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An optical lattice with sound


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 \({\boldsymbol{\omega }}({{\boldsymbol{k}}}_{\perp })\).

Data availability

The datasets generated during the current study are available in the Harvard Dataverse Repository,


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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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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).

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