symmetry broken supersolid in spin–orbit-coupled Bose–Einstein condensates

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 $\mathbb{Z}_n$ supersolid resulting from spontaneous breaking of a discrete $\mathbb{Z}_n$ symmetry, or equivalently, a discrete translation symmetry. This $\mathbb{Z}_n$ 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 $n\unicode{x2A7E}2$ , there are n degenerate ground states with spontaneously broken lattice translation symmetry. The low-energy excitations of $\mathbb{Z}_n$ 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 $\mathbb{Z}_n$ supersolid. With the integer n tunable using the experimental technique of generating subwavelength optical lattice, the $\mathbb{Z}_n$ supersolid proposed here offers a cold atom platform to simulate physics related with generic $\mathbb{Z}_n$ symmetry breaking in a highly controllable setting.

Keywords

• supersolid
• spin–orbit coupled Bose–Einstein condensate
• pseudo-Goldstone mode