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  • Letter
  • Open Access

Probing spontaneously symmetry-broken phases with spin-charge separation through noise correlation measurements

Kerman Gallego-Lizarribar1, Sergi Julià-Farré2, Maciej Lewenstein2,3, Christof Weitenberg4,5,6, Luca Barbiero7, and Javier Argüello-Luengo1,2,*

  • *Contact author: javier.arguello.luengo@upc.edu
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Phys. Rev. Research 6, L042048 – Published 22 November, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042048

Abstract

Spontaneously symmetry-broken (SSB) phases are locally ordered states of matter characterizing a large variety of physical systems. Because of their specific ordering, their presence is usually witnessed by means of local order parameters. Here, we propose an alternative approach based on statistical correlations of noise after the ballistic expansion of an atomic cloud. We indeed demonstrate that probing such noise correlators allows one to discriminate among different SSB phases characterized by spin-charge separation. As a particular example, we test our prediction on a 1D extended Fermi-Hubbard model, where the competition between local and nonlocal couplings gives rise to three different SSB phases: a charge density wave, a bond-ordering wave, and an antiferromagnet. Our numerical analysis shows that this approach can accurately capture the presence of these different SSB phases, thus representing an alternative and powerful strategy to characterize strongly interacting quantum matter.

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References (55)

  1. W. Ludwig and C. Falter, Symmetries in Physics: Group Theory Applied to Physical Problems, 2nd ed. (Springer, Berlin, 1996).
  2. A. J. Beekman, L. Rademaker, and J. van Wezel, An introduction to spontaneous symmetry breaking, SciPost Phys. Lect. Notes 11, (2019).
  3. J. Fröhlich, Phase transitions, spontaneous symmetry breaking, and Goldstone's theorem, in Encyclopedia of Condensed Matter Physics, 2nd ed., edited by T. Chakraborty (Academic Press, Oxford, 2024), pp. 158–173.
  4. P. C. Hohenberg, Existence of long-range order in one and two dimensions, Phys. Rev. 158, 383 (1967).
  5. N. D. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17, 1133 (1966).
  6. L. D. Landau, E. M. Lifshitz, and M. Pitaevskii, Statistical Physics (Butterworth-Heinemann, New York, 1999).
  7. M. Lewenstein, A. Sanpera, and V. Ahufinger, Ultracold Atoms in Optical Lattices: Simulating Quantum Many-Body Systems, 2nd ed. (Oxford University Press, Oxford, 2017).
  8. I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008).
  9. L. Su, A. Douglas, M. Szurek, R. Groth, S. F. Ozturk, A. Krahn, A. H. Hébert, G. A. Phelps, S. Ebadi, S. Dickerson, F. Ferlaino, O. Marković, and M. Greiner, Dipolar quantum solids emerging in a Hubbard quantum simulator, Nature (London) 622, 724 (2023).
  10. H. P. Zahn, V. P. Singh, M. N. Kosch, L. Asteria, L. Freystatzky, K. Sengstock, L. Mathey, and C. Weitenberg, Formation of spontaneous density-wave patterns in dc driven lattices, Phys. Rev. X 12, 021014 (2022).
  11. L. Tanzi, S. M. Roccuzzo, E. Lucioni, F. Famá, A. Fioretti, C. Gabbanini, G. Modugno, A. Recati, and S. Stringari, Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas, Nature (London) 574, 382 (2019).
  12. M. Guo, F. Böttcher, J. Hertkorn, J.-N. Schmidt, M. Wenzel, H. P. Büchler, T. Langen, and T. Pfau, The low-energy Goldstone mode in a trapped dipolar supersolid, Nature (London) 574, 386 (2019).
  13. L. Chomaz, D. Petter, P. Ilzhöfer, G. Natale, A. Trautmann, C. Politi, G. Durastante, R. M. W. van Bijnen, A. Patscheider, M. Sohmen, M. J. Mark, and F. Ferlaino, Long-lived and transient supersolid behaviors in dipolar quantum gases, Phys. Rev. X 9, 021012 (2019).
  14. A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, A cold-atom Fermi-Hubbard antiferromagnet, Nature (London) 545, 462 (2017).
  15. P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, A. M. Läuchli, and A. Browaeys, Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms, Nature (London) 595, 233 (2021).
  16. H.-J. Shao, Y.-X. Wang, D.-Z. Zhu, Y.-S. Zhu, H.-N. Sun, S.-Y. Chen, C. Zhang, Z.-J. Fan, Y. Deng, X.-C. Yao, Y.-A. Chen, and J.-W. Pan, Observation of the antiferromagnetic phase transition in the fermionic Hubbard model, arXiv:2402.14605.
  17. C. Gross and W. S. Bakr, Quantum gas microscopy for single atom and spin detection, Nat. Phys. 17, 1316 (2021).
  18. 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).
  19. 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).
  20. M. Boll, T. A. Hilker, G. Salomon, A. Omran, J. Nespolo, L. Pollet, I. Bloch, and C. Gross, Spin- and density-resolved microscopy of antiferromagnetic correlations in Fermi-Hubbard chains, Science 353, 1257 (2016).
  21. T. A. Hilker, G. Salomon, F. Grusdt, A. Omran, M. Boll, E. Demler, I. Bloch, and C. Gross, Revealing hidden antiferromagnetic correlations in doped Hubbard chains via string correlators, Science 357, 484 (2017).
  22. J. Vijayan, P. Sompet, G. Salomon, J. Koepsell, S. Hirthe, A. Bohrdt, F. Grusdt, I. Bloch, and C. Gross, Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains, Science 367, 186 (2020).
  23. S. Baier, M. J. Mark, D. Petter, K. Aikawa, L. Chomaz, Z. Cai, M. Baranov, P. Zoller, and F. Ferlaino, Extended Bose-Hubbard models with ultracold magnetic atoms, Science 352, 201 (2016).
  24. J. Fraxanet, D. González-Cuadra, T. Pfau, M. Lewenstein, T. Langen, and L. Barbiero, Topological quantum critical points in the extended Bose-Hubbard model, Phys. Rev. Lett. 128, 043402 (2022).
  25. M. Sohmen, M. J. Mark, M. Greiner, and F. Ferlaino, A ship-in-a-bottle quantum gas microscope setup for magnetic mixtures, SciPost Phys. 15, 182 (2023).
  26. E. Altman, E. Demler, and M. D. Lukin, Probing many-body states of ultracold atoms via noise correlations, Phys. Rev. A 70, 013603 (2004).
  27. S. Fölling, F. Gerbier, A. Widera, O. Mandel, T. Gericke, and I. Bloch, Spatial quantum noise interferometry in expanding ultracold atom clouds, Nature (London) 434, 481 (2005).
  28. 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).
  29. C. Carcy, H. Cayla, A. Tenart, A. Aspect, M. Mancini, and D. Clément, Momentum-space atom correlations in a Mott insulator, Phys. Rev. X 9, 041028 (2019).
  30. T. Rom, T. Best, D. van Oosten, U. Schneider, S. Fölling, B. Paredes, and I. Bloch, Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice, Nature (London) 444, 733 (2006).
  31. M. Messer, R. Desbuquois, T. Uehlinger, G. Jotzu, S. Huber, D. Greif, and T. Esslinger, Exploring competing density order in the ionic Hubbard model with ultracold fermions, Phys. Rev. Lett. 115, 115303 (2015).
  32. S. Tomonaga, Remarks on Bloch's method of sound waves applied to many-Fermion problems, Prog. Theor. Phys. 5, 544 (1950).
  33. J. Luttinger, An exactly soluble model of a many-Fermion system, J. Math. Phys. 4, 1154 (1963).
  34. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, New York, 2004).
  35. M. Nakamura, Tricritical behavior in the extended Hubbard chains, Phys. Rev. B 61, 16377 (2000).
  36. L. Barbiero, A. Montorsi, and M. Roncaglia, How hidden orders generate gaps in one-dimensional fermionic systems, Phys. Rev. B 88, 035109 (2013).
  37. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L042048 for further details on the derivations of the NCMs.
  38. A. Impertro, S. Karch, J. F. Wienand, S. 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).
  39. S. Nascimbène, Y.-A. Chen, M. Atala, M. Aidelsburger, S. Trotzky, B. Paredes, and I. Bloch, Experimental realization of plaquette resonating valence-bond states with ultracold atoms in optical superlattices, Phys. Rev. Lett. 108, 205301 (2012).
  40. V. Guarrera, N. Fabbri, L. Fallani, C. Fort, K. M. R. van der Stam, and M. Inguscio, Noise correlation spectroscopy of the broken order of a Mott insulating phase, Phys. Rev. Lett. 100, 250403 (2008).
  41. R. Bach and K. Rzążewski, Correlations in atomic systems: Diagnosing coherent superpositions, Phys. Rev. Lett. 92, 200401 (2004).
  42. M. Fabrizio, A. O. Gogolin, and A. A. Nersesyan, From band insulator to Mott insulator in one dimension, Phys. Rev. Lett. 83, 2014 (1999).
  43. A. A. Aligia, A. Anfossi, L. Arrachea, C. Degli Esposti Boschi, A. O. Dobry, C. Gazza, A. Montorsi, F. Ortolani, and M. E. Torio, Incommmensurability and unconventional superconductor to insulator transition in the Hubbard model with bond-charge interaction, Phys. Rev. Lett. 99, 206401 (2007).
  44. N. Baldelli, A. Montorsi, S. Julià-Farré, M. Lewenstein, M. Rizzi, and L. Barbiero, Deconfined quantum critical points in fermionic systems with spin-charge separation, arXiv:2407.04073.
  45. G. I. Japaridze and E. Müller-Hartmann, Triplet superconductivity in a one-dimensional ferromagnetic t-J model, Phys. Rev. B 61, 9019 (2000).
  46. A. W. Sandvik, L. Balents, and D. K. Campbell, Ground state phases of the half-filled one-dimensional extended Hubbard model, Phys. Rev. Lett. 92, 236401 (2004).
  47. For each of those phases, both symmetry sectors are degenerate in the thermodynamic limit. However, in a real experiment one of the symmetry sectors will be preferred by imperfections, the state preparation, and/or finite-size effects. To account for this, the degeneracy breaks in our tensor networks calculation with the choice of the initial state to be optimized (see Ref. [37]).
  48. M. Di Dio, L. Barbiero, A. Recati, and M. Dalmonte, Spontaneous Peierls dimerization and emergent bond order in one-dimensional dipolar gases, Phys. Rev. A 90, 063608 (2014).
  49. S. Julià-Farré, D. González-Cuadra, A. Patscheider, M. J. Mark, F. Ferlaino, M. Lewenstein, L. Barbiero, and A. Dauphin, Revealing the topological nature of the bond order wave in a strongly correlated quantum system, Phys. Rev. Res. 4, L032005 (2022).
  50. L. Asteria, H. P. Zahn, M. N. Kosch, K. Sengstock, and C. Weitenberg, Quantum gas magnifier for sub-lattice-resolved imaging of 3D quantum systems, Nature (London) 599, 571 (2021).
  51. E. Guardado-Sanchez, B. M. Spar, P. Schauss, R. Belyansky, J. T. Young, P. Bienias, A. V. Gorshkov, T. Iadecola, and W. S. Bakr, Quench dynamics of a Fermi gas with strong nonlocal interactions, Phys. Rev. X 11, 021036 (2021).
  52. P. Weckesser, K. Srakaew, T. Blatz, D. Wei, D. Adler, S. Agrawal, A. Bohrdt, I. Bloch, and J. Zeiher, Realization of a Rydberg-dressed extended Bose Hubbard model, arXiv:2405.20128.
  53. N. Bigagli, W. Yuan, S. Zhang, B. Bulatovic, T. Karman, I. Stevenson, and S. Will, Observation of Bose-Einstein condensation of dipolar molecules, Nature (London) 631, 289 (2024).
  54. J. S. Rosenberg, L. Christakis, E. Guardado-Sanchez, Z. Z. Yan, and W. S. Bakr, Observation of the Hanbury Brown–Twiss effect with ultracold molecules, Nat. Phys. 18, 1062 (2022).
  55. J. Hauschild and F. Pollmann, Efficient numerical simulations with tensor networks: Tensor Network Python (TeNPy), SciPost Phys. Lect. Notes 5 (2018).

Outline

Information

Phys. Rev. Research 6, L042048– Published 22 November, 2024
  • Received 23 April 2024
  • Revised 11 July 2024
  • Accepted 12 September 2024
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