- 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

Quench spectroscopy for Lieb-Liniger bosons in the presence of harmonic trap

Jiachen Yu1,*, Yuanzhe Hu1,*, Wenhan Chen1, Jianing Yang1, Xuzong Chen1,2,†, and Hepeng Yao1,‡

  • 1School of Electronics, Peking University, Beijing 100871, China
  • 2School of Computing and Artificial Intelligence, Fuyao University of Science and Technology, Fuzhou 350109, China

  • *These authors contributed equally to this work.
  • †Contact author: xuzongchen@pku.edu.cn
  • ‡Contact author: hepeng.yao@pku.edu.cn
PDF

Phys. Rev. Research 7, L042066 – Published 22 December, 2025

DOI: https://doi.org/10.1103/f4jf-6gt5

Abstract

Quench spectroscopy has emerged as a powerful technique for probing the energy spectrum of various quantum phases for quantum systems from out-of-equilibrium dynamics. While its efficacy has been demonstrated in the homogeneous systems theoretically, most experimental setups feature a confining potential, such as a harmonic trap, which complicates the practical implementations. In this work, we experimentally probe the quench spectroscopy for one-dimensional bosons in optical lattices with the presence of a harmonic trap, and compare our results with the density matrix renormalization group simulation. For the Mott insulator phase, although a gap is still observed, the band signal is broadened along the frequency space and cut at the half Brillouin zone, which can be explained by the nearest-neighbor tunneling excitations under harmonic confinement. Comparing with the superfluid spectrum, we can see a clear distinction between the two phases and find that the inverse quench with larger amplitude yields the clearest spectrum. Our work offers pivotal insights into conducting quench spectroscopy effectively in practical systems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (59)

  1. A. Damascelli, Probing the electronic structure of complex systems by ARPES, Phys. Scr. 2004, 61 (2004).
  2. G. Roux, A. Minguzzi, and T. Roscilde, Dynamic structure factor of one-dimensional lattice bosons in a disordered potential: A spectral fingerprint of the Bose-glass phase, New J. Phys. 15, 055003 (2013).
  3. T. Ernst, T. Paul, and P. Schlagheck, Transport of ultracold Bose gases beyond the Gross-Pitaevskii description, Phys. Rev. A 81, 013631 (2010).
  4. V. Gritsev, E. Demler, M. Lukin, and A. Polkovnikov, Spectroscopy of collective excitations in interacting low-dimensional many-body systems using quench dynamics, Phys. Rev. Lett. 99, 200404 (2007).
  5. S. Gupta, Z. Hadzibabic, M. W. Zwierlein, C. A. Stan, K. Dieckmann, C. H. Schunck, E. G. M. van Kempen, B. J. Verhaar, and W. Ketterle, Radio-frequency spectroscopy of ultracold fermions, Science 300, 1723 (2003).
  6. H. Yao, L. Tanzi, L. Sanchez-Palencia, T. Giamarchi, G. Modugno, and C. D’Errico, Mott transition for a Lieb-Liniger gas in a shallow quasiperiodic potential: Delocalization induced by disorder, Phys. Rev. Lett. 133, 123401 (2024).
  7. J. T. Stewart, J. P. Gaebler, and D. S. Jin, Using photoemission spectroscopy to probe a strongly interacting Fermi gas, Nature (London) 454, 744 (2008).
  8. T.-H. Han, J. S. Helton, S. Chu, D. G. Nocera, J. A. Rodriguez-Rivera, C. Broholm, and Y. S. Lee, Fractionalized excitations in the spin-liquid state of a Kagome-lattice antiferromagnet, Nature (London) 492, 406 (2012).
  9. E. Altman, E. Demler, and M. D. Lukin, Probing many-body states of ultracold atoms via noise correlations, Phys. Rev. A 70, 013603 (2004).
  10. K. B. Davis, M. O. Mewes, M. R. Andrews, N. J. Van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, Bose-Einstein condensation in a gas of sodium atoms, Phys. Rev. Lett. 75, 3969 (1995).
  11. S. Richard, F. Gerbier, J. H. Thywissen, M. Hugbart, P. Bouyer, and A. Aspect, Momentum spectroscopy of 1D phase fluctuations in Bose-Einstein condensates, Phys. Rev. Lett. 91, 010405 (2003).
  12. T. Stöferle, H. Moritz, C. Schori, M. Köhl, and T. Esslinger, Transition from a strongly interacting 1D superfluid to a Mott insulator, Phys. Rev. Lett. 92, 130403 (2004).
  13. F. Gerbier, A. Widera, S. Fölling, O. Mandel, T. Gericke, and I. Bloch, Phase coherence of an atomic Mott insulator, Phys. Rev. Lett. 95, 050404 (2005).
  14. M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms, Nature (London) 415, 39 (2002).
  15. I. B. Spielman, W. D. Phillips, and J. V. Porto, Mott-insulator transition in a two-dimensional atomic Bose gas, Phys. Rev. Lett. 98, 080404 (2007).
  16. R. Jördens, N. Strohmaier, K. Günter, H. Moritz, and T. Esslinger, A Mott insulator of fermionic atoms in an optical lattice, Nature (London) 455, 204 (2008).
  17. Q. Huang, Z. Zhu, Y. Wang, L. Liang, Q. Zheng, and X. Chen, Measurement of interacting quantum phases: A band mapping scheme, Front. Phys. 18, 52307 (2023).
  18. M. Cheneau, P. Barmettler, D. Poletti, M. Endres, P. Schauß, T. Fukuhara, C. Gross, I. Bloch, C. Kollath, and S. Kuhr, Light-cone-like spreading of correlations in a quantum many-body system, Nature (London) 481, 484 (2012).
  19. D. Greif, M. F. Parsons, A. Mazurenko, C. S. Chiu, S. Blatt, F. Huber, G. Ji, and M. Greiner, Site-resolved imaging of a fermionic Mott insulator, Science 351, 953 (2016).
  20. K. D. Nelson, X. Li, and D. S. Weiss, Imaging single atoms in a three-dimensional array, Nat. Phys. 3, 556 (2007).
  21. J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, Single-atom-resolved fluorescence imaging of an atomic Mott insulator, Nature (London) 467, 68 (2010).
  22. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, and M. Greiner, A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice, Nature (London) 462, 74 (2009).
  23. C. Weitenberg, P. Schauß, T. Fukuhara, M. Cheneau, M. Endres, I. Bloch, and S. Kuhr, Coherent light scattering from a two-dimensional Mott insulator, Phys. Rev. Lett. 106, 215301 (2011).
  24. E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, Single-atom imaging of fermions in a quantum-gas microscope, Nat. Phys. 11, 738 (2015).
  25. T. P. Devereaux and R. Hackl, Inelastic light scattering from correlated electrons, Rev. Mod. Phys. 79, 175 (2007).
  26. E. Haller, R. Hart, M. J. Mark, J. G. Danzl, L. Reichsöllner, M. Gustavsson, M. Dalmonte, G. Pupillo, and H.-C. Nägerl, Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons, Nature (London) 466, 597 (2010).
  27. N. Fabbri, M. Panfil, D. Clément, L. Fallani, M. Inguscio, C. Fort, and J.-S. Caux, Dynamical structure factor of one-dimensional Bose gases: Experimental signatures of beyond-Luttinger-liquid physics, Phys. Rev. A 91, 043617 (2015).
  28. E. Altuntaş, R. G. Lena, S. Flannigan, A. J. Daley, and I. B. Spielman, Dynamical structure factor from weak measurements, Quantum Sci. Technol. 10, 035045 (2025).
  29. M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schauß, C. Gross, E. Demler, S. Kuhr, and I. Bloch, The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition, Nature (London) 487, 454 (2012).
  30. J. Mun, P. Medley, G. K. Campbell, L. G. Marcassa, D. E. Pritchard, and W. Ketterle, Phase diagram for a Bose-Einstein condensate moving in an optical lattice, Phys. Rev. Lett. 99, 150604 (2007).
  31. L. Villa, J. Despres, and L. Sanchez-Palencia, Unraveling the excitation spectrum of many-body systems from quantum quenches, Phys. Rev. A 100, 063632 (2019).
  32. L. Villa, J. Despres, S. J. Thomson, and L. Sanchez-Palencia, Local quench spectroscopy of many-body quantum systems, Phys. Rev. A 102, 033337 (2020).
  33. J. Despres, Quench spectroscopy for dissipative and non-Hermitian quantum lattice models, Phys. Rev. A 112, 033320 (2025).
  34. T. Giamarchi and H. J. Schulz, Localization and interactions in one-dimensional quantum fluids, Europhys. Lett. 3, 1287 (1987).
  35. T. Giamarchi and H. J. Schulz, Anderson localization and interactions in one-dimensional metals, Phys. Rev. B 37, 325 (1988).
  36. C. D'Errico, E. Lucioni, L. Tanzi, L. Gori, G. Roux, I. P. McCulloch, T. Giamarchi, M. Inguscio, and G. Modugno, Observation of a disordered bosonic insulator from weak to strong interactions, Phys. Rev. Lett. 113, 095301 (2014).
  37. Z. Zhu, H. Yao, and L. Sanchez-Palencia, Thermodynamic phase diagram of two-dimensional bosons in a quasicrystal potential, Phys. Rev. Lett. 130, 220402 (2023).
  38. H. Yao, T. Giamarchi, and L. Sanchez-Palencia, Lieb-Liniger bosons in a shallow quasiperiodic potential: Bose glass phase and fractal Mott lobes, Phys. Rev. Lett. 125, 060401 (2020).
  39. M. Yan, H.-Y. Hui, M. Rigol, and V. W. Scarola, Equilibration dynamics of strongly interacting bosons in 2D lattices with disorder, Phys. Rev. Lett. 119, 073002 (2017).
  40. M. Yan, H.-Y. Hui, and V. W. Scarola, Dynamics of disordered states in the Bose-Hubbard model with confinement, Phys. Rev. A 95, 053624 (2017).
  41. P. Russ, M. Yan, N. Kowalski, L. Wadleigh, V. W. Scarola, and B. DeMarco, Compressibility measurement of the thermal MI–BG transition in an optical lattice, arXiv:2506.16466.
  42. See Supplemental Material at https://link.aps.org/supplemental/10.1103/f4jf-6gt5 for details about DMRG method, density distribution in harmonic trap, data processing steps, finite temperature effect, atom number distribution effect, and analysis of experimental data, which includes Refs. [56, 57, 58, 59].
  43. G. Boéris, L. Gori, M. D. Hoogerland, A. Kumar, E. Lucioni, L. Tanzi, M. Inguscio, T. Giamarchi, C. D’Errico, G. Carleo, G. Modugno, and L. Sanchez-Palencia, Mott transition for strongly interacting one-dimensional bosons in a shallow periodic potential, Phys. Rev. A 93, 011601(R) (2016).
  44. L. Villa, S. J. Thomson, and L. Sanchez-Palencia, Quench spectroscopy of a disordered quantum system, Phys. Rev. A 104, L021301 (2021).
  45. L. Villa, S. J. Thomson, and L. Sanchez-Palencia, Finding the phase diagram of strongly correlated disordered bosons using quantum quenches, Phys. Rev. A 104, 023323 (2021).
  46. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).
  47. U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Ann. Phys. (NY) 326, 96 (2011).
  48. J. Hauschild, et al., Tensor network Python (TeNPy) version 1, SciPost Phys. Codebases 41 (2024).
  49. L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation (Clarendon Press, Oxford, 2004).
  50. J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Many-body localization in a quantum simulator with programmable random disorder, Nat. Phys. 12, 907 (2016).
  51. R. Gautier, H. Yao, and L. Sanchez-Palencia, Strongly interacting bosons in a two-dimensional quasicrystal lattice, Phys. Rev. Lett. 126, 110401 (2021).
  52. C. Chen, G. Emperauger, G. Bornet, F. Caleca, B. Gély, M. Bintz, S. Chatterjee, V. Liu, D. Barredo, N. Y. Yao, T. Lahaye, F. Mezzacapo, T. Roscilde, and A. Browaeys, Spectroscopy of elementary excitations from quench dynamics in a dipolar XY Rydberg simulator, Science 389, 483 (2025).
  53. S. Bocini, F. Caleca, F. Mezzacapo, and T. Roscilde, Nonlocal quench spectroscopy of fermionic excitations in quantum spin chains, Phys. Rev. B 111, L121114 (2025).
  54. J. T. Schneider, J. Despres, S. J. Thomson, L. Tagliacozzo, and L. Sanchez-Palencia, Spreading of correlations and entanglement in the long-range transverse Ising chain, Phys. Rev. Res. 3, L012022 (2021).
  55. J. Yu, Y. Hu, W. Chen, J. Yang, X. Chen, and H. Yao, Quench spectroscopy for Lieb-Liniger bosons in the presence of harmonic trap, Zenodo (2025), https://zenodo.org/records/16791072.
  56. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  57. B. Goyal, A. Dogra, S. Agrawal, B. Sohi, and A. Sharma, Image denoising review: From classical to state-of-the-art approaches, Inf. Fusion 55, 220 (2020).
  58. M. Wang, S. Zheng, X. Li, and X. Qin, A new image denoising method based on Gaussian filter, in 2014 International Conference on Information Science, Electronics and Electrical Engineering (IEEE, Sapporo, Japan, 2014), Vol. 1, pp. 163–167.
  59. Q. Huang, H. Yao, X. Chen, and L. Sanchez-Palencia, Direct measurement of tan's contact in a one-dimensional Lieb-Liniger gas, Sci. Adv. 11, eadv3727 (2025).

Outline

Information

Phys. Rev. Research 7, L042066– Published 22 December, 2025
  • Received 10 July 2025
  • Accepted 23 November 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