Phase transitions with finite atom number in the Dicke Model

Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are the number of photons inside the cavity and the number of excited atoms. Coherent states provide a mean field description, which becomes exact in the thermodynamic limit. Employing symmetry adapted (SA) SU(2) coherent states (SACS) the critical behavior can be described for a finite number of atoms. A variation after projection treatment, involving a numerical minimization of the SA energy surface, associates the finite number phase transition with a discontinuity in the order parameters, which originates from a competition between two local minima in the SA energy surface.Comment: 8 pages, 10 figures, Conference Proceedings of CEWQO-2012, to be published as a Topical Issue of the journal Physica Script

Searching for pairing energies in phase space

We obtain a representation of pairing energies in phase space, for the Lipkin-Meshkov-Glick and general boson Bardeen-Cooper-Schrieffer pairing models. This is done by means of a probability distribution of the quantum state in phase space. In fact, we prove a correspondence between the points at which this probability distribution vanishes and the pairing energies. In principle, the vanishing of this probability distribution is experimentally accessible and additionally gives a method to visualize pairing energies across the model control parameter space. This result opens new ways to experimentally approach quantum pairing systems.Comment: 5 pages, 4 figure

Linear Time-Dependent Invariants for Scalar Fields and Noether's Theorem

The infinite number of time-dependent linear in field and conjugated momenta invariants is derived for the scalar field using the Noether's theorem procedure.Comment: LaTeX, 6 pages, preprint of Instituto de Ciencias Nucleares, UNAM, Departamento de F\ii sica and Matem\'aticas Aplicadas, M\'exico D. F. , M\'exico No. 04 (1994

Squeezing in a 2-D generalized oscillator

A two-dimensional generalized oscillator with time-dependent parameters is considered to study the two-mode squeezing phenomena. Specific choices of the parameters are used to determine the dispersion matrix and analytic expressions, in terms of standard hermite polynomials, of the wavefunctions and photon distributions. (to be publish in the Third Workshop on Squeezed States and Uncertainty Relations, Baltimore, USA, (August 1993))Comment: LaTeX, 5 pages, preprint of Instituto de Ciencias Nucleares, UNAM Departamento de F\ii sica and Matem\'aticas Aplicadas, No. 02 (1994