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F. Soto-Eguibar

Publications and source records attributed to F. Soto-Eguibar.

At least 37 records · Page 2Linked to original sources
arXiv2023

Optical ladder operators in the Glauber-Fock oscillator array

In this study, we investigate the stationary states of the Glauber-Fock oscillator waveguide array. We begin by transforming the associated Hamiltonian into the form of a quantum harmonic oscillator Hamiltonian, allowing the implementation of a supersymmetric (SUSY) approach. By considering the simplest case for the intertwining operator, the optical ladder operators are straightforwardly constructed and shown to map eigensolutions into eigensolutions of the corresponding Hamiltonian operator, in pretty much the same manner as it is done for the quantum harmonic oscillator case. The ladder of the corresponding (eigen) supermodes is then easily established.

physics.optics↗
arXiv2023

Temporal factorization of a non-stationary electromagnetic cavity field

When an electromagnetic field is confined in a cavity of variable length, real photons may be generated from vacuum fluctuations due to highly nonadiabatic boundary conditions. The corresponding effective Hamiltonian is time-dependent and contains infinite intermode interactions. Considering one of the cavity mirrors fixed and the other describing uniform motion (zero acceleration), we show that it is possible to factorize the entire temporal dependency and write its formal solution, i.e., the Hamiltonian becomes a product of a time-dependent function and a time-independent operator. With this factorization, we prove in detail that the photon production is proportional to the Planck factor involving a velocity-dependent effective temperature. This temperature significantly limits photon generation even for ultra-relativistic motion. The time-dependent unitary transformations we introduce to obtain temporal factorization help establishing connections with the shortcuts to adiabaticity of quantum thermodynamics and with the quantum Arnold transformation.

quant-ph↗
arXiv2023

Effects of squeezing on the power broadening and shifts of micromaser lineshapes

It is well known that AC Stark shifts have an impact on the dynamics of atoms interacting with a near-resonant quantized single-mode cavity field, which is relevant for single-atom micromasers. In this study, we demonstrate that when the field is in a squeezed coherent state, the micromaser lines are highly sensitive to the squeezing parameter. Furthermore, we show that when considering a superposition of squeezed coherent states with equal amplitude, the displacement of the transition lines depends significantly not only on the squeezing parameter but also on its sign.

quant-ph↗
arXiv2023

Discriminating coherent states superpositions by line shapes

This article investigates the effect of near non-resonant levels on the spectral lines of atoms interacting with an electromagnetic field. Specifically, we examine the AC Stark effect that occurs when the field frequency matches the transition frequency between two lower levels and the field has a small average number of photons ($|α|^2 <4$). Our research demonstrates that the changes in spectral line shape can be used to distinguish between Schrödinger cat states with opposite phases in $π$, namely, the states $|α\rangle + |-α\rangle$ and $|α\rangle - |-α\rangle$.

quant-ph↗
arXiv2023

Exact solution for the interaction of two decaying quantized fields

We show that the Markovian dynamics of two coupled harmonic oscillators may be analyzed using a Schrödinger equation and an effective non-Hermitian Hamiltonian. This may be achieved by a non-unitary transformation that involves superoperators; such transformation enables the removal of quantum jump superoperators, that allows us to rewrite the Lindblad master equation in terms of a von Neumann-like equation with an effective non-Hermitian Hamiltonian. This may be generalized to an arbitrary number of interacting fields. Finally, by applying an extra non-unitary transformation, we may diagonalize the effective non-Hermitian Hamiltonian to obtain the evolution of any input state in a fully quantum domain.

quant-ph↗
arXiv2023

Exotic light transition between superluminal and subliminal group velocity in a $\mathcal{PT}$ coupled slab waveguide

We propose a rigorous full-wave modal analysis based on the eigenmodes approach (\textquotedblleft supermodes\textquotedblright), that allows the calculation of the transverse electric ($TE$) and transverse magnetic ($TM$) stationary propagation eigenmodes in a coupled $\mathcal{PT}$-symmetric slab waveguide. Our findings show that the group velocity, for the fundamental $TE_{0}$ supermode, passes from superluminal to subluminal speed over both sides of a critical point (CP), located near to the exceptional point (EP). We also demonstrate that the first higher-order supermode, $TE_{1}$, exhibits a slow light phenomenon around the EP.

physics.optics↗
arXiv2022

Exact solution for the time dependent non-Hermitian generalized Swanson oscillator

We produce an exact solution of the Schrödinger 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 model is reduced to a time independent harmonic oscillator.

quant-ph↗
arXiv2021

Mathieu-Bragg photonic lattices

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.

quant-ph↗
arXiv2021

Modeling displaced squeezed number states in waveguide arrays

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 results. The implication of a linear index of refraction changing as a function of the site number is also studied. In this case, we show that the first neighbor interaction strongly influences the periodicity of Bloch oscillations.

quant-ph↗
arXiv2021

Approximate solutions for the ion-laser interaction in the high intensity regime: Matrix method perturbative analysis

We provide an explicit expression for the second-order perturbative solution of a single trapped-ion interacting with a laser 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 state fits well with former results.

quant-ph↗
arXiv2021

Spectroscopy and critical quantum thermometry in the ultrastrong coupling regime

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 be considered spectral signatures of the counterintuitive decoupling effect. Using the coupled system as a thermometer for quantum thermodynamics applications, we obtain the ultimate bounds on the estimation of temperature that remain valid in the ultrastrong coupling regime. Remarkably, if the system performs a quantum phase transition, the quantum Fisher information exhibits periodic divergences, suggesting that one can have several points of arbitrarily high thermometric precision for such a critical quantum sensor.

quant-ph↗
arXiv2020

Electromagnetic field theory for invariant beams using scalar potentials

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 circular cylindrical symmetry.

physics.optics↗
arXiv2018

Conversion of any finite bandwidth optical field into a shape invariant beam

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 region of a finite non-diffracting field to an unbounded domain.

physics.optics↗
arXiv2018

Structure invariant wave packets

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.

quant-ph↗
arXiv2017

Normalization of the wavefunction obtained from perturbation theory based on a matrix method

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 coinciding with the exact known solution.

physics.optics↗
arXiv2016

Generalized revival and splitting of an arbitrary optical field in GRIN media

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 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 reflected version of it. We also prove that for particular wavelengths, there is a revival and a splitting of the initial field. We apply this results, first to an initial field given by a Bessel function and show that it splits into two generalized Bessel functions, and second, to an Airy function. In both cases our results are compared with the exact numerical ones.

physics.optics↗
arXiv2015

The Pegg-Barnett phase operator and the discrete Fourier transform

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 that the structure of the London-Susskind-Glogower phase operator, whose natural logarithm give rise the Pegg-Barnett phase operator, is contained into the Hamiltonian of circular waveguide arrays. Our results may find applications in the development of new finite-dimensional photonic systems with interesting phase-dependent properties.

quant-ph↗