Schrodinger-Cat-Likeness in Adiabatic Approximation for Generalized Quantum Rabi Model without and with A^2-Term

TL;DR

This paper develops an adiabatic approximation method for the generalized quantum Rabi model, analyzing Schrodinger-cat-like states with and without quadratic interactions, revealing the influence of energy bias and tunnel splitting.

Contribution

It introduces a mathematical procedure for adiabatic approximation in the generalized quantum Rabi model, including quadratic interactions, and clarifies conditions for Schrodinger-cat-like states.

Findings

Schrodinger-cat-like states depend on energy bias without quadratic interaction.

All eigenstates form cat-like states with quadratic interaction, regardless of bias.

Tunnel splitting influences the formation of entangled states.

Abstract

We give a mathematical procedure to obtain the adiabatic approximation for the generalized quantum Rabi Hamiltonian both without and with a quadratic interaction. We consider the Hamiltonian as the energy of a model describing the interaction system of a two-level artificial atom and a one-mode microwave photon in circuit QED. In the case without the quadratic interaction, we show in the adiabatic approximation that whether each bare eigenstate forms a Schrodinger-cat-like entangled state or not depends on whether the energy bias of the atom is zero or non-zero, and then, the effect of the tunnel splitting of the atom is ignored. On the other hand, in the case with the quadratic interaction, we show in the adiabatic approximation that all the physical eigenstates obtained by the (meson) pair theory form individual Schrodinger-cat-like entangled states for every energy bias. We conclude that this fact comes from the effect of the tunnel splitting.