Time Crystals in Open Quantum Systems

Abstract

Ever since the existence of a time crystal was theorised by Frank Wilczek in 2012, physicists have proposed several possible realisations. Some of these have been experimentally realised, such as excited state time crystals and Floquet (or driven) time crystals. Yet another possible realisation is offered in [PRB 76, 214303 (2007)]. It shows that the coupling of a particle to a reservoir of two-level systems can lead under certain conditions to a long term oscillation of the particle. This thesis revisits this research from a time crystal perspective and aims to understand the parameters controlling the time crystalline phase. The particle-bath system is essentially a modified Caldeira-Leggett model and can be solved analytically. By examining the position of the particle and the pole structure of its Laplace transform, we can conclude that a time crystal phase is indeed present. The parameters that govern this phase are the damping constant, the temperature, and the long term properties of the bath. Depending on these parameters, we observe either persistent or decaying oscillations. Investigating the pole structure, we find properties that describe a phase transition between these two phases.