Exploring nonlinear dynamics in periodically driven time crystal: from synchronized to chaotic motion

TL;DR

This paper investigates nonlinear dynamics and chaos in a periodically driven electron-nuclear spin system, revealing entrainment, bifurcations, and chaotic regimes linked to time crystalline behavior.

Contribution

It demonstrates how periodic modulation induces complex nonlinear phenomena, including entrainment and chaos, in a spin system exhibiting time-crystalline-like oscillations.

Findings

Identification of Arnold tongue in the system's response

Observation of devil's staircase in frequency spectrum

Emergence of chaos through bifurcation sequences

Abstract

The coupled electron-nuclear spin system in an InGaAs semiconductor as testbed of nonlinear dynamics can develop auto-oscillations, resembling time-crystalline behavior, when continuously excited by a circularly polarized laser. We expose this system to deviations from continuous driving by periodic modulation of the excitation polarization, revealing a plethora of nonlinear phenomena that depend on modulation frequency and depth. We find ranges in which the system's oscillations are entrained with the modulation frequency. The width of these ranges depends on the polarization modulation depth, resulting in an Arnold tongue. Outside the tongue, the system shows a variety of fractional subharmonic responses connected through bifurcation jets when varying the modulation frequency. Here, each branch in the frequency spectrum forms a devil's staircase. When an entrainment range is approached by going through an increasing order of bifurcations, chaotic behavior emerges. These findings can be described by an advanced model of the periodically pumped electron-nuclear spin system. We discuss the connection of the obtained results to different phases of time matter.