Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions

Abstract

We study the non-integrable Dicke model, and its integrable approximation, the Tavis-Cummings model, as functions of both the coupling constant and the excitation energy. Excited-state quantum phase transitions (ESQPT) are found analyzing the density of states in the semi-classical limit and comparing it with numerical results for the quantum case in large Hilbert spaces, taking advantage of efficient methods recently developed. Two different ESQPTs are identified in both models, which are signaled as singularities in the semi-classical density of states, one {\em static} ESQPT occurs for any coupling, whereas a dynamic ESQPT is observed only in the superradiant phase. The role of the unstable fixed points of the Hamiltonian semi-classical flux in the occurrence of the ESQPTs is discussed and determined. Numerical evidence is provided that shows that the semi-classical result describes very well the tendency of the quantum energy spectrum for any coupling in both models. Therefore the semi-classical density of states can be used to study the statistical properties of the fluctuation in the spectra, a study that is presented in a companion paper.

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• Approximated integrability of the Dicke model
• Signatures of excited state quantum phase transitions in quantum many body systems: Phase space analysis
• Characterizing the dynamical phase diagram of the Dicke model via classical and quantum probes
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• Adiabatic invariants for the regular region of the Dicke model
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• Thermodynamics and Superradiant Phase Transitions in a three-level Dicke Model
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• Mechanism of dynamical phase transitions: The complex-time survival amplitude
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• Anomalous Thermalization in Quantum Collective Models
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• Dispersive Regimes of the Dicke Model
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• Comment on 'Revisiting the phase transitions of the Dicke model'
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• Excited-state quantum phase transitions in constrained systems
• Excited stated quantum phase transitions and the entropy of the work distribution in the anharmonic Lipkin-Meshkov-Glick model
• Dynamics of Coherent States in Regular and Chaotic Regimes of the Non-integrable Dicke Model
• Experimental observation of phase transitions of a deformed Dicke model using a reconfigurable, bi-parametric electronic platform
• Loss of integrability in a system with two-photon interactions
• Energy cat states induced by a parity-breaking excited-state quantum phase transition
• Quantifying the breakdown of the rotating-wave approximation in single-photon superradiance
• Comparison of the semiclassical and quantum optical field dynamics in a pulse-excited optical cavity with a finite number of quantum emitters
• Superradiant Phase is a Finite Size Effect in Two-photon Processes