- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

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
  • Open Access

Dual Spectroscopy of Quantum Simulated Fermi-Hubbard Systems

K. Knakkergaard Nielsen1,2, M. Zwierlein3, and G. M. Bruun4

PDF

Phys. Rev. Lett. 135, 043401 – Published 23 July, 2025

DOI: https://doi.org/10.1103/yfqr-y9ks

Abstract

Quantum gas microscopy with atoms in optical lattices provides remarkable insights into the real space properties of many-body systems, but does not directly reveal the nature of their fundamental excitation spectrum. Here, we demonstrate that radio-frequency spectroscopy can reveal the quasiparticle nature of doped quantum many-body systems, crucial for our understanding of, e.g., high-temperature superconductors. In particular, we showcase how the existence and energy of magnetic polaron quasiparticles in doped Fermi-Hubbard systems may be probed, revealed by hallmark peaks in the spectroscopic spectrum. In combination with fundamental dualities of the Fermi-Hubbard model, we describe how these findings may be tested using several experimental platforms.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (75)

  1. I. Bloch, J. Dalibard, and S. Nascimbène, Nat. Phys. 8, 267 (2012).
  2. C. Gross and I. Bloch, Science 357, 995 (2017).
  3. L. Tarruell and L. Sanchez-Palencia, C.R. Phys. 19, 365 (2018).
  4. F. Schäfer, T. Fukuhara, S. Sugawa, Y. Takasu, and Y. Takahashi, Nat. Rev. Phys. 2, 411 (2020).
  5. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, and M. Greiner, Nature (London) 462, 74 (2009).
  6. J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, Nature (London) 467, 68 (2010).
  7. L. W. Cheuk, M. A. Nichols, M. Okan, T. Gersdorf, V. V. Ramasesh, W. S. Bakr, T. Lompe, and M. W. Zwierlein, Phys. Rev. Lett. 114, 193001 (2015).
  8. E. Haller, J. Hudson, A. Kelly, D. A. Cotta, B. Peaudecerf, G. D. Bruce, and S. Kuhr, Nat. Phys. 11, 738 (2015).
  9. C. Gross and W. S. Bakr, Nat. Phys. 17, 1316 (2021).
  10. D. Greif, T. Uehlinger, G. Jotzu, L. Tarruell, and T. Esslinger, Science 340, 1307 (2013).
  11. R. A. Hart, P. M. Duarte, T.-L. Yang, X. Liu, T. Paiva, E. Khatami, R. T. Scalettar, N. Trivedi, D. A. Huse, and R. G. Hulet, Nature (London) 519, 211 (2015).
  12. M. Boll, T. A. Hilker, G. Salomon, A. Omran, J. Nespolo, L. Pollet, I. Bloch, and C. Gross, Science 353, 1257 (2016).
  13. M. F. Parsons, A. Mazurenko, C. S. Chiu, G. Ji, D. Greif, and M. Greiner, Science 353, 1253 (2016).
  14. L. W. Cheuk, M. A. Nichols, K. R. Lawrence, M. Okan, H. Zhang, E. Khatami, N. Trivedi, T. Paiva, M. Rigol, and M. W. Zwierlein, Science 353, 1260 (2016).
  15. A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, Nature (London) 545, 462 (2017).
  16. D. Mitra, P. T. Brown, E. Guardado-Sanchez, S. S. Kondov, T. Devakul, D. A. Huse, P. Schauß, and W. S. Bakr, Nat. Phys. 14, 173 (2018).
  17. T. Hartke, B. Oreg, C. Turnbaugh, N. Jia, and M. Zwierlein, Science 381, 82 (2023).
  18. J. Koepsell, J. Vijayan, P. Sompet, F. Grusdt, T. A. Hilker, E. Demler, G. Salomon, I. Bloch, and C. Gross, Nature (London) 572, 358 (2019).
  19. M. L. Prichard, B. M. Spar, I. Morera, E. Demler, Z. Z. Yan, and W. S. Bakr, Nature (London) 629, 323 (2024).
  20. M. Lebrat, M. Xu, L. H. Kendrick, A. Kale, Y. Gang, P. Seetharaman, I. Morera, E. Khatami, E. Demler, and M. Greiner, Nature (London) 629, 317 (2024).
  21. G. Ji, M. Xu, L. H. Kendrick, C. S. Chiu, J. C. Brüggenjürgen, D. Greif, A. Bohrdt, F. Grusdt, E. Demler, M. Lebrat, and M. Greiner, Phys. Rev. X 11, 021022 (2021).
  22. K. K. Nielsen, T. Pohl, and G. M. Bruun, Phys. Rev. Lett. 129, 246601 (2022).
  23. D. N. Sheng, Y. C. Chen, and Z. Y. Weng, Phys. Rev. Lett. 77, 5102 (1996).
  24. K. Wu, Z. Y. Weng, and J. Zaanen, Phys. Rev. B 77, 155102 (2008).
  25. Z. Zhu and Z.-Y. Weng, Phys. Rev. B 92, 235156 (2015).
  26. S. R. White, D. J. Scalapino, and S. A. Kivelson, Phys. Rev. Lett. 115, 056401 (2015).
  27. R.-Y. Sun, Z. Zhu, and Z.-Y. Weng, Phys. Rev. Lett. 123, 016601 (2019).
  28. J.-Y. Zhao, S. A. Chen, H.-K. Zhang, and Z.-Y. Weng, Phys. Rev. X 12, 011062 (2022).
  29. J. R. Schrieffer and J. S. Brooks, Handbook of High-Temperature Superconductivity (Springer, New York, 2007).
  30. A. Schirotzek, C.-H. Wu, A. Sommer, and M. W. Zwierlein, Phys. Rev. Lett. 102, 230402 (2009).
  31. C. Kohstall, M. Zaccanti, M. Jag, A. Trenkwalder, P. Massignan, G. M. Bruun, F. Schreck, and R. Grimm, Nature (London) 485, 615 (2012).
  32. M. Cetina, M. Jag, R. S. Lous, J. T. M. Walraven, R. Grimm, R. S. Christensen, and G. M. Bruun, Phys. Rev. Lett. 115, 135302 (2015).
  33. M. Cetina, M. Jag, R. S. Lous, I. Fritsche, J. T. M. Walraven, R. Grimm, J. Levinsen, M. M. Parish, R. Schmidt, M. Knap, and E. Demler, Science 354, 96 (2016).
  34. F. Scazza, G. Valtolina, P. Massignan, A. Recati, A. Amico, A. Burchianti, C. Fort, M. Inguscio, M. Zaccanti, and G. Roati, Phys. Rev. Lett. 118, 083602 (2017).
  35. C. Baroni, B. Huang, I. Fritsche, E. Dobler, G. Anich, E. Kirilov, R. Grimm, M. A. Bastarrachea-Magnani, P. Massignan, and G. M. Bruun, Nat. Phys. 20, 68 (2024).
  36. N. B. Jørgensen, L. Wacker, K. T. Skalmstang, M. M. Parish, J. Levinsen, R. S. Christensen, G. M. Bruun, and J. J. Arlt, Phys. Rev. Lett. 117, 055302 (2016).
  37. M.-G. Hu, M. J. Van de Graaff, D. Kedar, J. P. Corson, E. A. Cornell, and D. S. Jin, Phys. Rev. Lett. 117, 055301 (2016).
  38. Z. Z. Yan, Y. Ni, C. Robens, and M. W. Zwierlein, Science 368, 190 (2020).
  39. M. G. Skou, T. G. Skov, N. B. Jørgensen, K. K. Nielsen, A. Camacho-Guardian, T. Pohl, G. M. Bruun, and J. J. Arlt, Nat. Phys. 17, 731 (2021).
  40. M. G. Skou, K. K. Nielsen, T. G. Skov, A. M. Morgen, N. B. Jørgensen, A. Camacho-Guardian, T. Pohl, G. M. Bruun, and J. J. Arlt, Phys. Rev. Res. 4, 043093 (2022).
  41. J. Etrych, G. Martirosyan, A. Cao, C. J. Ho, Z. Hadzibabic, and C. Eigen, Phys. Rev. X 15, 021070 (2025).
  42. J. E. Inglesfield and E. W. Plummer, in Angle-Resolved Photoemission, Studies in Surface Chemistry and Catalysis, edited by S. D. Kevan (Elsevier, Amsterdam, 1992), Vol. 74.
  43. P. T. Brown, E. Guardado-Sanchez, B. M. Spar, E. W. Huang, T. P. Devereaux, and W. S. Bakr, Nat. Phys. 16, 26 (2020).
  44. M. L. Prichard, Z. Ba, I. Morera, B. M. Spar, D. A. Huse, E. Demler, and W. S. Bakr, arXiv:2502.06757.
  45. V. Gritsev, E. Demler, M. Lukin, and A. Polkovnikov, Phys. Rev. Lett. 99, 200404 (2007).
  46. P. Jurcevic, P. Hauke, C. Maier, C. Hempel, B. P. Lanyon, R. Blatt, and C. F. Roos, Phys. Rev. Lett. 115, 100501 (2015).
  47. R. Menu and T. Roscilde, Phys. Rev. B 98, 205145 (2018).
  48. L. Villa, J. Despres, and L. Sanchez-Palencia, Phys. Rev. A 100, 063632 (2019).
  49. L. Villa, J. Despres, S. J. Thomson, and L. Sanchez-Palencia, Phys. Rev. A 102, 033337 (2020).
  50. 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, arXiv:2311.11726.
  51. S. Bocini, F. Caleca, F. Mezzacapo, and T. Roscilde, Phys. Rev. B 111, L121114 (2025).
  52. J. Sun, L. Vilchez-Estevez, V. Vedral, A. T. Boothroyd, and M. S. Kim, Nat. Commun. 16, 1403 (2025).
  53. G. Martinez and P. Horsch, Phys. Rev. B 44, 317 (1991).
  54. N. Diamantis and E. Manousakis, New J. Phys. 23, 123005 (2021).
  55. A. F. Ho, M. A. Cazalilla, and T. Giamarchi, Phys. Rev. A 79, 033620 (2009).
  56. H. Shiba, Prog. Theor. Phys. 48, 2171 (1972).
  57. A. Moreo and D. J. Scalapino, Phys. Rev. Lett. 98, 216402 (2007).

  58. The same mapping of the Néel state in the x−y plane leads to a superfluid state [16], showing that the CDW and superfluid state are degenerate at half filling.

  59. H. Schlömer, H. Lange, T. Franz, T. Chalopin, P. Bojović, S. Wang, I. Bloch, T. A. Hilker, F. Grusdt, and A. Bohrdt, PRX Quantum 5, 040341 (2024).
  60. D. K. Mark, H.-Y. Hu, J. Kwan, C. Kokail, S. Choi, and S. F. Yelin, arXiv:2412.13186.
  61. P. Massignan, M. Zaccanti, and G. M. Bruun, Rep. Prog. Phys. 77, 034401 (2014).
  62. P. Massignan, R. Schmidt, G. E. Astrakharchik, A. İmamoglu, M. Zwierlein, J. J. Arlt, and G. M. Bruun, arXiv:2501.09618.
  63. See Supplemental Material http://link.aps.org/supplemental/10.1103/yfqr-y9ks for details on the linear response calculation, derivation of the effective Hamiltonian, the self-consistent Born approximation, the ejection Green’s function, and fluctuations in probing frequency, which includes Ref. [64].
  64. A. Auerbach, Interacting Electrons and Quantum Magnetism, edited by J. L. Birman, H. Faissner, and J. W. Lynn (Springer-Verlag, New York, 1994).

  65. The mapping also leads to small next-nearest-neighbor density-dependent hopping term on the order of J [64]. While this may lead to minor quantitative changes, it should not alter the qualitative quasiparticle behavior described here.

  66. S. Schmitt-Rink, C. M. Varma, and A. E. Ruckenstein, Phys. Rev. Lett. 60, 2793 (1988).
  67. C. L. Kane, P. A. Lee, and N. Read, Phys. Rev. B 39, 6880 (1989).
  68. K. K. Nielsen, M. A. Bastarrachea-Magnani, T. Pohl, and G. M. Bruun, Phys. Rev. B 104, 155136 (2021).
  69. A. Bohrdt, D. Greif, E. Demler, M. Knap, and F. Grusdt, Phys. Rev. B 97, 125117 (2018).
  70. G. F. Reiter, Phys. Rev. B 49, 1536 (1994).
  71. A. Ramšak and P. Horsch, Phys. Rev. B 57, 4308 (1998).

  72. Note that |Ψppol⟩ has vanishing mean magnetization, ⟨S^(z)⟩=0, because holes in this state are uniformly created on all lattice sites, whereas |Ψ˜p⟩ has magnetization +1/2. Since the system is symmetric in spin-up and spin-down, they give equivalent spectral responses.

  73. T. Pohl (private communication) (2022).
  74. T. Hartke, B. Oreg, N. Jia, and M. Zwierlein, Phys. Rev. Lett. 125, 113601 (2020).
  75. K. K. Nielsen, 10.5281/zenodo.14967822 (2025).

Outline

Information

Phys. Rev. Lett. 135, 043401– Published 23 July, 2025
  • Received 5 March 2025
  • Accepted 2 July 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. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation