Majorana path integral for nonequilibrium dynamics of two-level systems

TL;DR

This paper introduces a novel Majorana fermion field-theoretic method to analytically study non-equilibrium dynamics of two-level systems, accurately predicting resonance features relevant to quantum decoherence.

Contribution

The paper develops a new Majorana path integral approach for non-equilibrium two-level systems, enabling precise analytical calculations of their nonlinear dynamics under periodic driving.

Findings

Accurately predicts resonance peaks in dielectric response

Matches numerical simulations for driven two-level systems

Provides analytical insights into decoherence mechanisms

Abstract

We present a new field-theoretic approach to anaylize non-equilirbium dynamics of two-level systems (TLS), which is based on a correspondence between a driven TLS and a Majorana fermion field theory coupled to bosonic fields. This approach allows us to calculate analytically properties of non-linear TLS dynamics with an arbitrary accuracy. We apply our method to analyze specific TLS dynamics under a monochromatic periodic drive that is relevant to the problem of decoherence in Josephson junction qubits. It is demonstrated that the method gives the precise positions of the resonance peaks in the non-linear dielectric response function that are in agreement with numerical simulations.