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Spectroscopic probes of quantum gases

Nature Physics volume 17, pages 1305–1315 (2021)Cite this article

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Abstract

The foundation of atomic physics is the arsenal of spectroscopic tools to probe individual atoms and molecules with astounding precision. With the advent of ultracold quantum degenerate gases, these spectroscopic techniques have been applied to many-body systems featuring strong correlations, interactions and phase transitions. This has delivered a wealth of insights into collective quantum phenomena, with direct implications for nuclear and condensed-matter physics. Here we review some of the key developments turning ultracold gases into a laboratory for precision many-body physics.

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Fig. 1: Radiofrequency spectroscopy.
Fig. 2: Two-photon (Bragg and Raman) spectroscopy.
Fig. 3: Spectroscopic measures of the contact and spin correlations.
Fig. 4: Quasiparticle spectroscopy.

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References

  1. Ramsey, N. F. A molecular beam resonance method with separated oscillating fields. Phys. Rev. 78, 695–699 (1950).

    Article  ADS  Google Scholar 

  2. Pitaevskii, L. P. & Stringari, S. Bose-Einstein Condensation and Superfluidity (Oxford Univ. Press, 2016).

    Book  MATH  Google Scholar 

  3. Törmä, P. in Quantum Gas Experiments: Exploring Many-Body States (eds Törmä, P. & Sengstock, K.) 199–250 (World Scientific, 2015).

  4. Gibble, K. & Chu, S. Laser-cooled Cs frequency standard and a measurement of the frequency shift due to ultracold collisions. Phys. Rev. Lett. 70, 1771 (1993).

    Article  ADS  Google Scholar 

  5. Gupta, S. et al. Radio-frequency spectroscopy of ultracold fermions. Science 300, 1723–1726 (2003).

  6. Regal, C. A. & Jin, D. S. Measurement of positive and negative scattering lengths in a Fermi gas of atoms. Phys. Rev. Lett. 90, 230404 (2003).

    Article  ADS  Google Scholar 

  7. Zwierlein, M. W., Hadzibabic, Z., Gupta, S. & Ketterle, W. Spectroscopic insensitivity to cold collisions in a two-state mixture of fermions. Phys. Rev. Lett. 91, 250404 (2003).

    Article  ADS  Google Scholar 

  8. Regal, C. A., Ticknor, C., Bohn, J. L. & Jin, D. S. Creation of ultracold molecules from a Fermi gas of atoms. Nature 424, 47–50 (2003).

    Article  ADS  Google Scholar 

  9. Chin, C. et al. Observation of the pairing gap in a srongly interacting Fermi gas. Science 305, 1128 (2004).

    Article  ADS  Google Scholar 

  10. Shin, Y., Schunck, C. H., Schirotzek, A. & Ketterle, W. Tomographic rf spectroscopy of a trapped Fermi gas at unitarity. Phys. Rev. Lett. 99, 90403 (2007).

    Article  ADS  Google Scholar 

  11. Schunck, C. H., Shin, Y., Schirotzek, A. & Ketterle, W. Determination of the fermion pair size in a resonantly interacting superfluid. Nature 454, 739–743 (2008).

    Article  ADS  Google Scholar 

  12. Schirotzek, A., Shin, Y., Schunck, C. H. & Ketterle, W. Determination of the superfluid gap in atomic Fermi gases by quasiparticle spectroscopy. Phys. Rev. Lett. 101, 140403 (2008).

    Article  ADS  Google Scholar 

  13. Stewart, J. T., Gaebler, J. P. & Jin, D. S. Using photoemission spectroscopy to probe a strongly interacting Fermi gas. Nature 454, 744–747 (2008).

    Article  ADS  Google Scholar 

  14. Schirotzek, A., Wu, C.-H., Sommer, A. & Zwierlein, M. W. Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms. Phys. Rev. Lett. 102, 230402 (2009).

  15. Cetina, M. et al. Ultrafast many-body interferometry of impurities coupled to a Fermi sea. Science 354, 96–99 (2016).

    Article  ADS  Google Scholar 

  16. Fletcher, R. J. et al. Two- and three-body contacts in the unitary Bose gas. Science 355, 377–380 (2017).

  17. Yan, Z. et al. Boiling a unitary Fermi liquid. Phys. Rev. Lett. 122, 093401 (2019).

  18. Mukherjee, B. et al. Spectral response and contact of the unitary Fermi gas. Phys. Rev. Lett. 122, 203402 (2019).

    Article  ADS  Google Scholar 

  19. Cheuk, L. W. et al. Observation of spatial charge and spin correlations in the 2D Fermi-Hubbard model. Science 353, 1260–1264 (2016).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  20. Hartke, T., Oreg, B., Jia, N. & Zwierlein, M. Doublon-hole correlations and fluctuation thermometry in a Fermi-Hubbard gas. Phys. Rev. Lett. 125, 113601 (2020).

    Article  ADS  Google Scholar 

  21. Gibble, K. Decoherence and collisional frequency shifts of trapped bosons and fermions. Phys. Rev. Lett. 103, 113202 (2009).

    Article  ADS  Google Scholar 

  22. Rey, A. M., Gorshkov, A. V. & Rubbo, C. Many-body treatment of the collisional frequency shift in fermionic atoms. Phys. Rev. Lett. 103, 260402 (2009).

    Article  ADS  Google Scholar 

  23. Campbell, S. L. et al. A Fermi-degenerate three-dimensional optical lattice clock. Science 358, 90–94 (2017).

    Article  ADS  Google Scholar 

  24. Ludlow, A. D., Boyd, M. M., Ye, J., Peik, E. & Schmidt, P. O. Optical atomic clocks. Rev. Mod. Phys. 87, 637–701 (2015).

    Article  ADS  Google Scholar 

  25. Harber, D. M., Lewandowski, H. J., McGuirk, J. M. & Cornell, E. A. Effect of cold collisions on spin coherence and resonance shifts in a magnetically trapped ultracold gas. Phys. Rev. A 66, 53616 (2002).

    Article  ADS  Google Scholar 

  26. Fried, D. G. et al. Bose-Einstein condensation of atomic hydrogen. Phys. Rev. Lett. 81, 3811–3814 (1998).

    Article  ADS  Google Scholar 

  27. Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225 (2010).

    Article  ADS  Google Scholar 

  28. Petrov, D. S., Salomon, C. & Shlyapnikov, G. V. Weakly bound dimers of fermionic atoms. Phys. Rev. Lett. 93, 090404 (2004).

    Article  ADS  Google Scholar 

  29. Zwerger, W. The BCS-BEC Crossover and the Unitary Fermi Gas Vol. 836 (Springer, 2012).

  30. Zwierlein, M. W. Thermodynamics of strongly interacting Fermi gases. In Proc. International School of Physics ‘Enrico Fermi’ (eds Inguscio, M. et al.) Vol. 191 https://doi.org/10.3254/978-1-61499-694-1-143 (IOS Press, 2016).

  31. Baym, G., Pethick, C.J., Yu, Z. & Zwierlein, M. W. Coherence and clock shifts in ultracold Fermi gases with resonant interactions. Phys. Rev. Lett. 99, 190407 (2007).

  32. Punk, M. & Zwerger, W. Theory of rf-spectroscopy of strongly interacting fermions. Phys. Rev. Lett. 99, 170404 (2007).

    Article  ADS  Google Scholar 

  33. Tan, S. Energetics of a strongly correlated Fermi gas. Ann. Phys. 323, 2952–2970 (2008).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  34. Tan, S. Large momentum part of a strongly correlated Fermi gas. Ann. Phys. 323, 2971–2986 (2008).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  35. Braaten, E. in The BCS-BEC Crossover and the Unitary Fermi Gas 193–231 (Springer, 2012).

  36. Bartenstein, M. et al. Precise determination of 6Li cold collision parameters by radio-frequency spectroscopy on weakly bound molecules. Phys. Rev. Lett. 94, 103201 (2004).

    Article  ADS  Google Scholar 

  37. Fröhlich, B. et al. Radio-frequency spectroscopy of a strongly interacting two-dimensional Fermi gas. Phys. Rev. Lett. 106, 105301 (2011).

    Article  ADS  Google Scholar 

  38. Sommer, A. T., Cheuk, L. W., Ku, M. J. H., Bakr, W. S. & Zwierlein, M. W. Evolution of fermion pairing from three to two dimensions. Phys. Rev. Lett. 108, 045302 (2012).

  39. Murthy, P. A. et al. High-temperature pairing in a strongly interacting two-dimensional Fermi gas. Science 359, 452–455 (2018).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  40. Mukherjee, B. et al. Spectral response and contact of the unitary Fermi Gas. Phys. Rev. Lett. 122, 203402 (2019).

    Article  ADS  Google Scholar 

  41. Zürn, G. et al. Precise characterization of 6Li Feshbach resonances using trap-sideband-resolved rf spectroscopy of weakly bound molecules. Phys. Rev. Lett. 110, 135301 (2013).

    Article  ADS  Google Scholar 

  42. Stewart, J. T., Gaebler, J. P., Drake, T. E. & Jin, D. S. Verification of universal relations in a strongly interacting Fermi gas. Phys. Rev. Lett. 104, 235301 (2010).

    Article  ADS  Google Scholar 

  43. Langmack, C., Barth, M., Zwerger, W. & Braaten, E. Clock shift in a strongly interacting two-dimensional Fermi gas. Phys. Rev. Lett. 108, 060402 (2012).

    Article  ADS  Google Scholar 

  44. Wild, R. J. et al. Measurements of Tan’s contact in an atomic Bose-Einstein condensate. Phys. Rev. Lett. 108, 145305 (2012).

    Article  ADS  Google Scholar 

  45. Zou, Y. Q. et al. Tan’s two-body contact across the superfluid transition of a planar Bose gas. Nat. Commun. 12, 760 (2021).

    Article  ADS  Google Scholar 

  46. Lompe, T. et al. Radio-frequency association of Efimov trimers. Science 330, 940–944 (2010).

    Article  ADS  Google Scholar 

  47. Nakajima, S., Horikoshi, M., Mukaiyama, T., Naidon, P. & Ueda, M. Measurement of an Efimov trimer binding energy in a three-component mixture of 6Li. Phys. Rev. Lett. 106, 143201 (2011).

    Article  ADS  Google Scholar 

  48. Machtey, O., Shotan, Z., Gross, N. & Khaykovich, L. Association of Efimov trimers from a three-atom continuum. Phys. Rev. Lett. 108, 210406 (2012).

    Article  ADS  Google Scholar 

  49. Klauss, C. E. et al. Observation of Efimov molecules created from a resonantly interacting Bose gas. Phys. Rev. Lett. 119, 143401 (2017).

    Article  ADS  Google Scholar 

  50. Ferlaino, F. et al. Efimov resonances in ultracold quantum gases. Few Body Syst. 51, 113 (2011).

    Article  ADS  Google Scholar 

  51. Kunitski, M. et al. Observation of the Efimov state of the helium trimer. Science 348, 551–555 (2015).

    Article  ADS  Google Scholar 

  52. Campbell, G. K. et al. Imaging the Mott insulator shells by using atomic clock shifts. Science 313, 649–652 (2006).

    Article  ADS  Google Scholar 

  53. Jordens, R., Strohmaier, N., Gunter, K., Moritz, H. & Esslinger, T. A Mott insulator of fermionic atoms in an optical lattice. Nature 455, 204–207 (2008).

    Article  ADS  Google Scholar 

  54. Scazza, F. et al. Observation of two-orbital spin-exchange interactions with ultracold SU(N)-symmetric fermions. Nat. Phys. 10, 779–784 (2014).

    Article  Google Scholar 

  55. Pagano, G. et al. Strongly interacting gas of two-electron fermions at an orbital Feshbach resonance. Phys. Rev. Lett. 115, 265301 (2015).

    Article  ADS  Google Scholar 

  56. Höfer, M. et al. Observation of an orbital interaction-induced Feshbach resonance in 173Yb. Phys. Rev. Lett. 115, 265302 (2015).

    Article  ADS  Google Scholar 

  57. Donley, E. A., Claussen, N. R., Thompson, S. T. & Wieman, C. E. Atom–molecule coherence in a Bose–Einstein condensate. Nature 417, 529 (2002).

    Article  ADS  Google Scholar 

  58. Greiner, M., Regal, C. A. & Jin, D. S. Probing the excitation spectrum of a Fermi gas in the BCS-BEC crossover regime. Phys. Rev. Lett. 94, 070403 (2004).

    Article  Google Scholar 

  59. Zwierlein, M. W., Schunck, C. H., Stan, C. A., Raupach, S. M. F. & Ketterle, W. Formation dynamics of a fermion pair condensate. Phys. Rev. Lett. 94, 180401 (2005).

  60. Fuchs, J. et al. Binding energies of 6Li p-wave Feshbach molecules. Phys. Rev. A 77, 053616 (2008).

    Article  ADS  Google Scholar 

  61. Behrle, A. et al. Higgs mode in a strongly interacting fermionic superfluid. Nat. Phys. 14, 781–785 (2018).

    Article  Google Scholar 

  62. Hartke, T., Oreg, B., Jia, N. & Zwierlein, M. Quantum register of fermion pairs. Preprint at https://arxiv.org/abs/2103.13992 (2021).

  63. Bakr, W. S. et al. Orbital excitation blockade and algorithmic cooling in quantum gases. Nature 480, 500–503 (2011).

    Article  ADS  Google Scholar 

  64. Dao, T.-L., Georges, A., Dalibard, J., Salomon, C. & Carusotto, I. Measuring the one-particle excitations of ultracold fermionic atoms by stimulated Raman spectroscopy. Phys. Rev. Lett. 98, 240402 (2007).

    Article  ADS  Google Scholar 

  65. Koschorreck, M. et al. Attractive and repulsive Fermi polarons in two dimensions. Nature 485, 619–622 (2012).

    Article  ADS  Google Scholar 

  66. Brown, P. T. et al. Angle-resolved photoemission spectroscopy of a Fermi–Hubbard system. Nat. Phys. 16, 26–31 (2020).

    Article  Google Scholar 

  67. Sagi, Y., Drake, T. E., Paudel, R. & Jin, D. S. Measurement of the homogeneous contact of a unitary Fermi gas. Phys. Rev. Lett. 109, 220402 (2012).

    Article  ADS  Google Scholar 

  68. McGuirk, J. M. et al. Spatial resolution of spin waves in an ultracold gas. Phys. Rev. Lett. 89, 090402 (2002).

    Article  ADS  Google Scholar 

  69. Stamper-Kurn, D. M. & Ueda, M. Spinor Bose gases: symmetries, magnetism, and quantum dynamics. Rev. Mod. Phys. 85, 1191–1244 (2013).

    Article  ADS  Google Scholar 

  70. Du, X., Luo, L., Clancy, B. & Thomas, J. E. Observation of anomalous spin segregation in a trapped Fermi gas. Phys. Rev. Lett. 101, 150401 (2008).

    Article  ADS  Google Scholar 

  71. Koschorreck, M., Pertot, D., Vogt, E. & Kohl, M. Universal spin dynamics in two-dimensional Fermi gases. Nat. Phys. 9, 405–409 (2013).

    Article  Google Scholar 

  72. Heinze, J. et al. Engineering spin waves in a high-spin ultracold Fermi gas. Phys. Rev. Lett. 110, 250402 (2013).

    Article  ADS  Google Scholar 

  73. Bardon, A. B. et al. Transverse demagnetization dynamics of a unitary Fermi gas. Science 344, 722–724 (2014).

    Article  ADS  Google Scholar 

  74. Trotzky, S. et al. Observation of the Leggett-Rice effect in a unitary Fermi gas. Phys. Rev. Lett. 114, 015301 (2015).

    Article  ADS  Google Scholar 

  75. Luciuk, C. et al. Observation of quantum-limited spin transport in strongly interacting two-dimensional Fermi gases. Phys. Rev. Lett. 118, 130405 (2017).

    Article  ADS  Google Scholar 

  76. Deutsch, C. et al. Spin self-rephasing and very long coherence times in a trapped atomic ensemble. Phys. Rev. Lett. 105, 020401 (2010).

    Article  ADS  Google Scholar 

  77. Krauser, J. S. et al. Giant spin oscillations in an ultracold Fermi sea. Science 343, 157–160 (2014).

    Article  ADS  Google Scholar 

  78. Gross, C., Zibold, T., Nicklas, E., Estève, J. & Oberthaler, M. K. Nonlinear atom interferometer surpasses classical precision limit. Nature 464, 1165–1169 (2010).

    Article  ADS  Google Scholar 

  79. Martin, P. J., Oldaker, B. G., Miklich, A. H. & Pritchard, D. E. Bragg scattering of atoms from a standing light wave. Phys. Rev. Lett. 60, 515–518 (1988).

    Article  ADS  Google Scholar 

  80. Stenger, J. et al. Bragg spectroscopy of a Bose-Einstein condensate. Phys. Rev. Lett. 82, 4569–4573 (1999).

    Article  ADS  Google Scholar 

  81. Gerbier, F. et al. Experimental study of the thermodynamics of an interacting trapped Bose-Einstein condensed gas. Phys. Rev. A 70, 013607 (2004).

    Article  ADS  Google Scholar 

  82. Stamper-Kurn, D. M. et al. Excitation of phonons in a Bose-Einstein condensate by light scattering. Phys. Rev. Lett. 83, 2876–2879 (1999).

    Article  ADS  Google Scholar 

  83. Steinhauer, J., Ozeri, R., Katz, N. & Davidson, N. Excitation spectrum of a Bose-Einstein condensate. Phys. Rev. Lett. 88, 120407 (2002).

    Article  ADS  Google Scholar 

  84. Ozeri, R., Katz, N., Steinhauer, J. & Davidson, N. Colloquium: bulk Bogoliubov excitations in a Bose-Einstein condensate. Rev. Mod. Phys. 77, 187–205 (2005).

    Article  ADS  Google Scholar 

  85. Vogels, J. M., Xu, K., Raman, C., Abo-Shaeer, J. R. & Ketterle, W. Experimental observation of the Bogoliubov transformation for a Bose-Einstein condensed gas. Phys. Rev. Lett. 88, 060402 (2002).

    Article  ADS  Google Scholar 

  86. Papp, S. B. et al. Bragg spectroscopy of a strongly interacting 85Rb Bose-Einstein condensate. Phys. Rev. Lett. 101, 135301 (2008).

    Article  ADS  Google Scholar 

  87. Lopes, R. et al. Quasiparticle energy in a strongly interacting homogeneous Bose-Einstein condensate. Phys. Rev. Lett. 118, 210401 (2017).

    Article  ADS  Google Scholar 

  88. Lopes, R. et al. Quantum depletion of a homogeneous Bose-Einstein condensate. Phys. Rev. Lett. 119, 190404 (2017).

    Article  ADS  Google Scholar 

  89. Seo, S. W., Ko, B., Kim, J. H. & Shin, Y.-I. Observation of vortex-antivortex pairing in decaying 2d turbulence of a superfluid gas. Sci. Rep. 7, 4587 (2017).

    Article  ADS  Google Scholar 

  90. Johnstone, S. P. et al. Evolution of large-scale flow from turbulence in a two-dimensional superfluid. Science 364, 1267–1271 (2019).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  91. Gauthier, G. et al. Giant vortex clusters in a two-dimensional quantum fluid. Science 364, 1264–1267 (2019).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  92. Deh, B., Marzok, C., Slama, S., Zimmermann, C. & Courteille, P. W. Bragg spectroscopy and Ramsey interferometry with an ultracold Fermi gas. Appl. Phys. B 97, 387 (2009).

    Article  ADS  Google Scholar 

  93. Cheuk, L. W. et al. Spin-injection spectroscopy of a spin-orbit coupled Fermi gas. Phys. Rev. Lett. 109, 095302 (2012).

    Article  ADS  Google Scholar 

  94. Wang, P. et al. Spin-orbit coupled degenerate Fermi Gases. Phys. Rev. Lett. 109, 95301 (2012).

    Article  ADS  Google Scholar 

  95. Veeravalli, G., Kuhnle, E., Dyke, P. & Vale, C. J. Bragg spectroscopy of a strongly interacting Fermi gas. Phys. Rev. Lett. 101, 250403 (2008).

    Article  ADS  Google Scholar 

  96. Inada, Y., Horikoshi, M., Nakajima, S., Kuwata-Gonokami, M., Ueda, M. & Mukaiyama, T. Critical temperature and condensate fraction of a fermion pair condensate. Phys. Rev. Lett. 101, 180406 (2008).

    Article  ADS  Google Scholar 

  97. Lingham, M. G., Fenech, K., Hoinka, S. & Vale, C. J. Local observation of pair condensation in a Fermi gas at unitarity. Phys. Rev. Lett. 112, 100404 (2014).

    Article  ADS  Google Scholar 

  98. Hoinka, S. et al. Goldstone mode and pair-breaking excitations in atomic Fermi superfluids. Nat. Phys. 13, 943–946 (2017).

    Article  Google Scholar 

  99. Biss, H. et al. Excitation spectrum and superfluid gap of an ultracold Fermi gas. Preprint at https://arxiv.org/abs/2105.09820 (2021).

  100. Navon, N., Smith, R. P. & Hadzibabic, Z. Quantum gases in optical boxes. Nat. Phys. https://doi.org/10.1038/s41567-021-01403-z (2021).

  101. Patel, P. B. et al. Universal sound diffusion in a strongly interacting Fermi gas. Science 370, 1222–1226 (2020).

    Article  MathSciNet  ADS  Google Scholar 

  102. Hohenberg, P. C. & Martin, P. C. Microscopic theory of superfluid helium. Ann. Phys. 34, 291–359 (1965).

    Article  ADS  Google Scholar 

  103. Kuhn, C. C. N. et al. High-frequency sound in a unitary Fermi gas. Phys. Rev. Lett. 124, 150401 (2020).

    Article  ADS  Google Scholar 

  104. Bohlen, M. et al. Sound propagation and quantum-limited damping in a two-dimensional Fermi gas. Phys. Rev. Lett. 124, 240403 (2020).

    Article  ADS  Google Scholar 

  105. Cao, C. et al. Universal quantum viscosity in a unitary Fermi gas. Science 331, 58–61 (2011).

    Article  ADS  Google Scholar 

  106. Adams, A., Carr, L. D., Schäfer, T., Steinberg, P. & Thomas, J. E. Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality. New J. Phys. 14, 115009 (2012).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  107. Enss, T. & Thywissen, J. H. Universal spin transport and quantum bounds for unitary fermions. Annu. Rev. Condens. Matter Phys. 10, 85–106 (2019).

    Article  ADS  Google Scholar 

  108. Richard, S. et al. Momentum spectroscopy of 1d phase fluctuations in Bose-Einstein condensates. Phys. Rev. Lett. 91, 010405 (2003).

    Article  ADS  Google Scholar 

  109. Cladé, P., Ryu, C., Ramanathan, A., Helmerson, K. & Phillips, W. D. Observation of a 2D Bose gas: from thermal to quasicondensate to superfluid. Phys. Rev. Lett. 102, 170401 (2009).

    Article  ADS  Google Scholar 

  110. Yang, T. L. et al. Measurement of the dynamical structure factor of a 1D interacting Fermi gas. Phys. Rev. Lett. 121, 103001 (2018).

    Article  ADS  Google Scholar 

  111. He, F. et al. Emergence and disruption of spin-charge separation in one-dimensional repulsive fermions. Phys. Rev. Lett. 125, 190401 (2020).

    Article  ADS  Google Scholar 

  112. Pagano, G. et al. A one-dimensional liquid of fermions with tunable spin. Nat. Phys. 10, 198–201 (2014).

    Article  Google Scholar 

  113. Sobirey, L. et al. Comparing fermionic superfluids in two and three dimensions. Preprint at https://arxiv.org/abs/2106.11893 (2021).

  114. Mottl, R. et al. Roton-type mode softening in a quantum gas with cavity-mediated long-range interactions. Science 336, 1570–1573 (2012).

    Article  ADS  Google Scholar 

  115. Léonard, J., Morales, A., Zupancic, P., Donner, T. & Esslinger, T. Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas. Science 358, 1415–1418 (2017).

    Article  ADS  Google Scholar 

  116. Li, J.-R. et al. A stripe phase with supersolid properties in spin–orbit-coupled Bose–Einstein condensates. Nature 543, 91–94 (2017).

    Article  ADS  Google Scholar 

  117. Guo, M. et al. The low-energy Goldstone mode in a trapped dipolar supersolid. Nature 574, 386–389 (2019).

    Article  ADS  Google Scholar 

  118. Tanzi, L. et al. Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas. Nature 574, 382–385 (2019).

    Article  ADS  Google Scholar 

  119. Chomaz, L. et al. Long-lived and transient supersolid behaviors in dipolar quantum gases. Phys. Rev. X 9, 021012 (2019).

    Google Scholar 

  120. Norcia, M. A. & Ferlaino, F. Developments in atomic control using ultracold magnetic lanthanides. Nat. Phys. https://doi.org/10.1038/s41567-021-01398-7 (2021).

  121. Petter, D. et al. Probing the roton excitation spectrum of a stable dipolar Bose gas. Phys. Rev. Lett. 122, 183401 (2019).

    Article  ADS  Google Scholar 

  122. Hertkorn, J. et al. Density fluctuations across the superfluid-supersolid phase transition in a dipolar quantum gas. Phys. Rev. X 11, 011037 (2021).

    Google Scholar 

  123. Greiner, M., Mandel, O., Esslinger, T., W Hänsch, T. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39–44 (2002).

    Article  ADS  Google Scholar 

  124. Stöferle, T., Moritz, H., Schori, C., Köhl, M. & Esslinger, T. Transition from a strongly interacting 1D superfluid to a Mott insulator. Phys. Rev. Lett. 92, 130403 (2004).

    Article  ADS  Google Scholar 

  125. Clément, D., Fabbri, N., Fallani, L., Fort, C. & Inguscio, M. Exploring correlated 1D Bose gases from the superfluid to the Mott-insulator state by inelastic light scattering. Phys. Rev. Lett. 102, 155301 (2009).

    Article  ADS  Google Scholar 

  126. Xu, K. et al. Observation of strong quantum depletion in a gaseous Bose-Einstein Condensate. Phys. Rev. Lett. 96, 180405 (2006).

    Article  ADS  Google Scholar 

  127. Ernst, P. T. et al. Probing superfluids in optical lattices by momentum-resolved Bragg spectroscopy. Nat. Phys. 6, 56–61 (2010).

    Article  Google Scholar 

  128. Bissbort, U. et al. Detecting the amplitude mode of strongly interacting lattice bosons by Bragg scattering. Phys. Rev. Lett. 106, 205303 (2011).

    Article  ADS  Google Scholar 

  129. Endres, M. et al. The ‘Higgs’ amplitude mode at the two-dimensional superfluid/Mott insulator transition. Nature 487, 454–458 (2012).

    Article  ADS  Google Scholar 

  130. Tarruell, L., Greif, D., Uehlinger, T., Jotzu, G. & Esslinger, T. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Nature 483, 302–305 (2012).

    Article  ADS  Google Scholar 

  131. Uehlinger, T. et al. Artificial graphene with tunable interactions. Phys. Rev. Lett. 111, 185307 (2013).

    Article  ADS  Google Scholar 

  132. Leung, T.-H. et al. Interaction-enhanced group velocity of bosons in the flat band of an optical kagome lattice. Phys. Rev. Lett. 125, 133001 (2020).

    Article  ADS  Google Scholar 

  133. Lin, Y.-J., Jiménez-García, K. & Spielman, I. B. Spin–orbit-coupled Bose–Einstein condensates. Nature 471, 83–86 (2011).

    Article  ADS  Google Scholar 

  134. Wang, P. et al. Spin-orbit coupled degenerate Fermi gases. Phys. Rev. Lett. 109, 095301 (2012).

    Article  ADS  Google Scholar 

  135. Galitski, V. & Spielman, I. B. Spin–orbit coupling in quantum gases. Nature 494, 49–54 (2013).

    Article  ADS  Google Scholar 

  136. Williams, R. A., Beeler, M. C., LeBlanc, L. J., Jiménez-García, K. & Spielman, I. B. Raman-induced interactions in a single-component Fermi gas near an s-wave Feshbach resonance. Phys. Rev. Lett. 111, 095301 (2013).

    Article  ADS  Google Scholar 

  137. Mancini, M. et al. Observation of chiral edge states with neutral fermions in synthetic Hall ribbons. Science 349, 1510–1513 (2015).

    Article  MathSciNet  MATH  ADS  Google Scholar 

  138. Khamehchi, M. A. et al. Negative-mass hydrodynamics in a spin-orbit–coupled Bose-Einstein condensate. Phys. Rev. Lett. 118, 155301 (2017).

    Article  ADS  Google Scholar 

  139. Aidelsburger, M. et al. Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices. Phys. Rev. Lett. 111, 185301 (2013).

  140. Miyake, H., Siviloglou, G. A., Kennedy, C. J., Burton, W. C. & Ketterle, W. Realizing the Harper Hamiltonian with laser-assisted tunneling in optical lattices. Phys. Rev. Lett. 111, 185302 (2013).

    Article  ADS  Google Scholar 

  141. Aidelsburger, M. et al. Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms. Nat. Phys. 11, 162–166 (2015).

    Article  Google Scholar 

  142. Partridge, G. B., Strecker, K. E., Kamar, R. I., Jack, M. W. & Hulet, R. G. Molecular probe of pairing in the BEC-BCS crossover. Phys. Rev. Lett. 95, 20404 (2005).

    Article  ADS  Google Scholar 

  143. Deiglmayr, J. et al. Formation of ultracold polar molecules in the rovibrational ground state. Phys. Rev. Lett. 101, 133004 (2008).

    Article  ADS  Google Scholar 

  144. Kinoshita, T., Wenger, T. & Weiss, D. S. Local pair correlations in one-dimensional Bose gases. Phys. Rev. Lett. 95, 190406 (2005).

    Article  ADS  Google Scholar 

  145. Werner, F., Tarruell, L. & Castin, Y. Number of closed-channel molecules in the BEC-BCS crossover. Eur. Phys. J. B 68, 401–415 (2009).

    Article  ADS  Google Scholar 

  146. Sagi, Y., Drake, T. E., Paudel, R. & Jin, D. S. Measurement of the homogeneous contact of a unitary Fermi gas. Phys. Rev. Lett. 109, 220402 (2012).

    Article  ADS  Google Scholar 

  147. Yan, Z. Z., Ni, Y., Robens, C. & Zwierlein, M. W. Bose polarons near quantum criticality. Science 368, 190–194 (2020).

    Article  MathSciNet  ADS  Google Scholar 

  148. Son, D. T. & Thompson, E. G. Short-distance and short-time structure of a unitary Fermi gas. Phys. Rev. A 81, 063634 (2010).

    Article  ADS  Google Scholar 

  149. Hoinka, S., Lingham, M., Delehaye, M. & Vale, C. J. Dynamic spin response of a strongly interacting Fermi gas. Phys. Rev. Lett. 109, 050403 (2012).

    Article  ADS  Google Scholar 

  150. Hoinka, S. et al. Precise determination of the structure factor and contact in a unitary Fermi gas. Phys. Rev. Lett. 110, 055305 (2013).

    Article  ADS  Google Scholar 

  151. Hofmann, J. & Zwerger, W. Deep inelastic scattering on ultracold gases. Phys. Rev. X 7, 011022 (2017).

    Google Scholar 

  152. Kuhnle, E. D. et al. Universal behavior of pair correlations in a strongly interacting Fermi gas. Phys. Rev. Lett. 105, 070402 (2010).

    Article  ADS  Google Scholar 

  153. Kuhnle, E. D. et al. Temperature dependence of the universal contact parameter in a unitary Fermi gas. Phys. Rev. Lett. 106, 170402 (2011).

    Article  ADS  Google Scholar 

  154. Carcy, C. et al. Contact and sum rules in a near-uniform Fermi gas at unitarity. Phys. Rev. Lett. 122, 203401 (2019).

    Article  ADS  Google Scholar 

  155. Hen, O. et al. Momentum sharing in imbalanced Fermi systems. Science 346, 614–617 (2014).

    Article  ADS  Google Scholar 

  156. Greif, D., Uehlinger, T., Jotzu, G., Tarruell, L. & Esslinger, T. Short-range quantum magnetism of ultracold fermions in an optical lattice. Science 340, 1307–1310 (2013).

    Article  ADS  Google Scholar 

  157. Hart, R. A. et al. Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms. Nature 519, 211–214 (2015).

    Article  ADS  Google Scholar 

  158. Gross, C. & Bakr, W. S. Quantum gas microscopy for single atom and spin detection. Nat. Phys. https://doi.org/10.1038/s41567-021-01370-5 (2021).

  159. Ni, K. K. et al. A high phase-space-density gas of polar molecules. Science 322, 231–235 (2008).

    Article  ADS  Google Scholar 

  160. Hazzard, K. R. A. et al. Many-body dynamics of dipolar molecules in an optical lattice. Phys. Rev. Lett. 113, 195302 (2014).

    Article  ADS  Google Scholar 

  161. Luciuk, C. et al. Evidence for universal relations describing a gas with p-wave interactions. Nat. Phys. 12, 599–605 (2016).

    Article  Google Scholar 

  162. Zeiher, J. et al. Many-body interferometry of a Rydberg-dressed spin lattice. Nat. Phys. 12, 1095–1099 (2016).

    Article  Google Scholar 

  163. Guardado-Sanchez, E. et al. Quench dynamics of a Fermi gas with strong nonlocal interactions. Phys. Rev. X 11, 021036 (2021).

    Google Scholar 

  164. Nascimbene, S. et al. Collective oscillations of an imbalanced Fermi gas: axial compression modes and polaron effective mass. Phys. Rev. Lett. 103, 170402–170404 (2009).

    Article  ADS  Google Scholar 

  165. Kohstall, C. et al. Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture. Nature 485, 615–618 (2012).

    Article  ADS  Google Scholar 

  166. Scazza, F. et al. Repulsive Fermi polarons in a resonant mixture of ultracold 6Li atoms. Phys. Rev. Lett. 118, 083602 (2017).

    Article  ADS  Google Scholar 

  167. Ness, G. et al. Observation of a smooth polaron-molecule transition in a degenerate Fermi gas. Phys. Rev. X 10, 041019 (2020).

    Google Scholar 

  168. Hu, M.-G. et al. Bose polarons in the strongly interacting regime. Phys. Rev. Lett. 117, 055301 (2016).

    Article  ADS  Google Scholar 

  169. Jørgensen, N. B. et al. Observation of attractive and repulsive polarons in a Bose-Einstein condensate. Phys. Rev. Lett. 117, 055302 (2016).

    Article  ADS  Google Scholar 

  170. Skou, M. G. et al. Non-equilibrium quantum dynamics and formation of the Bose polaron. Nat. Phys. 17, 731–735 (2021).

    Article  Google Scholar 

  171. Chevy, F. Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations. Phys. Rev. A 74, 63628 (2006).

    Article  ADS  Google Scholar 

  172. Massignan, P., Zaccanti, M. & Bruun, G. M. Polarons, dressed molecules and itinerant ferromagnetism in ultracold Fermi gases. Rep. Prog. Phys. 77, 034401 (2014).

    Article  ADS  Google Scholar 

  173. Schmidt, R. et al. Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress. Rep. Prog. Phys. 81, 024401 (2018).

    Article  MathSciNet  ADS  Google Scholar 

  174. Sidler, M. et al. Fermi polaron-polaritons in charge-tunable atomically thin semiconductors. Nat. Phys. 13, 255–261 (2017).

    Article  Google Scholar 

  175. Konishi, H., Roux, K., Helson, V. & Brantut, J.-P. Universal pair polaritons in a strongly interacting Fermi gas. Nature 596, 509–513 (2021).

    Article  ADS  Google Scholar 

  176. Edward Marti, G. et al. Coherent magnon optics in a ferromagnetic spinor Bose-Einstein condensate. Phys. Rev. Lett. 113, 155302 (2014).

    Article  ADS  Google Scholar 

  177. Fukuhara, T. et al. Microscopic observation of magnon bound states and their dynamics. Nature 502, 76–79 (2013).

    Article  ADS  Google Scholar 

  178. Weitenberg, C. & Simonet, J. Tailoring quantum gases by Floquet engineering. Nat. Phys. https://doi.org/10.1038/s41567-021-01316-x (2021).

  179. Danzl, J. G. et al. Quantum gas of deeply bound ground state molecules. Science 321, 1062–1066 (2008).

    Article  ADS  Google Scholar 

  180. Baranov, M. A., Dalmonte, M., Pupillo, G. & Zoller, P. Condensed matter theory of dipolar quantum gases. Chem. Rev. 112, 5012–5061 (2012).

    Article  Google Scholar 

  181. Moses, S., Covey, J., Miecnikowski, M., Jin, D. & Ye, J. New frontiers for quantum gases of polar molecules. Nat. Phys. 13, 13–20 (2017).

    Article  Google Scholar 

  182. Altman, E. et al. Quantum simulators: architectures and opportunities. PRX Quantum 2, 017003 (2021).

    Article  Google Scholar 

  183. Courtois, J.-Y., Grynberg, G., Lounis, B. & Verkerk, P. Recoil-induced resonances in cesium: an atomic analog to the free-electron laser. Phys. Rev. Lett. 72, 3017–3020 (1994).

    Article  ADS  Google Scholar 

  184. Kozuma, M. et al. Coherent splitting of Bose-Einstein condensed atoms with optically induced Bragg diffraction. Phys. Rev. Lett. 82, 871–875 (1999).

    Article  ADS  Google Scholar 

  185. Brunello, A., Dalfovo, F., Pitaevskii, L., Stringari, S. & Zambelli, F. Momentum transferred to a trapped Bose-Einstein condensate by stimulated light scattering. Phys. Rev. A 64, 063614 (2001).

    Article  ADS  Google Scholar 

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Acknowledgements

C.J.V. acknowledges financial support from the Australian Research Council Centre of Excellence in Future Low-Energy Electronics Technologies (CE170100039).

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  1. Optical Sciences Centre, ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Swinburne University of Technology, Hawthorn, VIC, Australia

    Chris J. Vale

  2. MIT-Harvard Centre for Ultracold Atoms, Massachusetts Institute of Technology, Cambridge, MA, USA

    Martin Zwierlein

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Vale, C.J., Zwierlein, M. Spectroscopic probes of quantum gases. Nat. Phys. 17, 1305–1315 (2021). https://doi.org/10.1038/s41567-021-01434-6

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