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arXiv:1609.09053 · Nature

Supersolid formation in a quantum gas breaking a continuous translational symmetry

Julian Léonard, Andrea Morales, Philip Zupancic, Tilman Esslinger, Tobias Donner

Published Feb 28, 2017• 542 citations
arXivHTMLPDF
DOI
10.1038/nature21067

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We simulate interaction quenches crossing from a superfluid to a supersolid state in a dipolar quantum gas of Dy 164 atoms, trapped in an elongated tube with periodic boundary conditions, via the extended Gross-Pitaevskii equation. A freeze-out time is observed through a delay in supersolid formation after crossing the critical point. We compute the density-density correlations at the freeze-out time and extract the frozen correlation length for the solid order. An analysis of the freeze-out time and correlation length versus the interaction quench rate allows us to extract universal exponents corresponding to the relaxation time and correlation length based on predictions of the Kibble-Zurek mechanism. Over several orders of magnitude, clear power-law scaling is observed for both the freeze-out time and the correlation length, and the corresponding exponents are compatible with predictions based on the excitation spectrum calculated via Bogoliubov theory. Defects due to independent local breaking of translational symmetry, contributing to globally incommensurate supersolid order, are identified, and their number at the freeze-out time is found to also scale as a power law. Our results support the hypothesis of a continuous transition whose universality class remains to be determined but appears to differ from that of the (1 + 1)-dimensional model.
Abstract Supersolid is an exotic state of matter characterized by both superfluid properties and periodic particle density modulation, due to spontaneous breaking of U(1) gauge symmetry and spatial translation symmetry, respectively. For conventional supersolids, continuous translation symmetry breaking is accompanied by one gapless Goldstone mode in the excitation spectra. An interesting question naturally arises: what is the consequence of breaking discrete translation symmetry for supersolids? In this work, we study the consequence of discrete symmetry breaking in a Z n supersolid resulting from spontaneous breaking of a discrete Z n symmetry, or equivalently, a discrete translation symmetry. This Z n supersolid is realized in the stripe phase of spin–orbit-coupled Bose–Einstein condensate under an external periodic potential with period 1 / n of intrinsic stripe period. For n ⩾ 2 , there are n degenerate ground states with spontaneously broken lattice translation symmetry. The low-energy excitations of Z n supersolid include a pseudo-Goldstone mode, whose excitation gap at long wavelength limit is found to decrease rapidly with n. We further numerically show that, when confined in a harmonic trap, a spin-dependent perturbation can result in the transition between degenerate ground states of Z n supersolid. With the integer n tunable using the experimental technique of generating subwavelength optical lattice, the Z n supersolid proposed here offers a cold atom platform to simulate physics related with generic Z n symmetry breaking in a highly controllable setting.
Supersolids are theoretically predicted quantum states that break the continuous rotational and translational symmetries of liquids while preserving superfluid transport properties. Over the last decade, much progress has been made in understanding and characterizing supersolid phases through numerical simulations for specific interaction potentials. The formulation of an analytically tractable framework for generic interactions still poses theoretical challenges. By going beyond the usually considered quadratic truncations, we derive a systematic higher-order generalization of the Gross-Pitaevskii mean-field model in conceptual similarity with the Swift-Hohenberg theory of pattern formation. We demonstrate the tractability of this broadly applicable approach by determining the ground-state phase diagram and the dispersion relations for the supersolid lattice vibrations in terms of the potential parameters. Our analytical predictions agree well with numerical results from direct hydrodynamic simulations and earlier quantum Monte Carlo studies. The underlying framework is universal and can be extended to anisotropic pair potentials with a complex Fourier-space structure.