Programmable time crystals from higher-order packing fields

TL;DR

This paper introduces a method to engineer customizable continuous time crystals with higher-order modes using higher-order packing fields, expanding the control and complexity of time-crystal phases in driven diffusive systems.

Contribution

It demonstrates how to create and control on-demand time crystals with arbitrary modes, revealing new critical behaviors and scaling properties in driven diffusive systems.

Findings

Engineered time crystals with arbitrary rotating condensates.

Identified a critical point and scaling laws for higher-order condensates.

Discovered explosive, first-order-like phase transitions in time crystal phases.

Abstract

Time crystals are many-body systems that spontaneously break time-translation symmetry, and thus exhibit long-range spatiotemporal order and robust periodic motion. Recent results have demonstrated how to build time-crystal phases in driven diffusive fluids using an external packing field coupled to density fluctuations. Here we exploit this mechanism to engineer and control on-demand custom continuous time crystals characterized by an arbitrary number of rotating condensates, which can be further enhanced with higher-order modes. We elucidate the underlying critical point, as well as general properties of the condensates density profiles and velocities, demonstrating a scaling property of higher-order traveling condensates in terms of first-order ones. We illustrate our findings by solving the hydrodynamic equations for various paradigmatic driven diffusive systems, obtaining along the way a number of remarkable results, e.g. the possibility of explosive time crystal phases characterized by an abrupt, first-order-type transition. Overall, these results demonstrate the versatility and broad possibilities of this promising route to time crystals.