Excited-state quantum phase transition in the Rabi model

TL;DR

This paper reveals that the Rabi model exhibits excited-state quantum phase transitions characterized by critical behavior and singularities in the density of states and observables, confirmed through analytical and numerical methods.

Contribution

It introduces the concept of excited-state QPTs in the Rabi model and derives analytical expressions for the density of states showing critical behavior.

Findings

Logarithmic divergence in density of states at critical energy

Singularities in photon number and atomic polarization

Analytical predictions confirmed by numerical solutions

Abstract

The Rabi model, a two-level atom coupled to a harmonic oscillator, can undergo a second-order quantum phase transition (QPT) [M. -J. Hwang et al, Phys. Rev. Lett. 115, 180404 (2015)]. Here we show that the Rabi QPT accompanies critical behavior in the higher energy excited states, i.e., the excited-state QPT (ESQPT). We derive analytic expressions for the semiclassical density of states, which shows a logarithmic divergence at a critical energy eigenvalue in the broken symmetry (superradiant) phase. Moreover, we find that the logarithmic singularities in the density of states leads to singularities in the relevant observables in the system such as photon number and atomic polarization. We corroborate our analytical semiclassical prediction of the ESQPT in the Rabi model with its numerically exact quantum mechanical solution.