Time crystals: Analysis of experimental conditions

Abstract

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultra-cold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various non-trivial condensed matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultra-cold atoms are bouncing on a randomly moving mirror.

Creating big time crystals with ultracold atoms

“…Time crystals involving resonantly bouncing ultracold atoms provide a platform for investigating a broad range of non-trivial condensed matter phenomena in the time domain. These include Mott insulator-like phases in the time-domain [23]; Anderson localization [6,23] and many-body localization [24] due to temporal disorder; dynamical quantum phase transitions in time crystals [6,25]; many-body systems with exotic long-range interactions [26]; time quasi-crystals  which are ordered but not periodic in time [26,27]; and topological time crystals [28].…”

“…Experimental signatures for the formation of a discrete time crystal for the case s = 40 were presented in Figs. 3 and 4 of [6].…”

“…1) and the corresponding eigenstates are Bloch waves. These eigenvalues are actually quasi-energies of a periodically driven particle while the eigenstates are Floquet states obtained in the frame moving along the resonant orbit [5,6,23,31]. In the quantum description we will apply the tight-binding approximation by restricting the analysis to the first energy band of the quantized version of the Hamiltonian (3).…”

“…In an earlier paper [6] we presented mean-field calculations for a BEC of interacting atoms bouncing resonantly on an oscillating mirror that exhibited dramatic breaking of timetranslation symmetry to form a discrete time crystal. These time crystals can evolve with a period more than an order of magnitude (s ≫ 10) longer than the driving period, thereby creating a large number of available 'lattice sites' in the time domain.…”

“…These time crystals can evolve with a period more than an order of magnitude (s ≫ 10) longer than the driving period, thereby creating a large number of available 'lattice sites' in the time domain. Such a system provides a platform for investigating a broad range of nontrivial condensed matter phenomena in the time domain [6,[23][24][25][26][27][28]. In Refs.…”