Discrete time quasi-crystal in Rydberg atomic chain

TL;DR

This paper proposes a method to generate and analyze discrete time quasi-crystals in Rydberg atomic chains by coupling two incommensurately driven time-crystals, revealing aperiodic responses caused by Rydberg blockade interactions.

Contribution

It introduces a novel approach to realize discrete time quasi-crystals in Rydberg systems through coupling, expanding the understanding of non-equilibrium quantum phases.

Findings

Demonstrates robustness of the proposed quasi-crystal behavior.

Computes the phase diagram of relevant observables.

Shows emergence of aperiodic response due to Rydberg blockade.

Abstract

Discrete time quasi-crystals are non-equilibrium quantum phenomena with quasi-periodic order in the time dimension, and are an extension of the discrete time-crystal phase. As a natural platform to explore the non-equilibrium phase of matter, the Rydberg atomic array has implemented the quantum simulation of the discrete-time crystal phase, associated with quantum many-body scar state. However, the existence of discrete time quasi-crystal on the Rydberg cold atom experiment platform has yet to be conceived. Here, we propose a method to generate the discrete time quasi-crystal behavior by coupling two discrete time-crystals, where associated two external driving frequencies have the maximum incommensurability. While we analysis its robustness and compute the phase diagram of corresponding observables. We significantly calculate the entanglement entropy between two parts of the system. Remarkably, we find the emergence of the aperiodic response is indeed caused by interaction between systems via Rydberg blockade effect. Our method thus offers the possibilities to explore the novel phases in quantum simulator.