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99

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February 1999 - present

## Publications

Publications (99)

We produce an exact solution of the Schr\"odinger equation for the generalized time dependent Swanson oscillator. The system studied is a non-Hermitian setup characterized by time dependent complex coefficients. The exact solution is obtained by applying two transformations and under the right choice of the relevant parameters. Consequently, the mo...

This work provides an explicit expression for the second-order perturbative solution of a single trapped ion at the high intensity regime. Unlike other perturbative schemes, where the ion-laser dynamics has been explored using unitary transformations and the Lamb-Dicke regime, this analysis relies instead on a direct perturbation method, that may b...

We show that two-mode squeezed vacuum-like states may be engineered in the Bohm-Madelung formalism by adequately choosing the phase of the wavefunction. The difference between our wavefunction and the one of the squeezed vacuum states is given precisely by the phase we selected. We would like to stress that the engineering of two-mode vacuum states...

In this work, we consider a single unitary transformation that enables us to diagonalize the Dirac Hamiltonian with an even potential. Its diagonal matrix elements are translated to the optical domain, which leads to a direct mapping onto a lattice with interactions to second neighbours. Consequently, Bloch oscillations arise naturally, if we consi...

We show that several Hamiltonians that are ${\mathcal PT}$ symmetric may be taken to Hermitian Hamiltonians via a non-unitary transformation and vice versa. We also show that for some specific Hamiltonians such non-unitary transformations may be associated, via a fractional-Wick rotation, to complex time.

By adapting the Madelung-Bohm formalism to paraxial wave propagation we show, by using Ermakov-Lewis techniques, that the Gouy phase is related to the form of the phase chosen in order to produce a Gaussian function as a propagated field. For this, we introduce a quantum mechanical invariant, that it is explicitly time dependent. We finally show th...

In the Madelung-Bohm approach to quantum mechanics, we consider a time dependent phase that depends quadratically on position and we show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.

We show that the time-dependent harmonic oscillator has a repulsive or inverted oscillator as a time domain SUSY-like partner. Examples of several kinds of super-symmetrical time dependent frequency systems are presented.

By adapting the Madelung-Bohm formalism to paraxial wave propagation we show, by using Ermakov-Lewis techniques, that the Gouy phase is related to the form of the phase chosen in order to produce a Gaussian function as a propagated field. For this, we introduce a quantum mechanical invariant , that it is explicitly time dependent despite the fact t...

We show that the Kapitza-Dirac effect may be modeled
by classical light propagation in photonic lattices having
a square power law for the refraction index coefficient.
The dynamics is shown to be fully soluble because
both systems share the same time-independent
Schrödinger equation: the angular Mathieu equation.
We examine the trajectories of cla...

We show that Bragg diffraction may be modeled by classical light propagation in photonic lattices having a square power law for the refraction index coefficient. The dynamics is shown to be fully integrable and therefore described in closed form. We examine the trajectories of classical light propagating in such structures.

We present an exact analytical solution for a one-dimensional zigzag waveguide array with first and second neighbor interactions. It is found that the waveguide system possess a classical analog to the displaced squeezed number states. The exact solution was compared directly with the numerical solution showing a perfect agreement between both resu...

We provide an explicit expression for the second-order perturbative solution of a single trapped-ion interacting
with a lser field in the strong excitation regime. From the perturbative analytical solution, based on a matrix method
and a final normalization of the perturbed solutions, we show that the probability to find the ion in its excited stat...

We present generalized expressions to calculate the orbital angular momentum for invariant beams using scalars potentials. The solutions can be separated into transversal electric TE, transversal magnetic TM and transversal electromagnetic TE/TM polarization modes. We show that the su-perposition of non-paraxial vectorial beams with axial symmetry...

We show that two-mode squeezed vacuum-like states may be engineered in the Bohm-Madelung formalism by adequately choosing the phase of the wavefunction. The difference between our wavefunction and the one of the squeezed vacuum states is given precisely by the phase we choose.

It is shown that field propagation in linear and quadratic gradient-index (GRIN) media obeys the same rules of free propagation in the sense that a field propagating in free space has a (mathematical) form that may be exported to those particular GRIN media. The Bohm potential is introduced in order to explain the reason of such behavior: it change...

In the Madelung-Bohm approach to quantum mechanics, we consider a (time dependent) phase that depends quadrati-cally on position and show that it leads to a Bohm potential that corresponds to a time dependent harmonic oscillator, provided the time dependent term in the phase obeys an Ermakov equation.

We present an exact analytical solution of the anisotropic Hopfield model, and we use it to investigate in detail the spectral and thermometric response of two ultrastrongly coupled quantum systems. Interestingly, we show that depending on the initial state of the coupled system, the vacuum Rabi splitting manifests significant asymmetries that may...

We analyze Bohm's potential effects both in the realms of Quantum Mechanics and Optics, as well as in the study of other physical phenomena described in terms of classical and quantum wave equations. We approach this subject by using theoretical arguments as well as experimental evidence. We find that the effects produced by Bohm's potential are bo...

We analyze Bohm's potential effects both in the realms of Quantum Mechanics and Optics, as well as in the study of other physical phenomena described in terms of classical and quantum wave equations. We approach this subject by using theoretical arguments as well as experimental evidence. We find that the effects produced by Bohm's potential are bo...

Following the scheme proposed by Eberly and Wodkiewicz for the physical spectrum, we calculate the fluorescence spectrum of the Jaynes-Cummings model when the two level system interacts with an electromagnetic field that initially is in a squeezed coherent state. We show the appearing of "ringing lines" in the fluorescence spectrum that are echoes...

A supersymmetric theory in the temporal domain is constructed for bi-spinor fields satisfying the Dirac equation. It is shown that using the Dirac matrices basis, it is possible to construct a simple time-domain supersymmetry for fermion fields with time-dependent mass. This theory is equivalent to a bosonic supersymmetric theory in the time-domain...

A supersymmetric theory in the temporal domain is constructed for bi-spinor fields satisfying the Dirac equation. It is shown that using the Dirac matrices basis, it is possible to construct a simple time-domain supersymmetry for fermion fields with time-dependent mass. This theory is equivalent to a bosonic supersymmetric theory in the time-domain...

It is shown that field propagation in linear and quadratic gradient-index (GRIN) media obeys the same rules of free propagation in the sense that a field propagating in free space has a (mathematical) form that may be {\it exported} to those particular GRIN media. The Bohm potential is introduced in order to explain the reason of such behavior: it...

We present generalized expressions to calculate the orbital angular momentum for invariant beams using scalars potentials. The solutions can be separated into transversal electric TE, transversal magnetic TM and transversal electromagnetic TE/TM polarization modes. We show that the superposition of non-paraxial vectorial beams with axial symmetry c...

Negative propagation is an uncommon response produced by the local sign change in Poynting vector components. We present a general Poynting vector expression for all invariant beams with cylindrical symmetry using scalar potentials in order to evaluate the possibility of negative propagation. We analyze the plausibility of negative propagation bein...

Many practical applications require the analysis of electromagnetic scattering properties of local structures using different sources of illumination. The Optical Theorem (OT) is a useful result in scattering theory, relating the extinction of a structure to the scattering amplitude in the forward direction. The most common derivation of the OT is...

We present a description of the electromagnetic field for propagation invariant beams using scalar potentials. Fundamental dynamical quantities are obtained: the energy density, the Poynting vector and the Maxwell stress tensor. As an example, all these quantities are explicitly calculated for the Bessel beams, which are the invariant beams with ci...

We study the repulsive harmonic oscillator and an extension of this system, with an additional linear anhar-monicity term. The system is solved in exact and perturbatively form, the latter by using the so-called normalized perturbative matrix method. The perturbative solution up to second order is compared with the exact solution when the system is...

We study the resonance fluorescence in the Jaynes-Cummings model when nearby levels are taking into account. We show that the Stark shift produced by such levels generates a displacement of the peaks of the resonance fluorescence due to an induced effective detuning and also induces an asymmetry. Specific results are presented assuming a coherent a...

We study the resonance fluorescence in the Jaynes-Cummings model when nearby levels are taking into account. We show that the Stark shift produced by such levels generates a displacement of the peaks of the resonance fluorescence due to an induced effective detuning and also induces an asymmetry. Specific results are presented assuming a coherent a...

We show that the Pegg-Barnett formalism accepts coherent states constructed as eigenstates of the annihilation operator, both in the number and phase basis. These operators are defined within a (s+1)-dimensional Hilbert space Hs and with periodic conditions. The coherent states that we find are determined by the eigenvalue of the annihilation opera...

The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants , is presented. Finite circular and linear arrays are studied using classical arguments, and their proper solution is given using methods often found in...

This contribution has two main purposes. First, using classical optics we show how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we present classical analogs of coupled harmonic oscillators that correspond to anisotropic quadratic graded indexed media in a rotated reference frame, and we use operato...

The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants , is presented. Finite circular and linear arrays are studied using classical arguments, and their proper solution is given using methods often found in...

A method to generate NOON states with three photons by injecting photons in an array of three waveguides is presented. Conditional measurements project the wave function in a given (desired) state. In passing, it is shown how the array of three waveguides, that effectively reproduces the interaction of three fields, may be reduced to the interactio...

We study single photon resonant transitions of a two level atom with a quantized electromagnetic field when conditional measurements take place, showing that squeezed states may be generated in the multiphoton processes that occur during evolution. We examine some field properties and show that the field not only acquires squeezing properties but a...

We analyse the paraxial field propagation in the realm of classical optics, showing that it can be written as the action of the fractional Fourier transform, followed by the squeeze operator applied to the initial field. Secondly, we show that a wavelet transform may be viewed as the application of a displacement and squeeze operator onto the mothe...

The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants , is presented. Finite circular and linear arrays are studied using classical arguments, and their proper solution is given using methods often found in...

This contribution has two main purposes. First, we show using classical optics how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we use quantum mechanical techniques to solve, exactly, the propagation of light through a particular type of graded index medium. In passing, we show that the system pres...

This contribution has two main purposes. First, we show using classical optics how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we use quantum mechanical techniques to solve, exactly, the propagation of light through a particular type of graded index medium. In passing, we show that the system pres...

We show that by adding a quadratic phase to an initial arbitrary wavefunction, its free evolution maintains an invariant structure while it spreads by the action of an squeeze operator. Although such invariance is an approximation, we show that it matches perfectly the exact evolution.

Based on the definition of the continuous Fourier transform in terms of the number operator of the quantum harmonic oscillator and in the corresponding definition of the continuous fractional Fourier transform, we have obtained the discrete fractional Fourier transform from the discrete Fourier transform in a completely analogous manner. To achieve...

We discuss a method to transform any optical field, with finite frequency bandwidth, into a shape invariant beam with transverse scaling, dependent on the propagation distance. The method consists in modulating the field with a quadratic phase of appropriate curvature radius. As a particular application, we employ the method to extend the existence...

We show how squeeze operators appear in paraxial field propagation,i.e., in classical optics. Then, we show how squeezed states may be generated in multiphoton processes that occur in single photon resonant transitions of the atom-field interaction when conditional measurements take place. We study field properties, to show that the field does not...

We discuss a method to transform any optical field, with finite frequency bandwidth, into a shape invariant beam with transverse scaling, dependent on the propagation distance. The method consists in modulating the field with a quadratic phase of appropriate curvature radius. As a particular application, we employ the method to extend the existence...

We show that by adding a quadratic phase to an initial arbitrary wavefunction, its free evolution maintains an invariant structure while it spreads by the action of an squeeze operator. Although such invariance is an approximation, we show that it matches perfectly the exact evolution.

We show that multiphoton processes may be generated in the interaction between three-level atoms and quantized fields. Such processes are produced, with good probability, by measuring Schmidt states of the atom. Furthermore, the Schmidt decomposition allows us to define the entropy operators associated with the atom and the field.
Graphical abstra...

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...

We solve exactly the master equation of the degenerate and nondegenerate parametric
oscillator in presence of a squeezed reservoir. We show that the formal solutions of both
systems can be obtained in terms of the density operator by applying squeeze transformations and using the superoperators formalism.

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...

We present the derivation of the normalization constant for the perturbation matrix method recently proposed. The method is tested on the problem of a binary waveguide array for which an exact and an approximate solution are known. In our analysis, we show that to third order the normalized matrix method approximate solution gives results coincidin...

We analyse the paraxial field propagation in the realm of classical optics, showing that it can be written as the action of the fractional Fourier transform, followed by the squeeze operator applied to the initial field. Secondly, we show that a wavelet transform may be viewed as the application of a displacement and squeeze operator onto the mothe...

The creation of non-classical states of light is an interesting problem, that we solve sending atoms through an optical cavity. We show that it is possible to add or subtract many photons from a cavity field by interacting it resonantly with a two-level atom. The atom, after entangling with the field inside the cavity and exiting it, may be measure...

Diverse measurements indicate that entropy grows as the universe evolves, we analyze from a quantum point of view plausible scenarios that allow such increase.

We present a method to obtain NOON states with three photons by injecting photons in an array of three waveguides. Conditional measurements project the wave function in the desired state. In passing, we show how the array of three waveguides, that effectively reproduces the interaction of three fields, may be reduced to the interaction of two field...

We present a method to obtain NOON states with three photons by injecting photons in an array of three waveguides. Conditional measurements project the wave function in the desired state. In passing, we show how the array of three waveguides, that effectively reproduces the interaction of three fields, may be reduced to the interaction of two field...

Many practical applications require the analysis of electromagnetic scattering properties of local structures using different sources of illumination. The Optical Theorem (OT) is a useful result in scattering theory, relating the extinction of a structure to the scattering amplitude in theforward direction. The most common derivation of the OT is g...

We develop a matrix perturbation method for the Lindblad master equation. The first- and second-order corrections are obtained and the method is generalized for higher orders. The perturbation method developed is applied to the problem of a lossy cavity filled with a Kerr medium; the second-order corrections are estimated and compared with the know...

Assuming a non-paraxial propagation operator, we study the propagation of an electromagnetic field with an arbitrary initial condition in a quadratic GRIN medium. We show analytically that at certain specific periodic distances, the propagated field is given by the fractional Fourier transform of a superposition of the initial field and of a reflec...

In quantum mechanics the position and momentum operators are related to each
other via the Fourier transform. In the same way, here we show that the
so-called Pegg-Barnett phase operator can be obtained by the application of the
discrete Fourier transform to the number operator defined in a
finite-dimensional Hilbert space. Furthermore, we show tha...

An explicit phase space representation of the wave function is build based
on a wavelet transformation. The wavelet transformation allows us to understand
the relationship between s−ordered Wigner function, (or Wigner
function when s = 0), and the Torres-Vega-Frederick’s wave functions. This
relationship is necessary to find a general solution of t...

We present the theoretical basis needed to work in the field of photonic lattices. We start by studying the field modes inside and outside a single waveguide. Then we use perturbation theory to deal with an array of coupled waveguides and construct a mode-coupling theory. Finally, we show how quantum optics models can be used as a toolbox to design...

The short range revival of an arbitrary monochromatic optical field, which propagates in a quadratic GRIN rod, is a well-known effect that is established assuming the first-order approximation of the propagation operator. We discuss the revival and multiple splitting of an off-axis Gaussian beam propagating to relatively long distances in a quadrat...

Based on operator algebras commonly used in quantum mechanics some properties
of special functions such as Hermite and Laguerre polynomials and Bessel
functions are derived.

We use a right unitary decomposition to study an ultracold two-level atom
interacting with a quantum field. We show that such a right unitary approach
simplifies the numerical evolution for arbitrary position-dependent atom-field
couplings. In particular, we provide a closed form, analytic time evolution
operator for atom-field couplings with quadr...

The time-dependent Schroedinger equation is solved for a linear potential using operational methods; in particular, an extension of the Baker-Campbell-Hausdorff formula is exposed and used. Several initial conditions are considered. A closed formfor the Wigner function is presented. The results can be extended to the propagation of an electromagnet...

By taking advantage of the superposition principle inherent to quantum mechanics, we show that it is possible, by interacting a quantized field with a trapped ion, to reach both high intensity and low intensity regimes simultaneously. We use the London operator in order to simplify the Hamiltonians involved in the problem.

We use the propagation of a conveniently shaped Gaussian beam in a GRIN media to mimic a quantum cavity filled with a Kerr medium. This is attained by introducing a second-order correction to the paraxial propagation of the beam. An additional result is that a Gaussian beam propagating in GRIN media may split into two Gaussian beams, corresponding...

We provide a squeeze-like transformation that allows one to remove a position
dependent mass from the Hamiltonian. Methods to solve the Schr\"{o}dinger
equation may then be applied to find the respective eigenvalues and
eigenfunctions. As an example, we consider a position-dependent-mass that leads
to the integrable Morse potential and therefore to...

In a cavity filled with a Kerr medium it is possible to generate the
superposition of coherent states, i.e. Schroodinger cat states may be realized
in this system. We show that such a medium may be mimicked by the propagation
of a conveniently shaped Gaussian beam in a GRIN device. This is attained by
introducing a second order correction to the pa...