Quantum Phase Transition and Universal Dynamics in the Rabi model

Abstract

We consider the Rabi Hamiltonian which exhibits a quantum phase transition (QPT) despite consisting only of a single-mode cavity field and a two-level atom. We prove QPT by deriving an exact solution in the limit where the atomic transition frequency in unit of the cavity frequency tends to infinity. The effect of a finite transition frequency is studied by analytically calculating finite-frequency scaling exponents as well as performing a numerically exact diagonalization. Going beyond this equilibrium QPT setting, we prove that the dynamics under slow quenches in the vicinity of the critical point is universal, that is, the dynamics is completely characterized by critical exponents. Our analysis demonstrates that the Kibble-Zurek mechanism can precisely predict the universal scaling of residual energy for a model without spatial degrees of freedom. Moreover, we find that the onset of the universal dynamics can be observed even with a finite transition frequency.

5 pages, 3 figures

References in corpus (7)

• Universal adiabatic dynamics across a quantum critical point
• Dynamical phase transition in the open Dicke model
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Quantum phase transition in the Dicke model with critical and non-critical entanglement
• Adiabatic quantum dynamics of the Lipkin-Meshkov-Glick model
• Variational study of a two-level system coupled to a harmonic oscillator in a ultrastrong coupling regime
• How to fix a broken symmetry: Quantum dynamics of symmetry restoration in a ferromagnetic Bose-Einstein condensate

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