TITLE:  Space-time crystal with trapped ions

ABSTRACT: Symmetry and its spontaneous breaking is a central topic in modern physics. The two most fundamental symmetries in nature are spatial and time translational symmetry, as they imply directly momentum and energy conservations. Spontaneous symmetry breaking of spatial translational symmetry leads to the well-known formation of crystal. One can thus imagine that 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”, which is the lowest energy state one can possibly get in the real world, that breaks time translational symmetry. In this talk, I will describe how such “effective ground state” can be obtained in a real world experimental setup with trapped ions, and how such state leads to a space-time crystal.