Hermite Coherent States for Quadratic Refractive Index Optical Media

Producción CientíficaLadder and shift operators are determined for the set of Hermite–Gaussian modes associated with an optical medium with quadratic refractive index profile. These operators allow to establish irreducible representations of the su(1, 1) and su(2) algebras. Glauber coherent states, as well as su(1, 1) and su(2) generalized coherent states, were constructed as solutions of differential equations admitting separation of variables. The dynamics of these coherent states along the optical axis is also evaluated.MINECO grant MTM2014-57129-C2-1-P and Junta de Castilla y Leon grant VA057U16

Revisiting the optical PTPT-symmetric dimer

Optics has proved a fertile ground for the experimental simulation of quantum mechanics. Most recently, optical realizations of $\mathcal{PT}$-symmetric quantum mechanics have been shown, both theoretically and experimentally, opening the door to international efforts aiming at the design of practical optical devices exploiting this symmetry. Here, we focus on the optical $\mathcal{PT}$-symmetric dimer, a two-waveguide coupler were the materials show symmetric effective gain and loss, and provide a review of the linear and nonlinear optical realizations from a symmetry based point of view. We go beyond a simple review of the literature and show that the dimer is just the smallest of a class of planar $N$-waveguide couplers that are the optical realization of Lorentz group in 2+1 dimensions. Furthermore, we provide a formulation to describe light propagation through waveguide couplers described by non-Hermitian mode coupling matrices based on a non-Hermitian generalization of Ehrenfest theorem.Comment: 25 pages, 12 figure

Quantum autoencoders via quantum adders with genetic algorithms

The quantum autoencoder is a recent paradigm in the field of quantum machine learning, which may enable an enhanced use of resources in quantum technologies. To this end, quantum neural networks with less nodes in the inner than in the outer layers were considered. Here, we propose a useful connection between approximate quantum adders and quantum autoencoders. Specifically, this link allows us to employ optimized approximate quantum adders, obtained with genetic algorithms, for the implementation of quantum autoencoders for a variety of initial states. Furthermore, we can also directly optimize the quantum autoencoders via genetic algorithms. Our approach opens a different path for the design of quantum autoencoders in controllable quantum platforms

Microcanonical finite-size scaling in specific heat diverging 2nd order phase transitions

A Microcanonical Finite Site Ansatz in terms of quantities measurable in a Finite Lattice allows to extend phenomenological renormalization (the so called quotients method) to the microcanonical ensemble. The Ansatz is tested numerically in two models where the canonical specific-heat diverges at criticality, thus implying Fisher-renormalization of the critical exponents: the 3D ferromagnetic Ising model and the 2D four-states Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows to simulate systems as large as L=1024 (Potts) or L=128 (Ising). The quotients method provides extremely accurate determinations of the anomalous dimension and of the (Fisher-renormalized) thermal $\nu$ exponent. While in the Ising model the numerical agreement with our theoretical expectations is impressive, in the Potts case we need to carefully incorporate logarithmic corrections to the microcanonical Ansatz in order to rationalize our data.Comment: 13 pages, 8 figure

Model of the meniscus of an ionic liquid ion source.

A simple model of the transfer of charge and ion evaporation in the meniscus of an ionic-liquid ion source working in the purely ionic regime is proposed on the basis of order-of-magnitude estimates which show that, in this regime, _i_ the flow in the meniscus is dominated by the viscosity of the liquid and is affected very little by the mass flux accompanying ion evaporation, and _ii_ the effect of the space charge around the evaporating surface is negligible and the evaporation current is controlled by the finite electrical conductivity of the liquid. The model predicts that a stationary meniscus of a very polar liquid undergoing ion evaporation is nearly hydrostatic and can exist only below a certain value of the applied electric field, at which the meniscus attains its maximum elongation but stays smooth. The electric current vs applied electric field characteristic displays a frozen regime of negligible ion evaporation at low fields and a conduction-controlled regime at higher fields, with a sharp transition between the two regimes owing to the high sensitivity of the ion evaporation rate to the electric field. A simplified treatment of the flow in the capillary or liquid layer through which liquid is delivered to the meniscus shows that the size of the meniscus decreases and the maximum attainable current increases when the feeding pressure is decreased, and that appropriate combinations of feeding pressure and pressure drop may lead to high maximum currents

Self-Averaging in the Three Dimensional Site Diluted Heisenberg Model at the critical point

We study the self-averaging properties of the three dimensional site diluted Heisenberg model. The Harris criterion \cite{critharris} states that disorder is irrelevant since the specific heat critical exponent of the pure model is negative. According with some analytical approaches \cite{harris}, this implies that the susceptibility should be self-averaging at the critical temperature ($R_\chi=0$). We have checked this theoretical prediction for a large range of dilution (including strong dilution) at critically and we have found that the introduction of scaling corrections is crucial in order to obtain self-averageness in this model. Finally we have computed critical exponents and cumulants which compare very well with those of the pure model supporting the Universality predicted by the Harris criterion.Comment: 11 pages, 11 figures, 14 tables. New analysis (scaling corrections in the g2=0 scenario) and new numerical simulations. Title and conclusions chang