arXiv subjects

B. M. Rodríguez-Lara

Publications and source records attributed to B. M. Rodríguez-Lara.

84 records · Page 5Linked to original sources

arXiv2012

The "Majoranon" and how to realize it in a tabletop experiment

We introduce the term Majoranon to describe particles that obey the Majorana equation, which are different from the Majorana fermions widely studied in various physical systems. A general procedure to simulate the corresponding Majoranon dynamics, based on a decomposition of the Majorana equation into two Dirac equations, is described in detail. It allows the simulation of the two-component chiral spinors, the building blocks of modern gauge theories, in the laboratory with current technology. Specifically, a Majoranon in one spatial dimension can be simulated with a single qubit plus a continuous degree of freedom, for example a single trapped ion. Interestingly, the dynamics of a Majoranon deviates most clearly from that of a Dirac particle in the rest frame, in which the continuous variable is redundant, making a possible laboratory implementation feasible with existing set ups.

quant-ph↗

arXiv2012

Quantum simulation of neutrino oscillations with trapped ions

We propose a scheme to simulate the dynamics of neutrino oscillations using trapped ions. For neutrinos in 1+1 dimensions, our scheme is experimentally implementable with existing trapped ion technology. We show that the three generation neutrino oscillations can be realized with three ions for 1+3 and 1+1 dimensions where the latter case only requires experimentally proven two-ion interactions. For this case, we discuss two setups utilizing different types of spin-spin interactions. Our method can be readily applied to two generation neutrino oscillations requiring fewer ions and lasers. We give a brief outline of a possible experimental scenario.

quant-ph↗

arXiv2012

Classical dynamics of a two-species Bose-Einstein condensate in the presence of nonlinear maser processes

The stability analysis of a generalized Dicke model, in the semi-classical limit, describing the interaction of a two-species Bose-Einstein condensate driven by a quantized field in the presence of Kerr and spontaneous parametric processes is presented. The transitions from Rabi to Josephson dynamics are identified depending on the relative value of the involved parameters. Symmetry-breaking dynamics are shown for both types of coherent oscillations due to the quantized field and nonlinear optical processes.

quant-ph↗

arXiv2011

Exact dynamics of finite Glauber-Fock photonic lattices

The dynamics of Glauber-Fock lattice of size N is given through exact diagonalization of the corresponding Hamiltonian; the spectra $\{λ_{k}\}$ is given as the roots of the $N$-th Hermite polynomial, $H_{N}(λ_k/\sqrt{2})=0$, and the eigenstates are given in terms of Hermite polynomials evaluated at these roots. The exact dynamics is used to study coherent phenomena in discrete lattices. Due to the symmetry and spacing of the eigenvalues $\{λ_{k}\}$, oscillatory behavior with highly localized spectra, that is, near complete revivals of the photon number and partial recovery of the initial state at given waveguides, is predicted.

quant-ph↗

arXiv2011

Solution to the Landau-Zener problem via Susskind-Glogower operators

We show that, by means of a right-unitary transformation, the fully quantized Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau-Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation.

quant-ph↗

arXiv2011

Classical dynamics of a two-species condensate driven by a quantum field

We present a stability analysis of an interacting two-species Bose-Einstein condensate driven by a quantized field in the semi-classical limit. Transitions from Rabi to Josephson dynamics are identified depending on both the inter-atomic interaction to field-condensate coupling ratio and the ratio between the total excitation number and the condensate size. The quantized field is found to produce asymmetric dynamics for symmetric initial conditions for both Rabi and Josephson oscillations.

quant-ph↗

arXiv2011

Probing the BCS-BEC crossover with photons in a nonlinear optical fiber

We propose a scheme where strongly correlated photons generated inside a hollow-core one-dimensional fiber filled with two cold atomic species can be used to simulate the BCS-BEC crossover. We first show how stationary light-matter excitations (polaritons) in the system can realize an optically tunable two component Bose-Hubbard model, and then analyze the optical parameters regime necessary to generate an effective Fermi-Hubbard model of photons exhibiting Cooper pairing. The characteristic correlated phases of the system can be efficiently observed due to the {\it in situ} accessibility of the photon correlations with standard optical technology.

quant-ph↗

arXiv2011

Quantifying momenta through the Fourier transform

Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be calculated using only Fourier transforms. This result is used to evaluate the mean value of momenta associated to the symmetries of the reduced wave equation. As an explicit example, the orbital angular momenta of plane and elliptic-cylindrical waves is presented.

math.AP↗

arXiv2010

Chaotic dynamics of thermal atoms in labyrinths created by optical lattices

We study the dynamics of non interacting thermal atoms embedded in structured optical lattices with non trivial geometry. The lattice would be generated by two counter propagating modes with parabolic cylindrical symmetry and we concentrate on the quasi conservative red detuned far-off-resonance regime. The system exhibits quasi periodic and chaotic behaviors whose probability can be controlled by varying the intensity of the beams. The spectral density of the trajectories is used as a chaos signature. An analysis of permanency times for chaotic trajectories that visit more than one potential well reveals a distribution with a long tail.

quant-ph↗

arXiv2010

Quantum phase transition of nonlinear light in the finite size Dicke Hamiltonian

We study the quantum phase transition of a N two-level atomic ensemble interacting with an optical degenerate parametric process, which can be described by the finite size Dicke Hamiltonian plus counter-rotating and quadratic field terms. Analytical closed forms of the critical coupling value and their corresponding separable ground states are derived in the weak and strong coupling regimes. The existence of bipartite entanglement between the two-level-system ensemble and photon field as well as between ensemble components for moderate coupling is shown through numerical analysis. Given a finite size, our results also indicate the co-existence of squeezed fields and squeezed atomic ensembles.

quant-ph↗

arXiv2009

On optical Weber waves and Weber-Gauss beams

The normalization of energy divergent Weber waves and finite energy Weber-Gauss beams is reported. The well-known Bessel and Mathieu waves are used to derive the integral relations between circular, elliptic, and parabolic waves and to present the Bessel and Mathieu wave decomposition of the Weber waves. The efficiency to approximate a Weber-Gauss beam as a finite superposition of Bessel-Gauss beams is also given.

physics.optics↗

arXiv2008

Dynamical constants for electromagnetic fields with elliptic-cylindrical symmetry

Taking into account the characteristics of a free scalar field in elliptic coordinates, a new dynamical variable is found for the free electromagnetic field. The conservation law associated to this variable cannot be obtained by direct application of standard Noether theorem since the symmetry generator is of second order. Consequences on the expected mechanical behavior of an atomic system interacting with electromagnetic waves exhibiting such a symmetry are also discussed.

physics.class-ph↗