Theory of Spectrum in Qubit-Oscillator Systems in the Ultrastrong Coupling Regime

TL;DR

This paper provides an exact theoretical analysis of the spectrum in qubit-oscillator systems operating in the ultra-strong coupling regime, surpassing the rotating-wave approximation and aligning with experimental results.

Contribution

It introduces an exact solution to the Jaynes-Cummings model in the ultra-strong coupling regime using extended bosonic coherent states, extending beyond previous approximations.

Findings

Numerically exact spectrum matches experimental data.

Predicted Bloch-Siegert shifts for various transitions.

Validated the ultra-strong coupling regime effects.

Abstract

Recent measurement on an LC resonator magnetically coupled to a superconducting qubit[arXiv:1005.1559] shows that the system operates in the ultra-strong coupling regime and crosses the limit of validity for the rotating-wave approximation of the Jaynes-Cummings model. By using extended bosonic coherent states, we solve the Jaynes-Cummings model exactly without the rotating-wave approximation. Our numerically exact results for the spectrum of the flux qubit coupled to the LC resonator are fully consistent with the experimental observations. The smallest Bloch-Siegert shift obtained is consistent with that observed in this experiment. In addition, the Bloch-Siegert shifts in arbitrary level transitions and for arbitrary coupling constants are predicted.