Measuring a transmon qubit in circuit QED: dressed squeezed states

TL;DR

This paper investigates the measurement process of a superconducting transmon qubit in circuit QED, revealing deviations from ideal behavior and proposing dressed squeezed states as a better approximation for the resonator's quantum state.

Contribution

It introduces the concept of dressed squeezed states as an improved model for resonator states during transmon qubit measurement, accounting for non-ideal coupling effects.

Findings

Resonator ring-up leaks populations into different eigenstate ladders.

Transmon nonlinearity shears the coherent state within an eigenstate ladder.

Dressed squeezed states provide a better approximation for the sheared state.

Abstract

Using circuit QED, we consider the measurement of a superconducting transmon qubit via a coupled microwave resonator. For ideally dispersive coupling, ringing up the resonator produces coherent states with frequencies matched to transmon energy states. Realistic coupling is not ideally dispersive, however, so transmon-resonator energy levels hybridize into joint eigenstate ladders of the Jaynes-Cummings type. Previous work has shown that ringing up the resonator approximately respects this ladder structure to produce a coherent state in the eigenbasis (a dressed coherent state). We numerically investigate the validity of this coherent state approximation to find two primary deviations. First, resonator ring-up leaks small stray populations into eigenstate ladders corresponding to different transmon states. Second, within an eigenstate ladder the transmon nonlinearity shears the coherent state as it evolves. We then show that the next natural approximation for this sheared state in the eigenbasis is a dressed squeezed state, and derive simple evolution equations for such states using a hybrid phase-Fock-space description.