A Real-time Instanton Approach to Quantum Activation

TL;DR

This paper introduces a quantum instanton approach within Keldysh field theory to analyze rare fluctuation-induced switching in driven nonlinear quantum systems, providing a semi-analytical method that aligns well with exact solutions.

Contribution

It develops a novel instanton method in Keldysh field theory for quantum activation, enabling semi-analytical computation of switching rates in quantum systems.

Findings

The approach accurately predicts switching rates over many orders of magnitude.

It aligns well with exact solutions across various drive amplitudes.

The method can be extended to many-body quantum systems.

Abstract

Driven-dissipative nonlinear systems exhibit rich critical behavior, related to bifurcation, bistability and switching, which underlie key phenomena in areas ranging from physics, chemistry and biology to social sciences and economics. The importance of rare fluctuations leading to a dramatic jump between two very distinct states, such as survival and extinction in population dynamics, success and bankruptcy in economics and the occurrence of earthquakes or of epileptic seizures, have been already established. In the quantum domain, switching is of importance in both chemical reactions and the devices used in quantum state detection and amplification. In particular, the simplest driven single oscillator model serves as an insightful starting point. Here we describe switching induced by quantum fluctuations and illustrate that an instanton approach within Keldysh field theory can provide a deep insight into such phenomena. We provide a practical recipe to compute the switching rates semi-analytically, which agrees remarkably well with exact solutions across a wide domain of drive amplitudes spanning many orders of magnitude. Being set up in the framework of Keldysh coherent states path integrals, our approach opens the possibility of studying quantum activation in many-body systems where other approaches are inapplicable.