Bäcker A Ketzmerick R 2024 Quantum transport through partial barriers in higher-dimensional systems Phys. Rev. Lett. 132 047201 10.1103/PhysRevLett.132.047201
Jaksch D Bruder C Cirac J I Gardiner C W Zoller P 1998 Cold bosonic atoms in optical lattices Phys. Rev. Lett. 81 3108 10.1103/PhysRevLett.81.3108
Trimborn F Witthaut D Korsch H J 2009 Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase-space approach Phys. Rev. A 79 013608 10.1103/PhysRevA.79.013608
Buchleitner A Kolovsky A R 2003 Interaction-induced decoherence of atomic bloch oscillations Phys. Rev. Lett. 91 253002 10.1103/PhysRevLett.91.253002
Kolovsky A R Buchleitner A 2004 Quantum chaos in the Bose-Hubbard model Europhys. Lett. 68 632 10.1209/epl/i2004-10265-7
Ponomarev A V Madro nero J Kolovsky A R Buchleitner A 2006 Atomic current across an optical lattice Phys. Rev. Lett. 96 050404 10.1103/PhysRevLett.96.050404
Biroli G Kollath C Läuchli A M 2010 Effect of rare fluctuations on the thermalization of isolated quantum systems Phys. Rev. Lett. 105 250401 10.1103/PhysRevLett.105.250401
Kollath C Roux G Biroli G Läuchli A M 2010 Statistical properties of the spectrum of the extended Bose-Hubbard model J. Stat. Mech. Theory Exp. 2010 08011 10.1088/1742-5468/2010/08/P08011
Beugeling W Moessner R Haque M 2014 Finite-size scaling of eigenstate thermalization Phys. Rev. E 89 042112 10.1103/PhysRevE.89.042112
Beugeling W Moessner R Haque M 2015 Off-diagonal matrix elements of local operators in many-body quantum systems Phys. Rev. E 91 012144 10.1103/PhysRevE.91.012144
Beugeling W Andreanov A Haque M 2015 Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy J. Stat. Mech. Theory Exp. 2015 02002 10.1088/1742-5468/2015/02/P02002
Dubertrand R Müller S 2016 Spectral statistics of chaotic many-body systems New J. Phys. 18 033009 10.1088/1367-2630/18/3/033009
Beugeling W Bäcker A Moessner R Haque M 2018 Statistical properties of eigenstate amplitudes in complex quantum systems Phys. Rev. E 98 022204 10.1103/PhysRevE.98.022204
de la Cruz J Lerma-Hernández S Hirsch J G 2020 Quantum chaos in a system with high degree of symmetries Phys. Rev. E 102 032208 10.1103/PhysRevE.102.032208
Russomanno A Fava M Fazio R 2020 Nonergodic behavior of the clean Bose-Hubbard chain Phys. Rev. B 102 144302 10.1103/PhysRevB.102.144302
Pausch L Carnio E G Rodríguez A Buchleitner A 2021 Chaos and ergodicity across the energy spectrum of interacting bosons Phys. Rev. Lett. 126 150601 10.1103/PhysRevLett.126.150601
Pausch L Carnio E G Buchleitner A Rodríguez A 2021 Chaos in the Bose-Hubbard model and random two-body Hamiltonians New J. Phys. 23 123036 10.1088/1367-2630/ac3c0d
Pausch L Buchleitner A Carnio E G Rodríguez A 2022 Optimal route to quantum chaos in the Bose-Hubbard model J. Phys. A 55 324002 10.1088/1751-8121/ac7e0b
Kollath C Läuchli A M Altman E 2007 Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model Phys. Rev. Lett. 98 180601 10.1103/PhysRevLett.98.180601
Läuchli A M Kollath C 2008 Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model J. Stat. Mech. Theory Exp. 2008 05018 10.1088/1742-5468/2008/05/P05018
Cramer M Flesch A McCulloch I P Schollwöck U Eisert J 2008 Exploring local quantum many-body relaxation by atoms in optical superlattices Phys. Rev. Lett. 101 063001 10.1103/PhysRevLett.101.063001
Roux G 2009 Quenches in quantum many-body systems: one-dimensional Bose-Hubbard model reexamined Phys. Rev. A 79 021608 (R) 10.1103/PhysRevA.79.021608
Roux G 2010 Finite-size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model Phys. Rev. A 81 053604 10.1103/PhysRevA.81.053604
Barmettler P Poletti D Cheneau M Kollath C 2012 Propagation front of correlations in an interacting Bose gas Phys. Rev. A 85 053625 10.1103/PhysRevA.85.053625
Vidmar L Langer S McCulloch I P Schneider U Schollwöck U Heidrich-Meisner F 2013 Sudden expansion of Mott insulators in one dimension Phys. Rev. B 88 235117 10.1103/PhysRevB.88.235117
Meinert F Mark M J Kirilov E Lauber K Weinmann P Gröbner M Nägerl H-C 2014 Interaction-Induced quantum phase revivals and evidence for the transition to the quantum chaotic regime in 1D atomic bloch oscillations Phys. Rev. Lett. 112 193003 10.1103/PhysRevLett.112.193003
Sorg S Vidmar L Pollet L Heidrich-Meisner F 2014 Relaxation and thermalization in the one-dimensional Bose-Hubbard model: a case study for the interaction quantum quench from the atomic limit Phys. Rev. A 90 033606 10.1103/PhysRevA.90.033606
Andraschko F Sirker J 2015 Propagation of a single-hole defect in the one-dimensional Bose-Hubbard model Phys. Rev. B 91 235132 10.1103/PhysRevB.91.235132
Despres J Villa L Sanchez-Palencia L 2019 Twofold correlation spreading in a strongly correlated lattice Bose gas Sci. Rep. 9 4135 10.1038/s41598-019-40679-3
Wittmann W. K Castro E R Foerster A Santos L F 2022 Interacting bosons in a triple well: preface of many-body quantum chaos Phys. Rev. E 105 034204 10.1103/PhysRevE.105.034204
Berke C Varvelis E Trebst S Altland A DiVincenzo D P 2022 Transmon platform for quantum computing challenged by chaotic fluctuations Nat. Commun. 13 2495 10.1038/s41467-022-29940-y
Basilewitsch D Börner S-D Berke C Altland A Trebst S Koch C P 2023 Chaotic fluctuations in a universal set of transmon qubit gates (arXiv: 2311.14592)
Börner S-D Berke C DiVincenzo D P Trebst S Altland A 2024 Classical chaos in quantum computers Phys. Rev. Res. 6 033128 10.1103/PhysRevResearch.6.033128
Choi J et al 2023 Preparing random states and benchmarking with many-body quantum chaos Nature 613 468 10.1038/s41586-022-05442-1
Mark D K Choi J Shaw A L Endres M Choi S 2023 Benchmarking quantum simulators using ergodic quantum dynamics Phys. Rev. Lett. 131 110601 10.1103/PhysRevLett.131.110601
Lewenstein M Sanpera A Ahufinger V Damski B Sen A Sen U 2007 Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond Adv. Phys. 56 243 10.1080/00018730701223200
Bloch I Dalibard J Zwerger W 2008 Many-body physics with ultracold gases Rev. Mod. Phys. 80 885 10.1103/RevModPhys.80.885
Cazalilla M A Citro R Giamarchi T Orignac E Rigol M 2011 One dimensional bosons: from condensed matter systems to ultracold gases Rev. Mod. Phys. 83 1405 10.1103/RevModPhys.83.1405
Krutitsky K V 2016 Ultracold bosons with short-range interaction in regular optical lattices Phys. Rep. 607 1 10.1016/j.physrep.2015.10.004
Pausch L 2022 Eigenstate structure and quantum chaos in the Bose-Hubbard Hamiltonian Dissertation Albert-Ludwigs-Universität Freiburg 10.6094/UNIFR/228554
Cheneau M Barmettler P Poletti D Endres M Schauß P Fukuhara T Gross C Bloch I Kollath C Kuhr S 2012 Light-cone-like spreading of correlations in a quantum many-body system Nature 481 484 10.1038/nature10748
Meinert F Mark M J Kirilov E Lauber K Weinmann P Grobner M Daley A J Nagerl H-C 2014 Observation of many-body dynamics in long-range tunneling after a quantum quench Science 344 1259 10.1126/science.1248402
Kaufman A M Tai M E Lukin A Rispoli M Schittko R Preiss P M Greiner M 2016 Quantum thermalization through entanglement in an isolated many-body system Science 353 794 10.1126/science.aaf6725
Rispoli M Lukin A Schittko R Kim S Tai M E Léonard J Greiner M 2019 Quantum critical behaviour at the many-body localization transition Nature 573 385 10.1038/s41586-019-1527-2
Lukin A Rispoli M Schittko R Tai M E Kaufman A M Choi S Khemani V Léonard J Greiner M 2019 Probing entanglement in a many-body-localized system Science 364 256 10.1126/science.aau0818
Bohrdt A Kim S Lukin A Rispoli M Schittko R Knap M Greiner M Léonard J 2021 Analyzing nonequilibrium quantum states through snapshots with artificial neural networks Phys. Rev. Lett. 127 150504 10.1103/PhysRevLett.127.150504
Takasu Y Yagami T Asaka H Fukushima Y Nagao K Goto S Danshita I Takahashi Y 2020 Energy redistribution and spatiotemporal evolution of correlations after a sudden quench of the Bose-Hubbard model Sci. Adv. 6 eaba9255 10.1126/sciadv.aba9255
Léonard J Kim S Rispoli M Lukin A Schittko R Kwan J Demler E Sels D Greiner M 2023 Probing the onset of quantum avalanches in a many-body localized system Nat. Phys. 19 481 10.1038/s41567-022-01887-3
Trotzky S Chen Y A Flesch A McCulloch I P Schollwöck U Eisert J Bloch I 2012 Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas Nat. Phys. 8 325 10.1038/nphys2232
Bordia P Lüschen H P Hodgman S S Schreiber M Bloch I Schneider U 2016 Coupling identical one-dimensional many-body localized systems Phys. Rev. Lett. 116 140401 10.1103/PhysRevLett.116.140401
Rubio-Abadal A Choi J-Y Zeiher J Hollerith S Rui J Bloch I Gross C 2019 Many-Body delocalization in the presence of a quantum bath Phys. Rev. X 9 041014 10.1103/PhysRevX.9.041014
Ronzheimer J P Schreiber M Braun S Hodgman S S Langer S McCulloch I P Heidrich-Meisner F Bloch I Schneider U 2013 Expansion dynamics of interacting bosons in homogeneous lattices in one and two dimensions Phys. Rev. Lett. 110 205301 10.1103/PhysRevLett.110.205301
Choi J-Y Hild S Zeiher J Schauß P Rubio-Abadal A Yefsah T Khemani V Huse D A Bloch I Gross C 2016 Exploring the many-body localization transition in two dimensions Science 352 1547 10.1126/science.aaf8834
Lindinger J Buchleitner A Rodríguez A 2019 Many-Body multifractality throughout bosonic superfluid and mott insulator phases Phys. Rev. Lett. 122 106603 10.1103/PhysRevLett.122.106603
Note that this staggered state is not uniquely defined, since the sites may be sorted into any order without changing the energy. However, as they all have the same energy and similar energy widths, they will exhibit qualitatively the same dynamical behavior.
This is due to the fact that the mean energy of any Fock state depends only on the interaction term. Thus, as γ → ∞, the corresponding ɛ is entirely defined by the spectral bounds E max = − E min = 2 N J, yielding ɛ → 0.5.
Haake F Gnutzmann S Kuś M 2018 Quantum Signatures of Chaos (Springer Series in Synergetics) Haken H Springer 10.1007/978-3-319-97580-1
It must be noted, though, that the thermodynamic limit here under closer inspection is distinct from the semiclassical limit which is at the very core of quantum chaos, inasmuch as, in the latter limit, characteristic quantum features are compared to a well-defined underlying classical phase space structure. Since the density is fixed in the thermodynamic limit, and the particle number N is increased, so has to increase the lattice’s length L, and thus the number of degrees of freedom, which, in turn, controls the dimension of phase space. Taking the thermodynamic limit we thus simultaneously send the phase space dimension to infinity.
Castro E R W. K W Chávez-Carlos J Roditi I Foerster A Hirsch J G 2024 Quantum-classical correspondence in a triple-well bosonic model: from integrability to chaos Phys. Rev. A 109 032225 10.1103/PhysRevA.109.032225
Hiller M Kottos T Geisel T 2006 Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates Phys. Rev. A 73 061604 (R) 10.1103/PhysRevA.73.061604
Hiller M Kottos T Geisel T 2009 Wave-packet dynamics in energy space of a chaotic trimeric Bose-Hubbard system Phys. Rev. A 79 023621 10.1103/PhysRevA.79.023621
Note that the oscillations observable on transient time scales before equilibration can be attributed to particles being reflected at the edge sites: such oscillations are prominently seen in the chaotic γ-range, and the their frequency is found to decrease as the lattice, and hence the time to travel from one edge to another, becomes larger.
Srednicki M 1996 Thermal fluctuations in quantized chaotic systems J. Phys. A: Math. Gen. 29 L75 10.1088/0305-4470/29/4/003
Srednicki M 1999 The approach to thermal equilibrium in quantized chaotic systems J. Phys. A: Math. Gen. 32 1163 10.1088/0305-4470/32/7/007
Venzl H Daley A J Mintert F Buchleitner A 2009 Statistics of Schmidt coefficients and the simulability of complex quantum systems Phys. Rev. E 79 056223 10.1103/PhysRevE.79.056223
Weiße A Fehske H 2008 Chebyshev expansion techniques Computational Many-Particle Physics Springer pp 545 77 pp 545-77
Balay S et al 2023 PETSc/TAO Users Manual Technical Report ANL-21/39 - Revision 3.20 Argonne National Laboratory 10.2172/2205494
Balay S Gropp W D McInnes L C Smith B F 1997 Efficient management of parallelism in object oriented numerical software libraries Modern Software Tools in Scientific Computing Arge E A M Bruaset H P Langtangen Birkhäuser Press 163 202 163-202
Balay S et al 2023 Petsc Web Page (available at: https://petsc.org/)
Hernandez V Roman J E Vidal V 2005 SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems ACM Trans. Math. Softw. 31 351 10.1145/1089014.1089019