arXiv subjects

F. H. Maldonado-Villamizar

Publications and source records attributed to F. H. Maldonado-Villamizar.

12 recordsLinked to original sources

arXiv2026

Affine spin-pencil factorization of generalized driven anisotropic Rabi--Stark Hamiltonians in an inhomogeneous orthosymplectic superalgebra

We construct a supersymmetric factorization for generalized driven anisotropic Rabi--Stark Hamiltonians using an affine factor $\hat{A}=\hat{C}+\hat{a}\hat{D}$ in an inhomogeneous orthosymplectic superalgebra, with two real invertible spin matrices $\hat{C}$ and $\hat{D}$. The six real pencil parameters constrain nine Hamiltonian frequencies and one energy offset up to an overall frequency scale. The normal product $\hat{A}^{\dagger}\hat{A}$ has an exact zero-energy ground doublet and, with its antinormal partner $\hat{A}\hat{A}^{\dagger}$, gives a Witten index of two. For distinct pencil roots with finite baseline slopes, coherent gauges define a Bargmann hierarchy and endpoint conditions for exceptional finite-polynomial states. The spin grading organizes four limiting cases, comprising two driven-oscillator families with every baseline exact and the constrained anisotropic-Rabi and Rabi--Stark sheets, which meet at the degenerate-qubit isotropic Rabi model. An aligned interior example adds direct and longitudinal drives, Stark deformation, and intensity-dependent coupling while retaining the factorization.

quant-ph↗

arXiv2026

Generalized vectorial ray tracing for optical analysis and design in freeform gradient-index media

Gradient-index (GRIN) media with freeform refractive-index distributions require ray tracing approaches capable of accurately modeling light propagation in complex three-dimensional environments. In this work, we develop a fully three-dimensional ray tracing method for arbitrary freeform GRIN media based on the local application of a set of vectorial relations of geometrical optics. At its core, the method constructs ray trajectories through successive local refractions using the vectorial form of Snell's law, while employing constant optical path length steps that naturally adapt the geometric step size within the medium. Unlike conventional continuous GRIN propagation approaches, the proposed method naturally handles refraction at the boundary of the medium as well as total internal reflection, enabling the treatment of both continuous media and discretized refractive-index distributions composed of isoindicial surfaces. The method is simple to implement and computationally efficient. Validation against an analytical solution demonstrates high accuracy, while applications to freeform GRIN configurations illustrate its capability not only for propagation analysis, but also for the direct design of complex tailor-made optical media.

physics.optics↗

arXiv2024

A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model

We revisit the Jaynes-Cummings and anti-Jaynes-Cummings model through the lens of Lie theory, aiming to highlight the efficacy of an operator-based approach for diagonalization. We focus on explicitly delineating the steps from an underlying abstract supersymmetry, provided by the $u(1 \vert 1)$ superalgebra, into concrete proper states and energies in the laboratory frame. Additionally, we explore the anisotropic Rabi model possessing an underlying supersymmetry, provided by the $osp(2 \vert 2)$ superalgebra, in a squeezed reference frame, where it is possible to approximate its spectral characteristics by an effective Jaynes--Cummings model. Finally, we identify a regime for a factorizable anisotropic Rabi model, exhibiting an equally spaced, double degenerate energy spectrum with a unique ground state energy. Our work aims to merge mathematical physics with practical quantum optics, underscoring the critical role of Lie theory.

quant-ph↗

arXiv2023

Optical coupling control of isolated mechanical resonators

We present a Hamiltonian model describing two pairs of mechanical and optical modes under standard optomechanical interaction. The vibrational modes are mechanically isolated from each other and the optical modes couple evanescently. We recover the ranges for variables of interest, such as mechanical and optical resonant frequencies and naked coupling strengths, using a finite element model for a standard experimental realization. We show that the quantum model, under this parameter range and external optical driving, may be approximated into parametric interaction models for all involved modes. As an example, we study the effect of detuning in the optical resonant frequencies modes and optical driving resolved to mechanical sidebands and show an optical beam splitter with interaction strength dressed by the mechanical excitation number, a mechanical bidirectional coupler, and a two-mode mechanical squeezer where the optical state mediates the interaction strength between the mechanical modes.

quant-ph↗

arXiv2022

Novel traversable wormhole in General Relativity and Einstein-Scalar-Gauss-Bonnet theory supported by nonlinear electrodynamics

Several traversable wormholes (T-WHs) of the Morris-Thorne type have been presented as exact solutions of Einstein-nonlinear electrodynamics gravity (GR-NLED), e.g. \cite{Arellano2009, Bronnikov2018,Bronnikov_Walia2021, Canate_Breton2018, Canate_Breton_Ortiz2020, Canate_Magos_Breton2020}. However, none of these solutions is support by a nonlinear electrodynamics model satisfying plausible conditions. In this work, we present the first traversable wormhole solution of Einstein-nonlinear electrodynamics gravity coupled to a self-interacting phantom scalar field (GR-NLED-SF) with a NLED model such that in the limit of weak field becomes the Maxwell electrodynamics, is presented. Furthermore, we show that this novel T-WH spacetime is also an exact solution of the Einstein-scalar-Gauss-Bonnet (EsGB) theory with a nonlinear electrodynamics source, but now with a real scalar field having a positive kinetic term.

gr-qc↗

arXiv2022

Non-local scattering control in coupled resonator networks

We demonstrate scattering control of Gaussian-like wave packets propagating with constant envelope velocity and invariant waist through coupled resonator optical waveguides (CROW) via an external resonator coupled to multiple sites of the CROW. We calculate the analytical reflectance and transmittance using standard scattering methods from waveguide quantum electrodynamics and show it is possible to approximate them for an external resonator detuned to the CROW. Our analytical and approximate results are in good agreement with numerical simulations. We engineer various configurations using an external resonator coupled to two sites of a CROW to show light trapping with effective exponential decay between the coupling sites, wave packet splitting into two pairs of identical Gaussian-like wave packets, and a non-local Mach-Zehnder interferometer.

physics.optics↗

arXiv2022

Optomechanical simulation of a parametric oscillator

We study an optomechhanical device supporting at least three optical modes in the infrared telecommunication band and three mechanical vibration modes. We model the coherent driving of each optical mode, independently of each other, to obtain an effective Hamiltonian showing the different types of parametric processes allowed in the device. We propose a bichromatic driving scheme, in the lossy optical cavity regime, under a mean field approximation, that provides the quantum simulation of a parametric oscillator with optical control of its parameters.

quant-ph↗

arXiv2020

Optical simulation of atomic decay enhancement and suppression

We discuss the decay of a two-level system into an engineered reservoir of coupled harmonic oscillators in the single-excitation manifold and propose its optical simulation with an homogeneous chain of coupled waveguides where individual elements couple to an external waveguide. We use two approaches to study the decay of the optical analogue for the probability amplitude of the two-level system being in the excited state. A Born approximation allows us to provide analytic closed-form amplitudes valid for small propagation distances. A Fourier-Laplace approach allows us to estimate an effective decay rate valid for long propagation distances. In general, our two analytic approximations match our numerical simulations using coupled mode theory and show non-Markovian decay into the engineered reservoir. In particular, we focus on two examples that provide enhancement or suppression of the decay decay rate using flat-top or Gaussian coupling distributions.

physics.optics↗

arXiv2020

Underlying SUSY in a generalized Jaynes-Cummings model

We propose a generalized Jaynes-Cummings model that includes but is not limited to an extensive collection of experimental and theoretical proposals from the literature. It covers nonlinear boson terms, nonlinear dispersive and multi-boson exchange interaction. Our model features an underlying Lie graded algebra symmetry reminiscent to supersymmetric quantum mechanics. This allows us to propose a diagonalization scheme and calculate its analytic time evolution. In consequence, we are able to construct closed forms for relevant observables and explore the dynamics of particular realizations of our model independent of their complexity. As an practical example, we show the evolution of the population inversion and the boson quadratures for an initial state consisting of the qubit in the ground state interacting with a coherent field for a selection of cases including the standard JC model with Stark shift, Kerr-like terms, intensity dependent coupling, multi-boson exchange and algebraic deformations.

quant-ph↗

arXiv2019

Spectral Collapse in the two-photon quantum Rabi model

Spectral collapse, the transition from discrete to continuous spectrum, is a characteristic in quantum Rabi models. We explore this phenomenon in the two-photon quantum Rabi model in optical phase space and find that, in the so-called degenerate qubit regime, the collapse is similar to that happening in the transition from a quantum harmonic to an inverted quadratic potential with the free-partical potential as transition point. In this regime, it is possible to construct Dirac-normalizable eigenfunctions for the model that show well defined parity. In the general model, we use parity to diagonalize the system in the qubit basis and numerically find that the qubit frequency does not change the critical point where spectral collapse occurs.

quant-ph↗

arXiv2019

Squeezed displaced entangled states in the quantum Rabi model

The quantum Rabi model accepts analytical solutions in the so-called degenerate qubit and relativistic regimes with discrete and continuous spectrum, in that order.We show that solutions in the laboratory frame are the superposition of even and odd displaced number states, in the former, and infinitely squeezed coherent states, in the latter, of the boson field correlated to the internal states of the qubit. We propose a single parameter model that interpolates between these discrete and continuous spectrum regimes to study the spectral statistics for first and second neighbor differences before the so-called spectral collapse. We find two central first neighbor differences that interweave and fluctuate keeping a constant second neighbor separation.

quant-ph↗

arXiv2014

Semitransparent One Dimensional Potential, A Green's Function Approach

We study the unstable harmonic oscillator and the unstable linear potential in the presence of the point potential, which is the superposition of the Dirac $δ(x)$ and the derivative $δ'(x)$. Using the \textit{physical} boundary conditions for the Green's function we derive for both systems the resonance poles and the resonance wave functions. The matching conditions for the resonance wave functions coincide with those obtained by the self-adjoint extensions of the point potentials and also by the modelling of the $δ'(x)$. We find that, with our definitions, the pure $bδ'(x)$ barrier is semi-transparent \textit{independent} of the value of $b$.

math-ph↗