Universal Critical Behavior in the Dicke Model

Abstract

The critical value of the atom-field coupling strength for a finite number of atoms is deter- mined by means of both, semiclassical and exact solutions. In the semiclassical approach we use a variational procedure with coherent and symmetry-adapted states, while for the exact quantum solution the concept of fidelity is employed. These procedures allow for the determination of the phase transitions in the model, and coincide in the thermodynamic limit. For the three cases men- tioned above, universal parametric curves are obtained for the expectation values of both the first quadrature of the electromagnetic field, and the atomic relative population, as implicit functions of the atom-field coupling parameter, valid for the ground- and first-excited states.

10 pages, 7 figures

References in corpus (8)

• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Atomic physics and quantum optics using superconducting circuits
• Ground state overlap and quantum phase transitions
• Fidelity approach to quantum phase transitions
• Entanglement and the Phase Transition in Single Mode Superradiance
• The Dicke model phase transition in the quantum motion of a Bose-Einstein condensate in an optical cavity
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• Mathematical Methods in Quantum Optics: the Dicke Model
• Nonlinear Atom-Photon Interaction Induced Population Inversion and Inverted Quantum Phase Transition of Bose-Einstein Condensate in an Optical Cavity
• Ground state of a resonant two-qubit Rabi model in the ultrastrong coupling regime
• Identifying the order of a quantum phase transition by means of Wehrl entropy in phase-space
• Revival times at quantum phase transitions
• Quantum Hysteresis in Coupled Light-Matter Systems
• Characterization of the quantum phase transition in a two-mode Dicke model for different cooperation numbers
• Pulsed Generation of Quantum Coherences and Non-classicality in Light-Matter Systems
• Singularities in large deviations of work in quantum quenches
• Phase transitions with finite atom number in the Dicke Model
• Quantum phases of a three-level matter-radiation interaction model using $SU(3)$ coherent states with different cooperation numbers
• Non-equilibrium dynamics of non-linear Jaynes-Cummings model in cavity arrays
• Entropy of entanglement between quantum phases of a three-level matter-radiation interaction model
• Quantum phase transition of two-level atoms interacting with a finite radiation field