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O. Castaños

Publications and source records attributed to O. Castaños.

30 records · Page 2Linked to original sources
arXiv2014

A triple point in 3-level systems

The energy spectrum of a 3-level atomic system in the $Ξ$-configuration is studied. This configuration presents a triple point independently of the number of atoms, which remains in the thermo- dynamic limit. This means that in a vicinity of this point any quantum fluctuation will drastically change the composition of the ground state of the system. We study the expectation values of the atomic population of each level, the number of photons, and the probability distribution of photons at the triple point.

quant-ph↗
arXiv2013

Fidelity, susceptibility and critical exponents in the Dicke model

We calculate numerically the fidelity and its susceptibility for the ground state of the Dicke model. A minimum in the fidelity identifies the critical value of the interaction where a quantum phase crossover, the precursor of a phase transition for finite number of atoms N, takes place. The evolution of these observables is studied as a function of N, and their critical exponents evaluated. Using the critical exponents the universal curve for the specific susceptibility is recovered. An estimate to the precision to which the ground state wave function is numerically calculated is given, and found to have its lowest value, for a fixed truncation, in a vicinity of the critical coupling.

quant-ph↗
arXiv2013

A semi-classical versus quantum description of the ground state of three-level atoms interacting with a one-mode electromagnetic field

We consider $N_a$ three-level atoms (or systems) interacting with a one-mode electromagnetic field in the dipolar and rotating wave approximations. The order of the quantum phase transitions is determined explicitly for each of the configurations $Ξ$, $Λ$ and $V$, with and without detuning. The semi-classical and exact quantum calculations for both the expectation values of the total number of excitations $\cal{M}=\langle \bm{M} \rangle$ and photon number $n=\langle \bm{n} \rangle$ have an excellent correspondence as functions of the control parameters. We prove that the ground state of the collective regime obeys sub-Poissonian statistics for the ${\cal M}$ and $n$ distribution functions. Therefore, their corresponding fluctuations are not well described by the semiclassical approximation. We show that this can be corrected by projecting the variational state to a definite value of ${\cal M}$.

quant-ph↗
arXiv2012

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.

quant-ph↗
arXiv2011

On the Superradiant Phase in Field-Matter Interactions

We show that semi-classical states adapted to the symmetry of the Hamiltonian are an excellent approximation to the exact quantum solution of the ground and first excited states of the Dicke model. Their overlap to the exact quantum states is very close to 1 except in a close vicinity of the quantum phase transition. Furthermore, they have analytic forms in terms of the model parameters and allow us to calculate analytically the expectation values of field and matter observables. Some of these differ considerably from results obtained via the standard coherent states, and by means of Holstein-Primakoff series expansion of the Dicke Hamiltonian. Comparison with exact solutions obtained numerically support our results. In particular, it is shown that the expectation values of the number of photons and of the number of excited atoms have no singularities at the phase transition. We comment on why other authors have previously found otherwise.

quant-ph↗
arXiv1999

IBM: parameter symmetry, hidden symmetries and transformations of boson operators

A symmetry of the parameter space of interacting boson models IBM-1 and IBM-2 is studied. The symmetry is associated with linear canonical transformations of boson operators, or, equivalently, with the existence of different realizations of the symmetry algebras of the models. The relevance of the parameter symmetry to physical observables is discussed.

nucl-th↗
arXiv1994

Double beta decay of $^{100}Mo$: the deformed limit

The double beta decay of $^{100}Mo$ to the ground state and excited states of $^{100}Ru$ is analysed in the context of the pseudo SU(3) scheme. The results of this deformed limit are compared with the vibrational one based on the QRPA formalism. Consistency between the deformed limit and the experimental information is found for various $ββ$ transitions, although, in this approximation some energies and B(E2) intensities cannot reproduced.

nucl-th↗
arXiv1994

Neutrinoless Double Beta Decay in Heavy Deformed Nuclei

The zero neutrino mode of the double beta decay in heavy deformed nuclei is investigated in the framework of the pseudo SU(3) model, which has provided an accurate description of collective nuclear structure and predicted half-lives for the two neutrino mode in good agreement with experiments. In the case of $^{238}U$ the calculated zero neutrino half-life is at least three orders of magnitude greater than the two neutrino one, giving strong support of the identification of the radiochemically determined half-life as being the two neutrino double beta decay. For $^{150}Nd$ the zero neutrino matrix elements are of the order of magnitude of, but lesser than, those evaluated using the QRPA. This result confirms that different nuclear models produce similar zero neutrino matrix elements, contrary to the two neutrino case. Using these pseudo SU(3) results and the upper limit for the neutrino mass we estimate the $ββ_{0ν}$ half-lives for six nuclei. An upper limit for majoron coupling constant is extracted from the experimental data.

nucl-th↗
arXiv1994

Variational Formulation of Linear Time-Dependent Invariants

It is shown that linear time-dependent invariants for arbitrary multi\-dimensional quadratic systems can be obtained from the Lagrangian and Hamiltonian formulation procedures by considering a variation of coordinates and momenta that follows the classical trajectory and defines a noetherian symmetry transformation.

hep-th↗
arXiv1994

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))

hep-th↗
arXiv1994

Noether's Theorem and time-dependent quantum invariants

The time dependent-integrals of motion, linear in position and momentum operators, of a quantum system are extracted from Noether's theorem prescription by means of special time-dependent variations of coordinates. For the stationary case of the generalized two-dimensional harmonic oscillator, the time-independent integrals of motion are shown to correspond to special Bragg-type symmetry properties. A detailed study for the non-stationary case of this quantum system is presented. The linear integrals of motion are constructed explicitly for the case of varying mass and coupling strength. They are obtained also from Noether's theorem. The general treatment for a multi-dimensional quadratic system is indicated, and it is shown that the time-dependent variations that give rise to the linear invariants, as conserved quantities, satisfy the corresponding classical homogeneous equations of motion for the coordinates.

hep-th↗