Characterizing Superradiant Phase of the Quantum Rabi Model

TL;DR

This paper provides a detailed analysis of the superradiant phase transition in the quantum Rabi model, revealing photon distribution behaviors and phase transition mechanisms across different coupling regimes.

Contribution

It introduces a two-step diagonalization scheme to accurately analyze the QRM's states and characterizes photon statistics during the phase transition.

Findings

Photon population follows Poissonian-like distribution after transition

Photon statistics evolve to Gaussian unitary ensemble with increasing coupling

Excited state photons exhibit Gaussian orthogonal ensemble statistics

Abstract

Recently, a superradiant phase transition first predicted theoretically in the quantum Rabi model (QRM) has been verified experimentally. This further stimulates the interest in the study of the process of phase transition and the nature of the superradiant phase since the fundamental role of the QRM in describing the interaction of light and matter, and more importantly, the QRM contains rich physics deserving further exploration despite its simplicity. Here we propose a scheme consisting of two successive diagonalization to accurately obtain the ground-state and excited states wavefunctions of the QRM in full parameter regime ranging from weak to deep-strong couplings. Thus one is able to see how the phase transition happens and how the photons populate in Fock space of the superradiant phase. We characterize the photon populations by borrowing the distribution concept in random matrix theory and find that the photon population follows a Poissonian-like distribution once the phase transition happens and further exhibits the statistics of Gaussian unitary ensemble as increasing coupling strength. More interestingly, the photons in the excited states behave even like the statistics of Gaussian orthogonal ensemble. Our results not only deepen understanding on the superradiant phase transition but also provide an insight on the nature of the superradiant phase of the QRM and related models.