Dynamics of spontaneous symmetry breaking in a space-time crystal
arXiv:2107.14505 · doi:10.1103/PhysRevA.104.043324
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.
arXiv comment15 pages, 5 figures
References in corpus (19)
- Quantum many-body systems out of equilibrium
- Collapse and Revival of the Matter Wave Field of a Bose-Einstein Condensate
- Observation of a Discrete Time Crystal
- Observation of discrete time-crystalline order in a disordered dipolar many-body system
- Quantum Time Crystals
- Dynamic clustering in active colloidal suspensions with chemical signaling
- Single-Spin Addressing in an Atomic Mott Insulator
- Berry phase correction to electron density of states in solids
- Classical Time Crystals
- Ultracold atoms out of equilibrium
- Observation of Discrete-Time-Crystal Signatures in an Ordered Dipolar Many-Body System
- Observation of a dissipative time crystal
- Observation of time quasicrystal and its transition to superfluid time crystal
- Observation of a space-time crystal in a superfluid quantum gas
- Temporal order in periodically driven spins in star-shaped clusters
- Phase-Space Berry Phases in Chiral Magnets: Dzyaloshinskii-Moriya Interaction and the Charge of Skyrmions
- Real space observation of magnon interaction with driven space-time crystals
- Spontaneous symmetry breaking in a driven-dissipative system
- On the long-term stability of space-time crystals