Relaxation dynamics and dissipative phase transition in quantum oscillators with period tripling

TL;DR

This paper investigates the relaxation dynamics and a dissipative phase transition in driven quantum oscillators exhibiting period tripling, revealing a quantum phase transition-like behavior near a threshold with implications for quantum regimes.

Contribution

It uncovers the quantum phase transition in period tripling oscillators by analyzing eigenvalues of the evolution generator and highlights the quantum activation process for switching between states.

Findings

Eigenvalue gap closes near the threshold, indicating a phase transition.

Transition from localized to delocalized states in phase space.

Quantum activation rates differ from semiclassical predictions.

Abstract

Period tripling in driven quantum oscillators reveals unique features absent for linear and parametric drive, but generic for all higher-order resonances. Here, we focus at zero temperature on the relaxation dynamics towards a stationary state starting initially from a domain around a classical fixed point in phase space. Beyond a certain threshold for the driving strength, the long-time dynamics is governed by a single time constant that sets the rate for switching between different states with broken time translation symmetry. By analyzing the lowest eigenvalues of the corresponding time evolution generator for the dissipative dynamics, we find that near the threshold the gap between these eigenvalues nearly closes. The closing becomes complete for a vanishing quantum parameter. We demonstrate that this behavior, reminiscent of a quantum phase transition, is associated with a transition from a stationary state which is localized in phase space to a delocalized one. We further show, that switching between domains of classical fixed points happens via quantum activation, however, with rates that differ from those obtained by a standard semiclassical treatment. As period tripling has been explored with superconducting circuits mainly in the quasi-classical regime recently, our findings may trigger new activities towards the deep quantum realm.