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arXiv · 2107.14505

Dynamics of spontaneous symmetry breaking in a space-time crystal

J. N. Stehouwer·J. Smits·P. van der Straten·H. T. C. Stoof
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Abstract

We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The non-equilibrium physics related to such a driven-dissipative system is discussed in both the Langevin as well as the Fokker-Planck formulation. We consider a semi-classical and a fully quantum approach, depending on the dissipation being either frequency independent or linearly dependent on frequency, respectively. For both cases, the Langevin equation and Fokker-Planck equation are derived, and the resulting equilibrium distribution is studied. We also study the time evolution of the space-time crystal and focus in particular on its formation and the associated dynamics of the spontaneous breaking of a Z2 symmetry out of the symmetry unbroken phase, i.e., the equilibrium Bose-Einstein condensate before the periodic drive is turned on. Finally, we compare our results with experiments and conclude that our theory provides a solid foundation for the observations.

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J. N. Stehouwer, J. Smits, P. van der Straten, H. T. C. Stoof. 2021-07-30. Dynamics of spontaneous symmetry breaking in a space-time crystal. https://doi.org/10.1103/physreva.104.043324

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