Time Crystal from Self-Amplification of Spontaneous Analog Hawking Radiation

TL;DR

This paper introduces a quantum time crystal based on a black-hole laser model, where spontaneous Hawking radiation self-amplifies to produce a periodic, non-equilibrium phase characterized by unique time operators.

Contribution

It presents a novel time crystal model derived from spontaneous Hawking radiation in a black-hole laser, with a new theoretical framework involving two distinct time operators.

Findings

Demonstrates periodic dependence of out-of-time correlation functions.

Shows spontaneous quantum emission of pairs of dispersive waves and solitons.

Establishes a theoretical link between parametric amplifiers and time operators.

Abstract

We propose a time crystal based on a quantum black-hole laser, where the genuinely spontaneous character of the symmetry breaking stems from the self-amplification of spontaneous Hawking radiation. The resulting Hawking time crystal (HTC) is characterized by the periodic dependence of the out-of-time density-density correlation function, while equal-time observables are time independent because they embody averages over different realizations with a random oscillation phase. The HTC provides a nonlinear periodic analog of the Andreev-Hawking effect, exhibiting anticorrelation bands resulting from the spontaneous, quantum emission of pairs of dispersive waves and solitons into the upstream and downstream regions. Remarkably, we prove that any parametric amplifier has associated a time operator, which leads to a unique characterization of the time-crystal formation in terms of two time operators: one associated with the initial black-hole laser and another associated with the final spontaneous Floquet state.