Blas Manuel Rodríguez-Lara

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We revisit electromagnetic field propagation through tight-binding arrays of coupled photonic waveguides, with properties independent of the propagation distance, and recast it as a symmetry problem. We focus our analysis on photonic lattices with underlying symmetries given by three well-known groups, SU(2), SU(1, 1) and Heisenberg-Weyl, to show that(More)
We implement a finite-dimensional representation of the 2+1D Lorentz group with a PT-symmetric waveguide array. Our device can be engineered to behave like a multi-port oscillator or directional coupler with amplification. We show that the two-waveguide coupler with linear losses, the Vernier effect in coupled asymmetric micro-cavity lasers, and the(More)
We analyze classical propagation in several configurations of waveguide arrays and, by using Scrhoedinger-like equations, show that these systems may mimic quantum systems such as Lewis-Ermakov systems, SUSY and Majorana dynamics. Such analogies may be achieved because in such photonic arrays, we may properly tune the interaction coefficients in order to(More)
We present a stability analysis of an interacting two-species Bose-Einstein condensate driven by a quantized field in the semiclassical limit. Transitions from Rabi to Josephson dynamics are identified depending on both the interatomic interaction to field-condensate coupling ratio and the ratio between the total excitation number and the condensate size.(More)
We study electromagnetic field propagation through a planar three-waveguide coupler with linear gain or loss in a configuration that is the optical analog of a quantum PT-symmetric system. This model is experimentally feasible on at least four proven architectures: lossy waveguide couplers, pumped waveguides couplers, non-Hermitian electronics and coupled(More)
We study the quantum phase transition of an N two-level system 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(More)
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(More)
We study continuous-wave light propagation through a twisted birefringent single-mode fiber amplifier with saturable nonlinearity. The corresponding coupled-mode system is isomorphic to a non-Hermitian nonlinear dimer and gives rise to analytic polarization-mode dynamics. It provides an optical simulation of the semi-classical non-Hermitian Bose-Hubbard(More)
The coherent transport of quantum states between distant qubits is one of the key milestones towards the realisation of large-scale quantum computers. For static qubits, this state transfer is often envisioned to be carried out only by the internal dynamics of the system, which has the great advantage that detrimental influences of the environment are(More)
We present a class of waveguide arrays that is the classical analog of a quantum harmonic oscillator, where the mass and frequency depend on the propagation distance. In these photonic lattices, refractive indices and second-neighbor couplings define the mass and frequency of the analog quantum oscillator, while first-neighbor couplings are a free parameter(More)