The rare event route to programmable time crystals

Abstract: Time crystals are many-body systems that spontaneously break time-translation symmetry, and thus exhibit long-range spatiotemporal order and robust periodic motion. Recent results have demonstrated how to build time-crystal phases in driven diffusive fluids, based on a particular class of symmetry-breaking dynamical phase transitions present in their rare event statistics. A main tool in this idea is the application of an external packing field coupled to density fluctuations, that triggers an instability to a time-crystal phase. In this seminar we will explore the connection between time crystals, rare events and dynamical phase transitions. We will also describe how to exploit this packing-field mechanism to engineer and control on demand programmable continuous time crystals characterized by an arbitrary number of rotating condensates, which can be further enhanced with higher-order modes. We will elucidate the underlying critical point, as well as general properties of the traveling condensates, illustrating our findings in various paradigmatic driven diffusive systems. Overall, these results demonstrate the versatility and broad possibilities of this promising route to time crystals.

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