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An optical lattice with sound

Abstract

Quantized sound waves—phonons—govern the elastic response of crystalline materials, and also play an integral part in determining their thermodynamic properties and electrical response (for example, by binding electrons into superconducting Cooper pairs)1,2,3. The physics of lattice phonons and elasticity is absent in simulators of quantum solids constructed of neutral atoms in periodic light potentials: unlike real solids, traditional optical lattices are silent because they are infinitely stiff4. Optical-lattice realizations of crystals therefore lack some of the central dynamical degrees of freedom that determine the low-temperature properties of real materials. Here, we create an optical lattice with phonon modes using a Bose–Einstein condensate (BEC) coupled to a confocal optical resonator. Playing the role of an active quantum gas microscope, the multimode cavity QED system both images the phonons and induces the crystallization that supports phonons via short-range, photon-mediated atom–atom interactions. Dynamical susceptibility measurements reveal the phonon dispersion relation, showing that these collective excitations exhibit a sound speed dependent on the BEC–photon coupling strength. Our results pave the way for exploring the rich physics of elasticity in quantum solids, ranging from quantum melting transitions5 to exotic ‘fractonic’ topological defects6 in the quantum regime.

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Fig. 1: Transverse, double-pumped confocal cavity quantum electrodynamics system coupled to a BEC.
Fig. 2: Efficacy of double-pumping scheme.
Fig. 3: Soft-mode dispersion of density-wave polaritons below threshold.
Fig. 4: Goldstone dispersion relation \({\boldsymbol{\omega }}({{\boldsymbol{k}}}_{\perp })\).

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Data availability

The datasets generated during the current study are available in the Harvard Dataverse Repository, https://doi.org/10.7910/DVN/LGT5O6.

References

  1. Kittel, C. Introduction to Solid State Physics (Wiley, 2004).

  2. Chaikin, P. M. & Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge Unive. Press, 1995).

  3. Tinkham, M. Introduction to Superconductivity (Dover, 2004).

  4. Grimm, R., Weidemüller, M. & Ovchinnikov, Y. B. in Advances In Atomic, Molecular, and Optical Physics Vol. 42 (eds. Bederson, B. & Walther, H.) 95–170 (Elsevier, 2000).

  5. Beekman, A. J. et al. Dual gauge field theory of quantum liquid crystals in two dimensions. Phys. Rep. 683, 1–110 (2017).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  6. Pretko, M. & Radzihovsky, L. Fracton-elasticity duality. Phys. Rev. Lett. 120, 195301 (2018).

    Article  ADS  CAS  Google Scholar 

  7. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

    Article  ADS  CAS  Google Scholar 

  8. González-Cuadra, D., Grzybowski, P. R., Dauphin, A. & Lewenstein, M. Strongly correlated bosons on a dynamical lattice. Phys. Rev. Lett. 121, 090402 (2018).

    Article  ADS  Google Scholar 

  9. 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  CAS  Google Scholar 

  10. Pethick, C. & Smith, H. Bose-Einstein Condensation in Dilute Gases (Cambridge Univ. Press, 2002).

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

    Article  ADS  MathSciNet  CAS  Google Scholar 

  12. Brown, P. T. et al. Bad metallic transport in a cold atom Fermi-Hubbard system. Science 363, 379–382 (2018).

    Article  ADS  Google Scholar 

  13. Carusotto,, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).

    Article  ADS  Google Scholar 

  14. Kirton, P., Roses, M. M., Keeling, J. & Dalla Torre, E. G. Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa. Adv. Quantum Technol. 2, 1800043 (2018).

    Article  Google Scholar 

  15. Mivehvar, F., Piazza, F., Donner, T. & Ritsch, H. Cavity QED with quantum gases: new paradigms in many-body physics. Preprint at https://arxiv.org/abs/2102.04473 (2021).

  16. Klinder, J., Keßler, H., Bakhtiari, M. R., Thorwart, M. & Hemmerich, A. Observation of a superradiant Mott insulator in the Dicke-Hubbard model. Phys. Rev. Lett. 115, 230403 (2015).

    Article  ADS  CAS  Google Scholar 

  17. Landig, R. et al. Quantum phases from competing short- and long-range interactions in an optical lattice. Nature 532, 476–479 (2016).

    Article  ADS  CAS  Google Scholar 

  18. Kollár, A. J. et al. Supermode-density-wave-polariton condensation with a Bose–Einstein condensate in a multimode cavity. Nat. Commun. 8, 14386 (2017).

    Article  ADS  Google Scholar 

  19. Kroeze, R. M., Guo, Y. & Lev, B. L. Dynamical spin-orbit coupling of a quantum gas. Phys. Rev. Lett. 123, 160404 (2019).

    Article  ADS  CAS  Google Scholar 

  20. Gopalakrishnan, S., Lev, B. L. & Goldbart, P. M. Emergent crystallinity and frustration with Bose Einstein condensates in multimode cavities. Nat. Phys. 5, 845–850 (2009).

    Article  CAS  Google Scholar 

  21. Gopalakrishnan, S., Lev, B. L. & Goldbart, P. M. Atom-light crystallization of Bose–Einstein condensates in multimode cavities: Nonequilibrium classical and quantum phase transitions, emergent lattices, supersolidity, and frustration. Phys. Rev. A 82, 043612 (2010).

    Article  ADS  Google Scholar 

  22. Mivehvar, F., Ostermann, S., Piazza, F. & Ritsch, H. Driven-dissipative supersolid in a ring cavity. Phys. Rev. Lett. 120, 123601 (2018).

    Article  ADS  CAS  Google Scholar 

  23. Schuster, S., Wolf, P., Ostermann, S., Slama, S. & Zimmermann, C. Supersolid properties of a Bose-Einstein condensate in a ring resonator. Phys. Rev. Lett. 124, 143602 (2020).

    Article  ADS  CAS  Google Scholar 

  24. Léonard, J., Morales, A., Zupancic, P., Esslinger, T. & Donner, T. Supersolid formation in a quantum gas breaking a continuous translational symmetry. Nature 543, 87–90 (2017).

    Article  ADS  Google Scholar 

  25. 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 

  26. Ballantine, K. E., Lev, B. L. & Keeling, J. Meissner-like effect for a synthetic gauge field in multimode cavity QED. Phys. Rev. Lett. 118, 045302 (2017).

    Article  ADS  Google Scholar 

  27. Rylands, C., Guo, Y., Lev, B. L., Keeling, J. & Galitski, V. Photon-mediated Peierls transition of a 1D gas in a multimode optical cavity. Phys. Rev. Lett. 125, 010404 (2020).

    Article  ADS  CAS  Google Scholar 

  28. Vaidya, V. D. et al. Tunable-range, photon-mediated atomic interactions in multimode cavity QED. Phys. Rev. X 8, 011002 (2018).

    CAS  Google Scholar 

  29. Guo, Y., Kroeze, R. M., Vaidya, V. D., Keeling, J. & Lev, B. L. Sign-changing photon-mediated atom interactions in multimode cavity quantum electrodynamics. Phys. Rev. Lett. 122, 193601 (2019).

    Article  ADS  CAS  Google Scholar 

  30. Guo, Y. et al. Emergent and broken symmetries of atomic self-organization arising from Gouy phase shifts in multimode cavity QED. Phys. Rev. A 99, 053818 (2019).

    Article  ADS  CAS  Google Scholar 

  31. Lewenstein, M. et al. in AIP Conference Proceedings Vol. 869 (eds Roos, C., Häffner, H. & Blatt, R.) 201–211 (AIP, 2006).

  32. Ostermann, S., Piazza, F. & Ritsch, H. Spontaneous crystallization of light and ultracold atoms. Phys. Rev. X 6, 021026 (2016).

    Google Scholar 

  33. Dimitrova, I. et al. Observation of two-beam collective scattering phenomena in a Bose-Einstein condensate. Phys. Rev. A 96, 051603 (2017).

    Article  ADS  Google Scholar 

  34. Monroe, C. et al. Programmable quantum simulations of spin systems with trapped ions. Rev. Mod. Phys. 93, 025001 (2021).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  35. Siegman, A. E. Lasers (University Science Books, 1986).

  36. 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  CAS  Google Scholar 

  37. Papageorge, A. T., Kollár, A. J. & Lev, B. L. Coupling to modes of a near-confocal optical resonator using a digital light modulator. Opt. Express 24, 11447–11457 (2016).

    Article  ADS  CAS  Google Scholar 

  38. Devreese, J. T. & Alexandrov, A. S. Fröhlich polaron and bipolaron: recent developments. Rep. Prog. Phys. 72, 066501 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. 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 

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

    Article  ADS  MathSciNet  CAS  Google Scholar 

  42. Werman, Y., Kivelson, S. A. & Berg, E. Nonquasiparticle transport and resistivity saturation: a view from the large-N limit. npj Quant. Mater. 2, 7 (2017).

    Article  ADS  Google Scholar 

  43. Kollár, A. J., Papageorge, A. T., Baumann, K., Armen, M. A. & Lev, B. L. An adjustable-length cavity and Bose-Einstein condensate apparatus for multimode cavity QED. New J. Phys. 17, 043012 (2015).

    Article  ADS  Google Scholar 

  44. Kroeze, R. M., Guo, Y., Vaidya, V. D., Keeling, J. & Lev, B. L. Spinor self-ordering of a quantum gas in a cavity. Phys. Rev. Lett. 121, 163601 (2018).

    Article  ADS  CAS  Google Scholar 

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Acknowledgements

We thank S. Kivelson, S. Hartnoll and V. Khemani for stimulating discussions. We acknowledge funding support from the Army Research Office. Y.G. and B.M. acknowledge funding from the Stanford Q-FARM Graduate Student Fellowship and the NSF Graduate Research Fellowship, respectively. S.G. acknowledges support from NSF grant no. DMR-1653271.

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All authors contributed to the work and contributed to writing the paper.

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Correspondence to Benjamin L. Lev.

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Peer review information Nature thanks Francesco Piazza and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 DMD momentum probes.

ag, Measured DMD probe transmission cavity field and their phase profile line cuts. The values of \({k}_{\perp }/{k}_{r}\) in panels af are \([0,2.1,4.2,6.3,8.5,10.6]\times {10}^{-3}\), respectively. The white dashed line in panel a shows the length of the cuts in panel g. Additional features around the main probe field are due to imperfections of the confocal cavity and stray light from the DMD probe beam. The grey area is the half plane that contains the mirror image of the probe field, and we do not show this redundant portion of the image in the main text figures.

Supplementary information

Supplementary Information

Supplementary Information sections 1–9, including Supplementary Figs. 1–5 and references.

Supplementary Video 1 Phonon dynamics animation

Phonon dynamics animation illustrating the phonon dynamics via change in the atomic density in a chequerboard lattice with lattice constant \(\sqrt{2}\)λ. The \({k}_{\perp }\)used, 0.3kr, has been exaggerated in magnitude for clarity in showing the lattice motion in which the maximum excursion of a lattice site is 0.2λ.

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Guo, Y., Kroeze, R.M., Marsh, B.P. et al. An optical lattice with sound. Nature 599, 211–215 (2021). https://doi.org/10.1038/s41586-021-03945-x

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