Application of polaron picture in the two-qubit quantum Rabi model

TL;DR

This paper applies the polaron picture to the two-qubit quantum Rabi model, accurately analyzing ground-state properties across all coupling regimes and discovering a novel transition from multipolaron to bipolaron states influenced by tunneling frequency.

Contribution

It introduces a polaron-based method for the two-qubit quantum Rabi model that works across all coupling strengths without frequency ratio constraints, revealing a new ground-state transition.

Findings

Accurate ground-state energy calculations across all coupling regimes.

Discovery of a transition from multipolaron to bipolaron states with increasing coupling.

Tunneling frequency suppresses the bipolaron transition, especially at zero tunneling.

Abstract

The polaron picture is employed to investigate and elucidate the physics of the two-qubit quantum Rabi model, which describes two identical qubits coupled to a common harmonic oscillator. This approach enables us to obtain the ground-state energy and some other simpler physical observables with high accuracy in all regimes of the coupling strengths $g$, while there is no constraint to the ration of tunneling frequency $\Omega$ and field frequency $\omega$, which is not simultaneously possible using previous methods. Besides, we also discover a new phenomenon which is not present in the one-qubit Rabi model: with the increase of coupling strength $g$, there is a transition of the ground state of the system from a multipolaron state to a bipolaron state. However, the tunneling frequency $\Omega$ counteracts this process. Specifically, when tunneling frequency $\Omega=0$, the system always stays in the bipolaron state.