Excited-state quantum phase transition in the Rabi model

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.

9 pages, 6 figures

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Cited by in corpus (10)

• Dissipative Phase Transition in the Open Quantum Rabi Model
• Excited-state quantum phase transitions
• Some remarks on 'superradiant' phase transitions in light-matter systems
• Approximated integrability of the Dicke model
• Floquet time crystals in driven spin systems with all-to-all $p$-body interactions
• Work statistics and symmetry breaking in an excited state quantum phase transition
• Nonlinear dynamics of the dissipative anisotropic two-photon Dicke model
• Comment on 'Revisiting the phase transitions of the Dicke model'
• Energy cat states induced by a parity-breaking excited-state quantum phase transition
• Ladder of Loschmidt anomalies in the deep strong-coupling regime of a qubit-oscillator system