We study a system composed of two nonidentical qubits coupled to a singlemode quantum field. We calculate the spectra of the system in the deep-strongcoupling regime via perturbation theory up to second-order corrections and show that it converges to two forced oscillator chains for cases well into that regime. Our predictions are confirmed by the numerical calculation of the spectra using a parity decomposition of the corresponding Hilbert space. The numerical results point to two interesting types of behavior in the ultra-strongcoupling regime: the rotating wave approximation is valid for some particular cases and there exist crossings in the spectra within each parity subspace. We also present the normal modes of the system and give an example of the time evolution of the mean photon number, population inversion, von Neumann entropy and Wootters concurrence in the ultra-strong-and deep-strong-coupling regimes.

We study two models describing the interaction of a two-level system with two quantum field modes. The first one is equivalent to a dissipative two-state system with just two boson fields in the absence of tunneling. The second describes two orthogonal fields interacting with the corresponding orthogonal dipoles of a two-level system. We show that both models present a partial two-mode SU (2) symmetry and that they can be solved in the exceptional case of resonant fields. We study their ground state configurations, that is, we find the quantum precursors of the corresponding semi-classical phase transitions, as well as their whole spectra to infer their integrability. We show that the first model in the exceptional case is isomorphic with the quantum Rabi model and allows just two ground state configurations, vacuum and non-vacuum. The second model allows four ground state configurations, one vacuum, two non-vacuum single mode and one non-vacuum dual mode, and give analytic and numerical pointers that may suggest its integrability. We also show that in the single excitation subspace these models can serve as a fast SU (2) beam splitter even in the ultra-strong coupling regime. * bmlara@inaoep.mx 1 arXiv:1504.02748v1 [quant-ph]

Spectral characterization is a fundamental step in the development of useful quantum technology platforms. Here, we study an ensemble of interacting qubits coupled to a single quantized field mode, an extended Dicke model that might be at the heart of Bose-Einstein condensate in a cavity or circuit-QED experiments for large and small ensemble sizes, respectively. We present a semiclassical and quantum analysis of the model. In the semi-classical regime, we show analytic results that reveal the existence of a third regime, in addition of the two characteristic of the standard Dicke model, characterized by one logarithmic and two jump discontinuities in the derivative of the density of states. We show that the finite quantum system shows two different types of clustering at the jump discontinuities, signaling a precursor of two excited quantum phase transitions. These are confirmed using Peres lattices where unexpected order arises around the new precursor. Interestingly, Peres conjecture regarding the relation between spectral characteristics of the quantum model and the onset of chaos in its semi-classical equivalent is valid in this model as a revival of order in the semi-classical dynamics occurs around the new phase transition. *

Abstract. We try to classify the spectrum of the two-qubit Dicke model by calculating two quantum information measures of its eigenstates: the Wooters concurrence and the mutual quantum information. We are able to detect four spectral sets in each parity subspace of the model: one set is regular and given by the product of a Fock state of the field times the singlet Bell state of the qubits; the rest are fairly regular and related to the triplet states of the Bell basis. The singlet states become trapping states when we couple the Dicke model to an environment of harmonic oscillators, making them candidates for generating maximally entangled states in experimental realizations of ion trap quantum electrodynamics (QED) and circuit QED. Furthermore, they are robust and survive the inclusion of driving and dipole-dipole interactions, pointing to their use for storing quantum correlations, and it is straightforward to provide a generalization of these trapping states to the Dicke model with even number of qubits.

We study the ground state of a finite size ensemble of interacting qubits driven by a quantum field. We find a maximally entangled W-state in the ensemble part of the system for a certain coupling parameters region. The area of this region decreases as the ensemble size increases and, in the classical limit, becomes the line in parameter space that defines the phase transition of the system. In the classical limit, we also study the dynamics of the system and its transition from order to disorder for initial energies close to the ground state energy. We find that a critical energy providing this transition is related to the minimum of the projection of the total angular momentum of the quantum system in the $z$-direction.Comment: 17 pages, 6 figure