Mathematical Methods in Quantum Optics: the Dicke Model

Abstract

We show how various mathematical formalisms, specifically the catastrophe formalism and group theory, aid in the study of relevant systems in quantum optics. We describe the phase transition of the Dicke model for a finite number N of atoms, via 3 different methods, which lead to universal parametric curves for the expectation value of the first quadrature of the electromagnetic field and the expectation value of the number operator, as functions of the atomic relative population. These are valid for all values of the matter-field coupling parameter, and valid for both the ground and first-excited states. Using these mathematical tools, the critical value of the atom-field coupling parameter is found as a function of the number of atoms, from which its critical exponent is derived.

14 pp, 9 figures

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Cited by in corpus (20)

• Comparative quantum and semi-classical analysis of Atom-Field Systems I: density of states and excited-state quantum phase transitions
• Perspective: Quantum Hamiltonians for Optical Interactions
• Comparative quantum and semi-classical analysis of Atom-Field Systems II: Chaos and regularity
• Classical chaos in atom-field systems
• Solution of the Dicke model for N=3
• Dissipation-driven entanglement between qubits mediated by plasmonic nanoantennas
• Delocalization and quantum chaos in atom-field systems
• Polychromatic phase diagram for $n$-level atoms interacting with $\ell$ modes of electromagnetic field
• Impurity in a bosonic Josephson junction: swallowtail loops, chaos, self-trapping and the poor man's Dicke model
• Regularity and chaos in cavity QED
• Experimental realization of the classical Dicke model
• Quantum Hysteresis in Coupled Light-Matter Systems
• Symmetry Adapted Coherent States for Three-Level Atoms Interacting with One-Mode Radiation
• Fidelity, susceptibility and critical exponents in the Dicke model
• Critical steady states of all-to-all squeezed and driven superradiance: An analytic approach
• A triple point in 3-level systems
• Geometry, quantum correlations, and phase transitions in the $\Lambda$-atomic configuration
• Quantum phase transition of two-level atoms interacting with a finite radiation field
• Collective excitations of atoms and field modes in coupled cavities
• Ultrastrong Coupling of a Qubit with a Nonlinear Optical Resonator