Floquet Time Crystals

Abstract

We define what it means for time translation symmetry to be spontaneously broken in a quantum system and show with analytical arguments and numerical simulations that this occurs in a large class of many-body-localized driven systems with discrete time-translation symmetry.

Observation of a discrete time crystal

“…These two states evolve at different rates corresponding to their respective quasi-energies, giving rise to the sub-harmonic periodic oscillations of physical observables. Such oscillations are expected to persist at increasingly long times as the system size increases 7,8,10 .In summary, we present the first experimental observation of discrete time translation symmetry breaking into a DTC. We measure persistent oscillations and synchronizations of interacting spins in a chain and show that the discrete time crystal is rigid, or robust to perturbations in the drive.…”

“…These two states evolve at different rates corresponding to their respective quasi-energies, giving rise to the sub-harmonic periodic oscillations of physical observables. Such oscillations are expected to persist at increasingly long times as the system size increases 7,8,10 .…”

“…Analogous to crystals in space, the breaking of translation symmetry in time and the emergence of a "time crystal" was recently proposed 2,3 , but later shown to be forbidden in thermal equilibrium [4][5][6] . However, nonequilibrium Floquet systems subject to a periodic drive can exhibit persistent time-correlations at an emergent sub-harmonic frequency [7][8][9][10] . This new phase of matter has been dubbed a "discrete time crystal" (DTC) 10,11 .…”

“…The proposal of such a "time crystal" 2 for time-independent Hamiltonians has led to much discussion, with the conclusion that such structures cannot exist in the ground state or any thermal equilibrium state of a quantum mechanical system [4][5][6] . A simple intuitive explanation is that quantum equilibrium states have time-independent observables by Time (100 Floquet periods) construction; thus, time translation symmetry can only be spontaneously broken in non-equilibrium systems [7][8][9][10] . In particular, the dynamics of periodically-driven Floquet systems possesses a discrete time translation symmetry governed by the drive period.…”

“…Such a response is analogous to commensurate charge density waves that break the discrete translation symmetry of their underlying lattice 1 . The robust subharmonic synchronization of the many-body Floquet system is the essence of the discrete time crystal phase [7][8][9][10] . In a DTC, the underlying Floquet drive should generally be accompanied by strong disorder, leading to manybody localization 13 and thereby preventing the quantum system from absorbing the drive energy and heating to infinite temperatures [14][15][16][17] .…”