Decay of transmon qubit in a broadband one-dimensional cavity

TL;DR

This paper analyzes the decay dynamics of a superconducting transmon qubit coupled to a broadband one-dimensional cavity, identifying Markovian and non-Markovian regimes and the influence of multi-level interactions.

Contribution

It provides analytical expressions for resonance shifts and widths, and explores the transition between dynamical regimes based on coupling strength and continuum bandwidth.

Findings

In the Markovian regime, resonance width is energy-independent.

In the non-Markovian regime, resonance width varies strongly with energy.

Coupling between the second and ground levels causes a fast two-photon decay channel.

Abstract

We investigate the decay dynamics of a three-level artificial atom, a superconducting transmon qubit, weakly coupled to a continuum of modes in a broadband, one-dimensional cavity. Using the resolvent formalism, we derive analytical expressions for the resonance frequency shifts and widths, which are then evaluated numerically for a Gaussian density of states. We identify two distinct dynamical regimes, differentiated by the ratio of the qubit's coupling strength to the continuum bandwidth. When this ratio is much less than one, the system exhibits a Markovian regime in which the resonance width is practically independent of energy within the continuum band. As the ratio increases, the system transitions to a non-Markovian regime where the resonance width becomes strongly energy-dependent. In this regime, the qubit interacts with the continuum faster than the continuum can erase the information from the qubit's past. Furthermore, we demonstrate that the coupling between the transmon's second level and its ground state significantly influences the decay dynamics of the third level. The interaction between these two levels opens a fast two-photon decay channel, which broadens the transmon's second level.