Unified analytical treatments to qubit-oscillator systems

TL;DR

This paper presents a unified analytical approach to qubit-oscillator systems using displaced bosonic operators, encompassing and extending previous methods like GRWA, applicable across various coupling strengths, detunings, and biases.

Contribution

The authors develop a unified analytical scheme that generalizes and improves existing treatments of qubit-oscillator systems, enabling explicit solutions over a wide parameter range.

Findings

The scheme recovers previous analytical methods such as GRWA and deep strong coupling expansion.

Explicit analytical expressions are derived that are valid across broad parameter regimes.

The approach can be extended to finite-bias cases and improves accuracy in relevant experimental conditions.

Abstract

An effective scheme within two displaced bosonic operators with equal positive and negative displacements is extended to study qubit-oscillator systems analytically in an unified way. Many previous analytical treatments, such as generalized rotating-wave approximation (GRWA) [Phys. Rev. Lett. 99, 173601 (2007)] and an expansion in the qubit tunneling matrix element in the deep strong coupling regime [Phys. Rev. Lett. 105, 263603 (2010)] can be recovered straightforwardly in the present scheme. Moreover, further improving GRWA and extension to the finite-bias case are implemented easily. The analytical expressions are then derived explicitly and uniquely, which work well in a wide range of the coupling strengthes, detunings, and static bias including the recent experimentally accessible parameters.