Time crystals in a shaken atom-cavity system*

Periodically driven atoms in a high finesse optical cavity enjoy a very rich phase diagram. By off resonant driving the equilibrium properties of the system can be renormalised in a controlled fashion, while resonant driving allows for new non-equilibrium phases such as time crystalline phases and dynamical density wave orders as recently reported. In this talk, I will discuss the emergence of an incommensurate time crystal by a phase-modulated transverse pump field resulting in a shaken pump lattice. This periodically driven system exhibits macroscopic oscillations in the number of cavity photons and order parameters at noninteger multiples of the driving period, which signals the appearance of an incommensurate time crystal. The subharmonic oscillatory motion corresponds to dynamical switching between symmetry-broken states, which are nonequilibrium bond ordered density wave states. Employing a semiclassical phase-space representation for the driven-dissipative quantum dynamics, we confirm the rigidity and persistence of the time crystalline phase. We identify experimentally relevant parameter regimes for which the time crystal phase is long lived, and map out the dynamical phase diagram. I will further present preliminary experimental results that confi​rm our theoretical predictions.