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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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## Data availability

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

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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.

## Author information

Authors

### Contributions

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

### Corresponding author

Correspondence to Benjamin L. Lev.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

• Accepted:

• Published:

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• DOI: https://doi.org/10.1038/s41586-021-03945-x

• ### Strain and pseudo-magnetic fields in optical lattices from density-assisted tunneling

• Maxime Jamotte
• Nathan Goldman
• Marco Di Liberto

Communications Physics (2022)

• ### Holographic supersolids

• Matteo Baggioli
• Giorgio Frangi

Journal of High Energy Physics (2022)