We investigate the quantum chaotic properties of the Dicke Hamiltonian; a quantum-optical model which describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. This model exhibits a zero-temperature quantum phase transition in the N → ∞ limit, which we describe exactly in an effective Hamiltonian approach. We then numerically investigate the system at finite N and, by analysing the level statistics, we demonstrate that the system undergoes a transition from quasi-integrability to quantum chaotic, and that this transition is caused by the precursors of the quantum phase-transition. Our considerations of the wavefunction indicate that this is connected with a delocalisation of the system and the emergence of macroscopic coherence. We also derive a semi-classical Dicke model, which exhibits analogues of all the important features of the quantum model, such as the phase transition and the concurrent onset of chaos.

We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zerotemperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable to quantum chaotic. By deriving an exact solution in the thermodynamic limit we relate this phenomenon to a localisation-delocalisation transition in which a macroscopic superposition is generated. We also describe the classical analogues of this behaviour.At zero temperature, systems of N interacting particles can exhibit a quantum phase transition (QPT) as a function of a coupling parameter λ in the limit that N → ∞. How do the precursors of such a transition influence quantum chaotic (and non-chaotic) behaviour of the same system for finite N ?One of the most direct indicators of the emergence of quantum chaos is the change in energy level spacing statistics from Poissonian to being described by the Gaussian ensembles of Random Matrix Theory. Although this change-over has been observed in many systems [1,2,3,4], only in a comparatively few, isolated cases has the onset of quantum chaos been correlated with the presence of a QPT. Important examples include spin glass shards, which have recently been used in modeling the onset of chaos in quantum computers [5], the Lipkin model [6], the interacting boson model [7], and the three-dimensional Anderson model [8,9], where the change in level statistics occurs at the metalinsulator (localisation-delocalisation) transition found in disordered electronic systems.In this Letter we consider the Dicke Hamiltonian (DH) [10], a quantum-optical model describing the interaction of N two-level atoms with a number of bosonic modes. We demonstrate that a crossover between Poisson and Wigner-Dyson statistics in this model for finite N is intimately connected to a mean-field type superradiance QPT.The simplicity and generality of the Dicke Hamiltonian have afforded it appeal both for the investigation of quantum chaos, and as a model for phase transitions at a critical coupling λ c induced by the interaction with light. The level statistics for finite N have revealed the existence of quantum chaos in certain isolated regimes of the model [11,12]. On the other hand, the QPT aspect for N → ∞ has been discussed in the context of superradiance [13,14], and recently for exciton condensation [15]. Here, we derive an exact solution for all eigenstates, eigenvalues and critical exponents in the thermodynamic limit, and show that above the critical point λ = λ c the ground-state wavefunction bifurcates into a macroscopic superposition for any N < ∞. Our numerical results indicate that a localisation-delocalisation transition for N → ∞ underlies the cross-over between Poissonian and Wigner level-spacing distributions for finite N . Furthermore, we use an exact Holstein-Primakoff transformation to derive the classical limit of the model for arbitrary N and find a transition at λ = λ c from regular to chaotic trajectories. The latter are delocalised around ...

We consider the entanglement properties of the quantum phase transition in the single-mode superradiance model, involving the interaction of a boson mode and an ensemble of atoms. For an infinite size system, the atom-field entanglement diverges logarithmically with the correlation length exponent. Using a continuous variable representation, we compare this to the divergence of the entropy in conformal field theories and derive an exact expression for the scaled concurrence and the cusplike nonanalyticity of the momentum squeezing.

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We expand the standard thermodynamic framework of a system coupled to a thermal reservoir by considering a stream of independently prepared units repeatedly put into contact with the system. These units can be in any nonequilibrium state and interact with the system with an arbitrary strength and duration. We show that this stream constitutes an effective resource of nonequilibrium free energy and identify the conditions under which it behaves as a heat, work or information reservoir. We also show that this setup provides a natural framework to analyze information erasure ("Landauer's principle") and feedback controlled systems ("Maxwell's demon"). In the limit of a short system-unit interaction time, we further demonstrate that this setup can be used to provide a thermodynamically sound interpretation to many effective master equations. We discuss how nonautonomously driven systems, micromasers, lasing without inversion, and the electronic Maxwell demon, can be thermodynamically analyzed within our framework. While the present framework accounts for quantum features (e.g. squeezing, entanglement, coherence), we also show that quantum resources do not offer any advantage compared to classical ones in terms of the maximum extractable work.