Generalized rotating-wave approximation to biased qubit-oscillator systems

TL;DR

This paper introduces a generalized rotating-wave approximation method for biased qubit-oscillator systems, providing analytical solutions that match experimental and numerical results across various parameters.

Contribution

It presents a new analytical approach that accurately describes biased qubit-oscillator systems, extending the rotating-wave approximation to include counter-rotating interactions.

Findings

Analytical eigenvalues and eigenstates are explicitly derived.

Spectra agree with experimental data for flux qubits.

Energy levels match exact diagonalization results across coupling strengths.

Abstract

The generalized rotating-wave approximation with counter-rotating interactions has been applied to a biased qubit-oscillator system. Analytical expressions are explicitly given for all eigenvalues and eigenstates. For a flux qubit coupled to superconducting oscillators, spectra calculated by our approach are in excellent agreement with experiment. Calculated energy levels for a variety of biases also agree well with those obtained via exact diagonalization for a wide range of coupling strengths. Dynamics of the qubit has also been examined, and results lend further support to the validity of the analytical approximation employed here. Our approach can be readily implemented and applied to superconducting qubit-oscillator experiments conducted currently and in the near future with a biased qubit and for all accessible coupling strengths.