Non-conditioned generation of Schroedinger cat states in a cavity

We investigate the dynamics of a two-level atom in a cavity filled with a nonlinear medium. We show that the atom-field detuning $\delta$ and the nonlinear parameter $\chi^{(3)}$ may be combined to yield a periodic dynamics and allowing the generation of almost exact superpositions of coherent states ({\sl Schr\"odinger} cats). By analysing the atomic inversion and the field purity, we verify that any initial atom-field state is recovered at each revival time, and that a coherent field interacting with an excited atom evolves to a superposition of coherent states at each collapse time. We show that a mixed field state (statistical mixture of two coherent states) evolves towards a pure field state ({\sl Schr\"odinger} cat) as well. We discuss the validity of those results by using the field fidelity and the {\sl Wigner} function.Comment: REVTeX4, 8 pages, 7 figures, link to an external animation fil

Quantum entanglement and phase transition in a two-dimensional photon-photon pair model

We propose a two-dimensional model consisting of photons and photon pairs. In the model, the mixed gas of photons and photon pairs is formally equivalent to a two-dimensional system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phases. Using the variational method, we discuss the quantum phase transition of the mixed gas and obtain the critical coupling line analytically. Moreover, we also find that the phase transition of the photon gas can be interpreted as second harmonic generation. We then discuss the entanglement between photons and photon pairs. Additionally, we also illustrate how the entanglement between photons and photon pairs can be associated with the phase transition of the system.Comment: 14 pages, 5 figure

Polynomial Lie algebra methods in solving the second-harmonic generation model: some exact and approximate calculations

We compare exact and SU(2)-cluster approximate calculation schemes to determine dynamics of the second-harmonic generation model using its reformulation in terms of a polynomial Lie algebra $su_{pd}(2)$ and related spectral representations of the model evolution operator realized in algorithmic forms. It enabled us to implement computer experiments exhibiting a satisfactory accuracy of the cluster approximations in a large range of characteristic model parameters.Comment: LaTex file, 13 pages, 3 figure

An algebraic approach to the Tavis-Cummings problem

An algebraic method is introduced for an analytical solution of the eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on polynomially deformed su(2), i.e. su_n(2), algebras. In this method the eigenvalue problem is solved in terms of a specific perturbation theory, developed here up to third order. Generalization to the N-atom case of the Rabi frequency and dressed states is also provided. A remarkable enhancement of spontaneous emission of N atoms in a resonator is found to result from collective effects.Comment: 13 pages, 7 figure

Nonlinear Jaynes-Cummings model of atom-field interaction

Interaction of a two-level atom with a single mode of electromagnetic field including Kerr nonlinearity for the field and intensity-dependent atom-field coupling is discussed. The Hamiltonian for the atom-field system is written in terms of the elements of a closed algebra, which has SU(1,1) and Heisenberg-Weyl algebras as limiting cases. Eigenstates and eigenvalues of the Hamiltonian are constructed. With the field being in a coherent state initially, the dynamical behaviour of atomic-inversion, field-statistics and uncertainties in the field quadratures are studied. The appearance of nonclassical features during the evolution of the field is shown. Further, we explore the overlap of initial and time-evolved field states.Comment: 14 pages, 6 figures is PS forma

Quantum statistical properties of the Jaynes-Cummings model in the presence of a classical homogeneous gravitational field

The temporal evolution of quantum statistical properties of an interacting atom-radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes-Cummings model. To analyse the dynamical evolution of the atom-radiation system a quantum treatment of the internal and external dynamics of the atom is presented based on an alternative su(2) dynamical algebraic structure. By solving the Schr\"{o}dinger equation in the interaction picture, the evolving state of the system is found by which the influence of the gravitational field on the dynamical behavior of the atom-radiation system is explored. Assuming that initially the radiation field is prepared in a coherent state and the two-level atom is in a coherent superposition of the excited and ground states, the influence of gravity on the collapses and revivals of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field is studied.Comment: 21 page

Multiphoton Quantum Optics and Quantum State Engineering

We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, with special emphasis on the engineering of nonclassical states of photons and atoms. We present a detailed analysis of the methods and techniques for the production of genuinely quantum multiphoton processes in nonlinear media, and the corresponding models of multiphoton effective interactions. We review existing proposals for the classification, engineering, and manipulation of nonclassical states, including Fock states, macroscopic superposition states, and multiphoton generalized coherent states. We introduce and discuss the structure of canonical multiphoton quantum optics and the associated one- and two-mode canonical multiphoton squeezed states. This framework provides a consistent multiphoton generalization of two-photon quantum optics and a consistent Hamiltonian description of multiphoton processes associated to higher-order nonlinearities. Finally, we discuss very recent advances that by combining linear and nonlinear optical devices allow to realize multiphoton entangled states of the electromnagnetic field, that are relevant for applications to efficient quantum computation, quantum teleportation, and related problems in quantum communication and information.Comment: 198 pages, 36 eps figure

The dynamics of a four-level three-mode system. Operator solution

In the dipole and rotating wave approximation the operator solutions for the level populations and photon numbers are found. The numerical results for the time-evolution of the level populations for the case of initially coherent pumping modes 1 and 3 (mode 2 initially in vacuum) are reported and compared with those for a three-level atom in the ladder and lambda configurations.Dans l'approximation dipolaire et dans l'approximation du champ tournant, on donne les solutions pour les opérateurs correspondant aux populations des niveaux et aux nombres de photons. Les résultats numériques pour l'évolution dans le temps des populations des niveaux, dans le cas de modes de pompage 1 et 3 initialement cohérents (le mode 2 étant initialement vide), sont donnés et comparés aux résultats pour un atome à trois niveaux dans les configurations en échelle et en lambda