Dissipative dynamics of a qubit coupled to a nonlinear oscillator

TL;DR

This paper analytically investigates the dissipative behavior of a qubit coupled to a nonlinear oscillator in an Ohmic environment, revealing complex oscillations and relaxation dynamics beyond the rotating wave approximation.

Contribution

It provides an analytical framework for the eigenstates and dynamics of a qubit-nonlinear oscillator system, including effects of nonlinearity and bath coupling.

Findings

Multiple damped oscillations in qubit populations

Relaxation rate peaks at resonance conditions

Analytical expressions valid beyond RWA

Abstract

We consider the dissipative dynamics of a qubit coupled to a nonlinear oscillator (NO) embedded in an Ohmic environment. By treating the nonlinearity up to first order and applying Van Vleck perturbation theory up to second order in the qubit-NO coupling, we derive an analytical expression for the eigenstates and eigenfunctions of the coupled qubit-NO system beyond the rotating wave approximation. In the regime of weak coupling to the thermal bath, analytical expressions for the time evolution of the qubit's populations are derived: they describe a multiplicity of damped oscillations superposed to a complex relaxation part toward thermal equilibrium. The long time dynamics is characterized by a single relaxation rate, which is maximal when the qubit is tuned to one of the resonances with the nonlinear oscillator.