Non-Markovian dynamics of a superconducting qubit in an open multimode resonator

TL;DR

This paper develops a comprehensive theoretical framework to analyze the non-Markovian dynamics of a superconducting transmon qubit coupled to an open multimode resonator, capturing dissipation and nonlinearity without common approximations.

Contribution

It introduces a method to derive effective Heisenberg-Langevin equations incorporating non-Markovian effects and resonator dissipation exactly, advancing understanding of qubit-resonator interactions.

Findings

Accurately models non-Markovian spontaneous emission dynamics.

Derives a systematic perturbation theory for transmon nonlinearity.

Valid for any qubit-resonator coupling strength.

Abstract

We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating wave, two level or Markov approximations. A well-behaved time domain perturbation theory is derived to systematically account for the nonlinearity of the transmon. We apply this method to the problem of spontaneous emission, capturing accurately the non-Markovian features of the qubit dynamics, valid for any qubit-resonator coupling strength.