Switching via quantum activation: A parametrically modulated oscillator

TL;DR

This paper investigates quantum activation as the primary switching mechanism between period-two states in a modulated quantum oscillator, highlighting the role of diffusion over quasienergy and its dependence on temperature and system parameters.

Contribution

It introduces a detailed analysis of quantum activation in a parametrically modulated oscillator, emphasizing the diffusion process over quasienergy and its dominance over tunneling.

Findings

Switching occurs via quantum activation across all temperatures.

The distribution over quasienergy differs at T=0 compared to near-zero temperature.

Quantum activation energy exhibits characteristic temperature dependence and bifurcation scaling.

Abstract

We study switching between period-two states of an underdamped quantum oscillator modulated at nearly twice its natural frequency. For all temperatures and parameter values switching occurs via quantum activation: it is determined by diffusion over oscillator quasienergy, provided the relaxation rate exceeds the rate of interstate tunneling. The diffusion has quantum origin and accompanies relaxation to the stable state. We find the semiclassical distribution over quasienergy. For T=0, where the system has detailed balance, this distribution differs from the distribution for $T\to 0$; the T=0 distribution is also destroyed by small dephasing of the oscillator. The characteristic quantum activation energy of switching displays a typical dependence on temperature and scaling behavior near the bifurcation point where period doubling occurs.