Exotic Behavior of Parity in the Superradiant Phase of Quantum Rabi Model

TL;DR

This paper reveals an unusual parity behavior in the superradiant phase of the quantum Rabi model, showing irregular eigenstate parities but a conserved sum within pairs, due to emergent double-well potential effects.

Contribution

It uncovers a novel exotic parity behavior in the quantum Rabi model's superradiant phase and explains its physical origin, highlighting limitations in quantum state measurement techniques.

Findings

Eigenstate parities behave irregularly in the superradiant phase.

The sum of parities for each eigenstate pair remains zero.

Emergent double-well potential causes the exotic parity behavior.

Abstract

Parity describing the symmetry of quantum mechanics wavefunction under space inversion transformation not only plays an essential role in solving quantum systems but also can be used to manipulate and measure the motional quantum states of such hybrid quantum systems as quantum Rabi model(QRM) and/or its variants through parity measurements. Here we address an exotic parity behavior of the QRM in its superradiant phase by numerical exact diagonalization, namely, the parities of eigenstates of the QRM behave irregular in the strong coupling regime but the sum of parities for each pair of eigenstates beginning from the ground state remains vanishing. It is found that this exotic behavior originates from the comparability of the photon distribution in the odd and even components of Fock basis when the eigenenergies of each pair of eigenstates approach enough to each other and physically is due to the emergent double-well potential induced by the strong coupling between the single-mode photon field and the two-level atom. The result not only uncovers the physics not known previously in the QRM but also makes an intrinsic limitation on the measurement precision of motional quantum states through parity measurements in modern quantum science and technologies.