Stabilizing a discrete time crystal against dissipation

TL;DR

This paper demonstrates that a discrete time crystal can be stabilized against environmental dissipation using coherent feedback, specifically through photon reflection, which preserves its nonergodic properties.

Contribution

The authors introduce a feedback mechanism using photon reflection to stabilize discrete time crystals against dissipation, supported by a new matrix product operator algorithm for non-Markovian dynamics.

Findings

Time crystalline signals can survive dissipation via photon reflection.

The stabilization mechanism is robust against weak imperfections.

A new matrix product operator algorithm was developed for non-Markovian dynamics.

Abstract

Eigenstate phases such as the discrete time crystal exhibit an inherent instability upon the coupling to an environment, which restores equipartition of energy and therefore acts against the protecting nonergodicity. Here, we demonstrate that a discrete time crystal can be stabilized against dissipation using coherent feedback. For a kicked random Ising chain subject to a radiative decay, we show that the time crystalline signal can survive through a mechanism of constructive interference upon reflecting the emitted photons by a mirror. We introduce a matrix product operator algorithm to solve the resulting non-Markovian dynamics. We find that the stabilization mechanism is robust against weak imperfections.