Critical fluctuations and the rates of interstate switching near excitation threshold of a quantum parametric oscillator

TL;DR

This paper investigates the quantum fluctuations and transition rates in a nonlinear quantum oscillator near its excitation threshold, revealing how quantum noise influences state switching and fluctuation times.

Contribution

It introduces the calculation of quantum activation energies and their scaling near the critical point of a quantum parametric oscillator.

Findings

Quantum activation energies scale with the driving amplitude near threshold.

Fluctuation correlation times depend on quantum noise parameters.

Transitions between states are driven by quantum fluctuations over a quasienergy barrier.

Abstract

We study the dynamics of a nonlinear oscillator near the critical point where period-two vibrations are first excited with the increasing amplitude of parametric driving. Above the threshold, quantum fluctuations induce transitions between the period-two states over the quasienergy barrier. We find the effective quantum activation energies for such transitions and their scaling with the difference of the driving amplitude from its critical value. We also find the scaling of the fluctuation correlation time with the quantum noise parameters in the critical region near the threshold.