Seminarium Optyczne

In analogy to spontaneous breaking of continuous space translation symmetry in the process of space crystal formation, it was proposed that spontaneous breaking of continuous time translation symmetry could lead to time crystal formation. In other words, a time-independent system prepared in the energy ground state is expected to reveal periodic motion under infinitely weak perturbation. In the case of the system proposed originally by Frank Wilczek, spontaneous breaking of time translation symmetry can not be observed if one starts with the ground state. We point out that the spontaneous time translation symmetry breaking can take place if the system is prepared in an excited eigenstate and may lead to a crystallization in time domain. The latter can be realized experimentally in ultra-cold atomic gases. By considering ultracold attractively interacting Bose gas we simulate the process of the spontaneous symmetry breaking due to measurements of particle positions and analyze the lifetime of the resulting symmetry broken state.