Ground state of the asymmetric Rabi model in the ultrastrong coupling regime

TL;DR

This paper investigates the ground states of asymmetric Rabi models with unequal coupling strengths, revealing quadratic energy dependence, dominant counterrotating interactions, and entanglement dynamics, using an analytical transformation method validated numerically.

Contribution

It introduces an approximate analytical approach for the ground states of asymmetric Rabi models and explores their energy and entanglement properties across parameter ranges.

Findings

Ground-state energy depends quadratically on coupling strengths.

Counterrotating-wave interaction mainly contributes to the ground-state energy.

Two-qubit entanglement peaks then diminishes with increasing coupling, surpassing symmetric models.

Abstract

We study the ground states of the single- and two-qubit asymmetric Rabi models, in which the qubit-oscillator coupling strengths for the counterrotating-wave and corotating-wave interactions are unequal. We take the transformation method to obtain the approximately analytical ground states for both models and numerically verify its validity for a wide range of parameters under the near-resonance condition. We find that the ground-state energy in either the single- or two-qubit asymmetric Rabi model has an approximately quadratic dependence on the coupling strengths stemming from different contributions of the counterrotating-wave and corotating-wave interactions. For both models, we show that the ground-state energy is mainly contributed by the counterrotating-wave interaction. Interestingly, for the two-qubit asymmetric Rabi model, we find that, with the increase of the coupling strength in the counterrotating-wave or corotating-wave interaction, the two-qubit entanglement first reaches its maximum then drops to zero. Furthermore, the maximum of the two-qubit entanglement in the two-qubit asymmetric Rabi model can be much larger than that in the two-qubit symmetric Rabi model.