- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Measurement of total phase fluctuation in cold-atomic quantum simulators

Taufiq Murtadho1,*, Federica Cataldini2, Sebastian Erne2, Marek Gluza1, Mohammadamin Tajik2, Jörg Schmiedmayer2, and Nelly H. Y. Ng1,†

  • *Contact author: fiqmurtadho@gmail.com
  • †Contact author: nelly.ng@ntu.edu.sg
PDF

Phys. Rev. Research 7, L022031 – Published 7 May, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022031

Abstract

Studying the dynamics of quantum many-body systems is often constrained by the limitations in probing relevant observables, especially in continuous systems. A powerful method to gain information about such systems is the reconstruction of local currents from the continuity equation. We show that this approach can be used to extract the total phase fluctuation of adjacent Bose gases. We validate our technique numerically and demonstrate its effectiveness by analyzing data from selected experiments simulating 1D quantum field theories through the phase difference of two parallel 1D Bose gases. This analysis reveals the previously hidden sector of the sum mode of the phase, which is important for studying long-time thermalization and out-of-equilibrium dynamics of the system. Our method is general and can be applied to other cold atom systems with spatial phase gradients, thereby expanding the scope and capabilities of cold-atomic quantum simulators.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (61)

  1. I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
  2. E. Altman, K. R. Brown, G. Carleo, L. D. Carr, E. Demler, C. Chin, B. DeMarco, S. E. Economou, M. A. Eriksson, K.-M. C. Fu, M. Greiner, K. R. Hazzard, R. G. Hulet, A. J. Kollár, B. L. Lev, M. D. Lukin, R. Ma, X. Mi, S. Misra, C. Monroe et al., Quantum simulators: Architectures and opportunities, PRX Quantum 2, 017003 (2021).
  3. A. J. Daley, Twenty-five years of analogue quantum simulation, Nat. Rev. Phys. 5, 702 (2023).
  4. I. Bloch, J. Dalibard, and S. Nascimbene, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012).
  5. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  6. C. Viermann, M. Sparn, N. Liebster, M. Hans, E. Kath, Á. Parra-López, M. Tolosa-Simeón, N. Sánchez-Kuntz, T. Haas, H. Strobel et al., Quantum field simulator for dynamics in curved spacetime, Nature (London) 611, 260 (2022).
  7. T. Langen, R. Geiger, and J. Schmiedmayer, Ultracold atoms out of equilibrium, Annu. Rev. Condens. Matter Phys. 6, 201 (2015).
  8. T. Barthel and J. Lu, Fundamental limitations for measurements in quantum many-body systems, Phys. Rev. Lett. 121, 080406 (2018).
  9. A. Impertro, S. Karch, J. F. Wienand, S. J. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Local readout and control of current and kinetic energy operators in optical lattices, Phys. Rev. Lett. 133, 063401 (2024).
  10. M. Gluza, T. Schweigler, B. Rauer, C. Krumnow, J. Schmiedmayer, and J. Eisert, Quantum read-out for cold atomic quantum simulators, Commun. Phys. 3, 12 (2020).
  11. E. Wybo, A. Bastianello, M. Aidelsburger, I. Bloch, and M. Knap, Preparing and analyzing solitons in the sine-Gordon model with quantum gas microscopes, PRX Quantum 4, 030308 (2023).
  12. M. Gring, M. Kuhnert, T. Langen, T. Kitagawa, B. Rauer, M. Schreitl, I. Mazets, D. A. Smith, E. Demler, and J. Schmiedmayer, Relaxation and prethermalization in an isolated quantum system, Science 337, 1318 (2012).
  13. T. Langen, R. Geiger, M. Kuhnert, B. Rauer, and J. Schmiedmayer, Local emergence of thermal correlations in an isolated quantum many-body system, Nat. Phys. 9, 640 (2013).
  14. M. Tajik, M. Gluza, N. Sebe, P. Schüttelkopf, F. Cataldini, J. Sabino, F. Møller, S.-C. Ji, S. Erne, G. Guarnieri et al., Experimental observation of curved light-cones in a quantum field simulator, Proc. Natl. Acad. Sci. USA 120, e2301287120 (2023).
  15. T. Langen, S. Erne, R. Geiger, B. Rauer, T. Schweigler, M. Kuhnert, W. Rohringer, I. E. Mazets, T. Gasenzer, and J. Schmiedmayer, Experimental observation of a generalized Gibbs ensemble, Science 348, 207 (2015).
  16. B. Rauer, S. Erne, T. Schweigler, F. Cataldini, M. Tajik, and J. Schmiedmayer, Recurrences in an isolated quantum many-body system, Science 360, 307 (2018).
  17. M. Tajik, I. Kukuljan, S. Sotiriadis, B. Rauer, T. Schweigler, F. Cataldini, J. Sabino, F. Møller, P. Schüttelkopf, S.-C. Ji et al., Verification of the area law of mutual information in a quantum field simulator, Nat. Phys. 19, 1022 (2023).
  18. S. Aimet, M. Tajik, G. Tournaire, P. Schüttelkopf, J. Sabino, S. Sotiriadis, G. Guarnieri, J. Schmiedmayer, and J. Eisert, Experimentally probing Landauer's principle in the quantum many-body regime, arXiv:2407.21690.
  19. T. Schweigler, V. Kasper, S. Erne, I. Mazets, B. Rauer, F. Cataldini, T. Langen, T. Gasenzer, J. Berges, and J. Schmiedmayer, Experimental characterization of a quantum many-body system via higher-order correlations, Nature (London) 545, 323 (2017).
  20. T. Schweigler, M. Gluza, M. Tajik, S. Sotiriadis, F. Cataldini, S.-C. Ji, F. S. Møller, J. Sabino, B. Rauer, J. Eisert et al., Decay and recurrence of non-Gaussian correlations in a quantum many-body system, Nat. Phys. 17, 559 (2021).
  21. D. A. Smith, S. Aigner, S. Hofferberth, M. Gring, M. Andersson, S. Wildermuth, P. Krüger, S. Schneider, T. Schumm, and J. Schmiedmayer, Absorption imaging of ultracold atoms on atom chips, Opt. Express 19, 8471 (2011).
  22. Y. D. van Nieuwkerk, J. Schmiedmayer, and F. Essler, Projective phase measurements in one-dimensional bose gases, SciPost Phys. 5, 046 (2018).
  23. T. Murtadho, M. Gluza, K. Z. Arifa, S. Erne, J. Schmiedmayer, and N. H. Y. Ng, Systematic analysis of relative phase extraction in one-dimensional Bose gases interferometry, SciPost Phys. 18, 065 (2025).
  24. T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, Oxford, 2003), Vol. 121.
  25. A. A. Burkov, M. D. Lukin, and E. Demler, Decoherence dynamics in low-dimensional cold atom interferometers, Phys. Rev. Lett. 98, 200404 (2007).
  26. I. Mazets and J. Schmiedmayer, Dephasing in two decoupled one-dimensional Bose-Einstein condensates and the subexponential decay of the interwell coherence, Eur. Phys. J. B 68, 335 (2009).
  27. S. Huber, M. Buchhold, J. Schmiedmayer, and S. Diehl, Thermalization dynamics of two correlated bosonic quantum wires after a split, Phys. Rev. A 97, 043611 (2018).
  28. H.-P. Stimming, N. J. Mauser, J. Schmiedmayer, and I. E. Mazets, Dephasing in coherently split quasicondensates, Phys. Rev. A 83, 023618 (2011).
  29. V. Gritsev, A. Polkovnikov, and E. Demler, Linear response theory for a pair of coupled one-dimensional condensates of interacting atoms, Phys. Rev. B 75, 174511 (2007).
  30. S. Dettmer, D. Hellweg, P. Ryytty, J. J. Arlt, W. Ertmer, K. Sengstock, D. S. Petrov, G. V. Shlyapnikov, H. Kreutzmann, L. Santos, and M. Lewenstein, Observation of phase fluctuations in elongated Bose-Einstein condensates, Phys. Rev. Lett. 87, 160406 (2001).
  31. D. Hellweg, S. Dettmer, P. Ryytty, J. Arlt, W. Ertmer, K. Sengstock, D. Petrov, G. Shlyapnikov, H. Kreutzmann, L. Santos et al., Phase fluctuations in Bose-Einstein condensates, Appl. Phys. B 73, 781 (2001).
  32. A. Imambekov, I. E. Mazets, D. S. Petrov, V. Gritsev, S. Manz, S. Hofferberth, T. Schumm, E. Demler, and J. Schmiedmayer, Density ripples in expanding low-dimensional gases as a probe of correlations, Phys. Rev. A 80, 033604 (2009).
  33. S. Manz, R. Bücker, T. Betz, C. Koller, S. Hofferberth, I. E. Mazets, A. Imambekov, E. Demler, A. Perrin, J. Schmiedmayer, and T. Schumm, Two-point density correlations of quasicondensates in free expansion, Phys. Rev. A 81, 031610(R) (2010).
  34. P. E. Tavares, A. R. Fritsch, G. D. Telles, M. S. Hussein, F. Impens, R. Kaiser, and V. S. Bagnato, Matter wave speckle observed in an out-of-equilibrium quantum fluid, Proc. Natl. Acad. Sci. USA 114, 12691 (2017).
  35. D. S. Petrov, G. V. Shlyapnikov, and J. T. M. Walraven, Phase-fluctuating 3D Bose-Einstein condensates in elongated traps, Phys. Rev. Lett. 87, 050404 (2001).
  36. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022031 for details on the sampling method, experimental protocols, and extended numerical and experimental data.
  37. T. Schumm, S. Hofferberth, L. M. Andersson, S. Wildermuth, S. Groth, I. Bar-Joseph, J. Schmiedmayer, and P. Krüger, Matter-wave interferometry in a double well on an atom chip, Nat. Phys. 1, 57 (2005).
  38. S. Hofferberth, I. Lesanovsky, T. Schumm, A. Imambekov, V. Gritsev, E. Demler, and J. Schmiedmayer, Probing quantum and thermal noise in an interacting many-body system, Nat. Phys. 4, 489 (2008).
  39. Throughout this paper, we ignore interaction-induced broadening which introduces a density-dependent width σ2(z)=σ021+asn0(z)≈σ02.
  40. M. J. Steel, M. K. Olsen, L. I. Plimak, P. D. Drummond, S. M. Tan, M. J. Collett, D. F. Walls, and R. Graham, Dynamical quantum noise in trapped Bose-Einstein condensates, Phys. Rev. A 58, 4824 (1998).
  41. A. Sinatra, C. Lobo, and Y. Castin, The truncated Wigner method for Bose-condensed gases: limits of validity and applications1, J. Phys. B 35, 3599 (2002).
  42. H.-P. Stimming, N. J. Mauser, J. Schmiedmayer, and I. E. Mazets, Fluctuations and stochastic processes in one-dimensional many-body quantum systems, Phys. Rev. Lett. 105, 015301 (2010).
  43. M. Olshanii, Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons, Phys. Rev. Lett. 81, 938 (1998).
  44. P. Ruggiero, L. Foini, and T. Giamarchi, Large-scale thermalization, prethermalization, and impact of temperature in the quench dynamics of two unequal Luttinger liquids, Phys. Rev. Res. 3, 013048 (2021).
  45. F. Møller, T. Schweigler, M. Tajik, J. a. Sabino, F. Cataldini, S.-C. Ji, and J. Schmiedmayer, Thermometry of one-dimensional Bose gases with neural networks, Phys. Rev. A 104, 043305 (2021).
  46. F. Cataldini, F. Møller, M. Tajik, J. A. Sabino, S.-C. Ji, I. Mazets, T. Schweigler, B. Rauer, and J. Schmiedmayer, Emergent Pauli blocking in a weakly interacting Bose gas, Phys. Rev. X 12, 041032 (2022).
  47. M. Gluza, T. Schweigler, M. Tajik, J. Sabino, F. Cataldini, F. S. Møller, S.-C. Ji, B. Rauer, J. Schmiedmayer, J. Eisert et al., Mechanisms for the emergence of Gaussian correlations, SciPost Phys. 12, 113 (2022).
  48. J. N. Kupferschmidt and E. J. Mueller, Role of interactions in time-of-flight expansion of atomic clouds from optical lattices, Phys. Rev. A 82, 023618 (2010).
  49. A. Burchianti, C. D'Errico, L. Marconi, F. Minardi, C. Fort, and M. Modugno, Effect of interactions in the interference pattern of Bose-Einstein condensates, Phys. Rev. A 102, 043314 (2020).
  50. S. Cuomo, V. S. Di Cola, F. Giampaolo, G. Rozza, M. Raissi, and F. Piccialli, Scientific machine learning through physics–informed neural networks: Where we are and what's next, J. Sci. Comput. 92, 88 (2022).
  51. Y. D. van Nieuwkerk and F. H. L. Essler, On the low-energy description for tunnel-coupled one-dimensional Bose gases, SciPost Phys. 9, 025 (2020).
  52. J.-F. Mennemann, I. E. Mazets, M. Pigneur, H. P. Stimming, N. J. Mauser, J. Schmiedmayer, and S. Erne, Relaxation in an extended bosonic Josephson junction, Phys. Rev. Res. 3, 023197 (2021).
  53. A. Imambekov and L. I. Glazman, Universal theory of nonlinear Luttinger liquids, Science 323, 228 (2009).
  54. A. Steffens, M. Friesdorf, T. Langen, B. Rauer, T. Schweigler, R. Hübener, J. Schmiedmayer, C. Riofrío, and J. Eisert, Towards experimental quantum-field tomography with ultracold atoms, Nat. Commun. 6, 7663 (2015).
  55. M. Aidelsburger, J. L. Ville, R. Saint-Jalm, S. Nascimbène, J. Dalibard, and J. Beugnon, Relaxation dynamics in the merging of n independent condensates, Phys. Rev. Lett. 119, 190403 (2017).
  56. S. Sunami, V. P. Singh, D. Garrick, A. Beregi, A. J. Barker, K. Luksch, E. Bentine, L. Mathey, and C. J. Foot, Observation of the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional Bose gas via matter-wave interferometry, Phys. Rev. Lett. 128, 250402 (2022).
  57. S. Sunami, V. P. Singh, D. Garrick, A. Beregi, A. J. Barker, K. Luksch, E. Bentine, L. Mathey, and C. J. Foot, Universal scaling of the dynamic BKT transition in quenched 2D Bose gases, Science 382, 443 (2023).
  58. S. Sunami, V. P. Singh, E. Rydow, A. Beregi, E. Chang, L. Mathey, and C. J. Foot, Detecting phase coherence of 2D Bose gases via noise correlations, arXiv:2406.03491.
  59. Y. Nakamura, Y. Takasu, J. Kobayashi, H. Asaka, Y. Fukushima, K. Inaba, M. Yamashita, and Y. Takahashi, Experimental determination of Bose-Hubbard energies, Phys. Rev. A 99, 033609 (2019).
  60. M. Atala, M. Aidelsburger, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Observation of chiral currents with ultracold atoms in bosonic ladders, Nat. Phys. 10, 588 (2014).
  61. T. Langen, T. Schweigler, E. Demler, and J. Schmiedmayer, Double light-cone dynamics establish thermal states in integrable 1D Bose gases, New J. Phys. 20, 023034 (2018).

Outline

Information

Phys. Rev. Research 7, L022031– Published 7 May, 2025
  • Received 18 October 2024
  • Accepted 28 February 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation