Publications by authors named "Hector Moya Cessa"

We present an integral of diffraction based on particular eigenfunctions of the Laplacian in two dimensions. We show how to propagate some fields, in particular a Bessel field, a superposition of Airy beams, both over the square root of the radial coordinate, and show how to construct a field that reproduces itself periodically in propagation, i.e.

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We study the propagation of superpositions of Airy beams and show that, by adequately choosing the parameters in the superposition, effects as opposite as autofocusing and quasi-adiffractional propagation may be obtained. We also give a simple analytical expression for free propagation of any initial field, based on so-called number states (eigenstates of the quantum harmonic oscillator), that allows us to study their self-healing properties.

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Article Synopsis
  • This work models two coupled quantum harmonic oscillators and quantized fields using classical optics.
  • It introduces classical analogs of coupled harmonic oscillators in anisotropic graded indexed media within a rotated reference frame.
  • The study employs operator techniques from quantum mechanics to analyze light propagation in these media and highlights the occurrence of phase transitions.
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The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state.

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Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville operator associated with the time-dependent frequency harmonic oscillator can be transformed using an Ermakov-Lewis invariant, which is also time dependent and commutes with itself at any time.

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We show how to produce a fast quantum Rabi model with trapped ions. Its importance resides not only in the acceleration of the phenomena that may be achieved with these systems, from quantum gates to the generation of nonclassical states of the vibrational motion of the ion, but also in reducing unwanted effects such as the decay of coherences that may appear in such systems.

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We investigate the propagation dynamics of accelerating beams that are shape-preserving solutions of the Maxwell equations, and explore the contribution of their evanescent field components in detail. Both apodized and nonapodized Bessel beam configurations are considered. We show that, in spite of the fact that their evanescent tails do not propagate, these nonparaxial beams can still accelerate along circular trajectories and can exhibit large deflections.

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Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive.

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Noise is generally thought as detrimental for energy transport in coupled oscillator networks. However, it has been shown that for certain coherently evolving systems, the presence of noise can enhance, somehow unexpectedly, their transport efficiency; a phenomenon called environment-assisted quantum transport (ENAQT) or dephasing-assisted transport. Here, we report on the experimental observation of such effect in a network of coupled electrical oscillators.

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We introduce a new class of paraxial optical beams exhibiting discrete-like diffraction patterns reminiscent to those observed in periodic evanescently coupled waveguide lattices. It is demonstrated that such paraxial beams are analytically described in terms of generalized Bessel functions. Such effects are elucidated via pertinent examples.

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We report the first experimental implementation of Glauber-Fock oscillator lattices. Bloch-like revivals are observed in these optical structures in spite of the fact that the photonic array is effectively semi-infinite and the waveguide coupling is not uniform. This behavior is entirely analogous to the dynamics exhibited by a driven quantum harmonic oscillator.

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Coherent states and their generalizations, displaced Fock states, are of fundamental importance to quantum optics. Here we present a direct observation of a classical analogue for the emergence of these states from the eigenstates of the harmonic oscillator. To this end, the light propagation in a Glauber-Fock waveguide lattice serves as equivalent for the displacement of Fock states in phase space.

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We investigate the propagation of Airy beams in linear gradient index inhomogeneous media. We demonstrate that by controlling the gradient strength of the medium it is possible to reduce to zero their acceleration. We show that the resulting Airy wave beam propagates in straight line due to the balance between two opposite effects, one due to the inhomogeneous medium and the other to the diffraction of the beam, in a similar way as a solitary wave in a nonlinear inhomogeneous medium.

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We show that classical analogs to quantum coherent and displaced Fock states can emerge in one-dimensional semi-infinite photonic lattices having a square root law for the coupling coefficients. Beam dynamics in these fully integrable structures is described in closed form, irrespective of the site of excitation. The trajectories of these beams are closely examined, and pertinent examples are provided for their realization.

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