Higher-order discrete time crystals in a quantum chaotic top

TL;DR

This paper explores higher-order discrete time crystal phases in a quantum chaotic top, revealing stable 4-DTC phases beyond known 2-DTC phases, linked to classical phase space structures and system size.

Contribution

It demonstrates the existence of stable 4-DTC phases in a quantum chaotic system, extending the understanding of time crystals beyond previous symmetry-based explanations.

Findings

Identification of robust 2-DTC and DF phases near symmetric points

Discovery of stable 4-DTC phases at higher angular momentum

Classical phase portraits explain emergence of higher-order DTCs

Abstract

We characterize various dynamical phases of the simplest version of the quantum kicked-top model, a paradigmatic system for studying quantum chaos. This system exhibits both regular and chaotic behavior depending on the kick strength. The existence of the $2$-DTC phase has previously been reported around the rotationally symmetric point of the system, where it displays regular dynamics. We show that the system hosts robust $2$-DTC and dynamical freezing (DF) phases around alternating rotationally symmetric points. Interestingly, we also identify $4$-DTC phases that cannot be explained by the system's $\mathbb{Z}_2$ symmetry; these phases become stable for higher values of angular momentum. We explain the emergence of higher-order DTC phases through classical phase portraits of the system, connected with spin coherent states (SCSs). The $4$-DTC phases appear for certain initial states that are close to the spiral saddle points identified in the classical picture. Moreover, the linear entropy decreases as the angular momentum increases, indicating enhanced stability of the $4$-DTC phases. We also find an emergent conservation law for both the $2$-DTC and DF phases, while dynamical conservation arises periodically for the $4$-DTC phases.