Space-time crystal with trapped ions & Dynamical Phase Transition with trapped ions
Spontaneous Symmetry Breaking of spatial translational symmetry leads to formation of crystal. A simultaneous breaking of time translational symmetry would lead to a “space-time crystal”, with persistent periodical motion in ground state. Although quantum mechanics prevent one from having any motion in exact ground state, it is found that for strong interacting many-body system, one may however obtain an “effective ground state” that breaks time translational symmetry, and is arbitrarily close to exact ground state. We propose the first possible realization a “space-time crystal”, by using ultra-cold ions confined in a ring geometry. Under a fractional magnetic flux, the ion crystal will rotate persistently when cooled down to ground state. The effective ground state can be prepared through stimulated Raman process, and the broken time translational symmetry can be detected by state-dependent fluorescence.
A dynamical phase transition occurs when a non-equilibrium initial state of an isolated quantum many-body system evolves into states with distinctive configurations at different time regions. A typical example is the phenomenon of pre-thermalization, where a set of physical observables evolve into non-thermal steady values at intermediate time scale, and eventually relax into thermal values at a much longer time scale. Here we find such pre-thermalization occurs in a long-range transverse field Ising Hamiltonian, generated by optical spin-dependent force on a trapped ion chain. The thermalized state and pre-thermalized state have different symmetry of spin configurations, leading to a symmetry-breaking dynamical phase transition. The dynamical phase transition disappears when the laser detuning that controls Ising interaction pattern is tuned above a critical value. This distinctive dynamical behavior can be readily tested by current ion trap technology.