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Kibble-Zurek scaling of the superfluid-supersolid transition in an elongated dipolar gas

Wyatt Kirkby1,2, Hayder Salman3,4, Thomas Gasenzer1,5, and Lauriane Chomaz2

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Phys. Rev. Research 7, 023248 – Published 11 June, 2025

DOI: https://doi.org/10.1103/x51r-vdyf

Abstract

We simulate interaction quenches crossing from a superfluid to a supersolid state in a dipolar quantum gas of Dy164 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 XY model.

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Phys. Rev. Research 7, 023248– Published 11 June, 2025
  • Received 27 November 2024
  • Accepted 15 May 2025
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