arXiv subjects

B. M. Rodríguez-Lara

Publications and source records attributed to B. M. Rodríguez-Lara.

At least 19 recordsLinked to original sources

arXiv2026

Conditional Gaussian filtering by Arthurs--Kelly readout in a three-mode cluster wire

Measurement readout programs the Gaussian operation implemented by a continuous-variable cluster wire. For the standard three-node wire, momentum homodyne readout gives an additive parity channel with finite-squeezing noise. We classify the pattern-resolved input--output covariance transformations generated by calibrated uncorrelated Arthurs--Kelly readout on one or both consumed nodes. Any finite Arthurs--Kelly position record produces a conditional Gaussian filter whose gain and residual covariance depend on the input covariance entries, rather than an input-independent additive Gaussian channel. Writing $\mathrm{A}$ for Arthurs--Kelly readout and $\mathrm{H}$ for homodyne readout, the readout pattern selects the filtered sector, with $\mathrm{AH}$ selecting position, $\mathrm{HA}$ selecting momentum, and $\mathrm{AA}$ retaining both. The hierarchy $0 < τ_{\mathrm{AA}} < \min \left\{ τ_{\mathrm{AH}}, τ_{\mathrm{HA}} \right\} < 1 = τ_{\mathrm{HH}}$ shows that finite Arthurs--Kelly position records contract the gain-transferred covariance area. Our results identify calibrated uncorrelated Arthurs--Kelly readout as a measurement-level method for covariance-sensitive Gaussian filtering inside a fixed cluster graph.

quant-ph↗

arXiv2026

Products of displaced Laguerre-Gaussian beams

We study the free-space propagation of products of displaced Laguerre--Gaussian beams. Each displaced factor admits an exact representation as a superposition of standard Laguerre--Gaussian beam modes through the optical analog of displaced number states. We reduce the resulting product to a single modal expansion with closed-form weight coefficients and explicit azimuthal selection rules. Working in the reference frame defined by the centroid of the transverse displacements, we evaluate the net orbital angular momentum directly from the modal weights, which provides a criterion to predict transverse rotation. We identify three propagation regimes: no transverse rotation for zero net orbital angular momentum, rigid rotation for products of identical factors with zero radial index, and nonrigid rotation with intensity redistribution otherwise. Our framework enables engineering structured light beams whose transverse rotation encodes propagation information, relevant to depth-sensitive optical microscopy, imaging, and tracking.

physics.optics↗

arXiv2025

Mapping continuous-variable quantum states onto optical scalar beams

Optical fields provide an accessible platform to explore connections between classical and quantum mechanics. We introduce a group-theoretic framework based on the $\mathrm{su}(1,1)$ Lie algebra to construct classical analogs of continuous-variable quantum states using the spatial degree of freedom of paraxial scalar beams. Our framework maps squeezed number states onto scalar beams expanded in orthonormal Gaussian modal bases, encompassing both Gaussian and non-Gaussian classical analogs, including one- and two-mode squeezed beams. To characterize the structural changes induced by squeezing, we examine phase-space redistribution through Fourier analysis and optical Wigner distribution functions. We derive analytical expressions for the waist, curvature, and Gouy phase of two-mode squeezed Laguerre-Gaussian beams, and establish a relation between the number of accessible modes and the achievable squeezing under finite numerical aperture. While squeezing introduces spatial and spectral correlations that reshape the beam structure, these beams remain constrained by the diffraction limit, as confirmed by the numerical propagation of apodized beams. These correlations give rise to classical entanglement. We establish a classical analog of the Duan--Simon inseparability criterion for continuous-variable two-mode Gaussian states. For non-Gaussian squeezed states, we analyze the marginal optical Wigner distribution functions and identify phase-space features, such as negativity, that act as witnesses of classical continuous-variable entanglement. Our framework unifies classical analogs of continuous-variable quantum states through beam engineering, enabling quantum-inspired applications in optical imaging, metrology, and communication.

physics.optics↗

arXiv2025

Noisy Cyclic Quantum Random Walk

We explore static noise in a discrete quantum random walk over a homogeneous cyclic graph, focusing on spectral and dynamical properties. Using a three-parameter unitary coin, we control the spectral structure of the noiseless step operator on the unit circle. One parameter induces two spectral bands separated by a gap proportional to its value, while the half-sum of the two phase parameters rotates the spectrum and enables twofold degeneracy under specific conditions. Degenerate spectra yield sinusoidal probability distributions; non-degenerate ones produce flat profiles. We introduce static phase noise on the sites and analyze its effects in two propagation regimes. In the walk-on-the-line regime, preceding a full graph traversal, we extract the spreading exponent $β$ from the step-resolved mean squared displacement. Low participation ratios correlate with sub-diffusive spread; high ratios indicate ballistic or super-diffusive evolution. Once the walker completes a cycle, finite-size effects dominate. In this walk-on-the-cycle regime, $β$ no longer characterizes the dynamics. Instead, we quantify localization using the coefficient of variation of the mean squared displacement. In both regimes, we observe a sharp crossover near static site noise $ϕ_s = π/3$, marked by a drop in participation ratio, a transition from diffusive to sub-diffusive spread in the walk-on-the-line regime, and a reduced saturation level in the walk-on-the-cycle regime. Our results show that the eigenstate participation ratio is an efficient spectral diagnostic that anticipates localization across both regimes, offering an alternative to full dynamical simulations.

quant-ph↗

arXiv2024

Majorana constellations for optical scalar beams and vector fields

We explore Majorana stellar representation on the Riemann sphere for optical scalar beams and vector fields, leveraging the spin and orbital angular momentum of light. For scalar beams, the star constellations for the Laguerre-Gaussian beam basis reside at the poles of the sphere. For vector fields, these constellations represent well-defined circular polarization. The underlying $su(2)$ symmetry of angular momenta enables populating the sphere through generalized unitary rotations of the basis elements, resulting in optical analogues of Bloch and generalized $su(2)$ coherent states for both scalar beams and vector fields. Constellations for scalar Hermite-Gaussian beams and vector Hermite-Gaussian partial Poincaré fields, restricted to linear polarization, occupy the equator of the sphere as a result of these rotations. Additionally, we investigate scalar and vector analogues of cat codes and kings of quantumness, providing insights into the visualization and characterization of complex optical beams and fields with potential applications in optical communications.

physics.optics↗

arXiv2024

Decoding physics identity: A Spanish-language adaptation on an instrument and its correlation with STEM achievement

The representation of Spanish-speaking students in STEM identity literature, particularly in physics identity, is conspicuously minimal. This study addresses this gap with a two-pronged approach. First, a physics identity instrument was adapted for Spanish-speaking STEM students to promote inclusivity in educational research. Data from 334 Mexican STEM students was collected and analysed for validation through factor analyses and Cronbach's alpha, confirming the structural integrity and reliability of the adapted instrument. Second, the instrument was employed to examine the correlation between physics identity and academic performance in a separate dataset from 200 engineering students, using multivariate linear and logistic regressions. The findings underscore gender's impact on physics course grades. Notably, variations in physics identity among engineering students indicated a potential link with their chosen field. Despite the importance of physics in engineering, physics identity was lower than expected, and performance in physics courses did not consistently correlate with a strong physics identity. However, the `interest in physics topics` subconstruct did correlate with physics course grades. This research fills a critical void by providing an adapted instrument for assessing physics identity in Spanish-speaking students and underscores the need for pedagogical shifts to enhance physics identity and STEM outcomes for Latino students.

physics.ed-ph↗

arXiv2024

Orbital Angular Momentum Coherent State Beams

We explore a family of paraxial beams constructed by the linear superposition of Laguerre-Gaussian beams, representing an optical analogue to generalized $SU(2)$ Lie group coherent states. A single complex parameter controls a smooth transition between Laguerre-Gaussian and Hermite-Gaussian beams, with intermediate beams that merge characteristics of both families. Our beams exhibit propagation-invariant properties, up to a scaling factor, a highly desirable feature for optical applications, validated via holographic experimental results.

physics.optics↗

arXiv2024

Spatial light mode analogues of generalized quantum coherent states

We use the spatial degree of freedom of light modes to construct optical analogues of generalized quantum coherent states for Hermite- and Laguerre-Gauss modes. Our optical analogues preserve the statistical properties of their quantum counterparts, encoded in their amplitude and phase distributions. We explore three basic symmetries that provide generalized displaced, rotated, and squeezed coherent states. Given the substantial interest in squeezed states for probing matter, we believe that the optical analogues introduced here have significant implications for optical sensing. Specifically, the single-particle nature of our spatial modes makes them robust candidates for sensing photosensitive materials. Overall, our approach opens the door to optical metrology and sensing protocols that mimic those already existing in the quantum realm, and facilitates further exploration of the quantum state zoo through classical optical analogues.

physics.optics↗

arXiv2024

Coherent states of the Laguerre-Gauss modes

Large quantum photonic systems hold promise for surpassing classical computational limits, yet their state preparation remains a challenge. We propose an alternative approach to study multiparticle dynamics by mapping the excitation mode of these systems to physical properties of the Laguerre-Gauss modes. We construct coherent states establishing a direct link between excitation number dynamics and the evolution of the Laguerre-Gauss mode. This highlights the photon transverse spatial degree of freedom as a versatile platform for testing fundamental aspects of quantum multiparticle systems.

quant-ph↗

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

Harmonic motion modes in parabolic GRIN fibers

We report electromagnetic field modes solving the inhomogeneous Maxwell equations for parabolic gradient index fibers in the low refractive index contrast approximation. The first family comprises accelerating fields characterized by an intensity distribution center tracing a circular trajectory transverse to the fiber optical axis. These fields maintain an invariant shape for both their intensity and phase distributions while rotating around their center. The second family comprises breathing fields characterized by an intensity distribution center aligned with the fiber optical axis. These fields exhibit intensity distribution scaling along propagation, while their phase swirls and rotates around the optical axis without changing their intensity distribution shape and topological charge.

physics.optics↗

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↗

arXiv2023

Quadratic Time-dependent Quantum Harmonic Oscillator

We present a Lie algebraic approach to a Hamiltonian class covering driven, parametric quantum harmonic oscillators where the parameter set -- mass, frequency, driving strength, and parametric pumping -- is time-dependent. Our unitary-transformation-based approach provides a solution to our general quadratic time-dependent quantum harmonic model. As an example, we show an analytic solution to the periodically driven quantum harmonic oscillator without the rotating wave approximation; it works for any given detuning and coupling strength regime. For the sake of validation, we provide an analytic solution to the historical Caldirola--Kanai quantum harmonic oscillator and show that there exists a unitary transformation within our framework that takes a generalized version of it onto the Paul trap Hamiltonian. In addition, we show how our approach provides the dynamics of generalized models whose Schrödinger equation becomes numerically unstable in the laboratory frame.

quant-ph↗

arXiv2023

Continuous-time quantum harmonic oscillator state engineering

The center of mass motion of trapped ions and neutral atoms is suitable for approximation by a time-dependent driven quantum harmonic oscillator whose frequency and driving strength may be controlled with high precision. We show the time evolution for these systems with continuous differentiable time-dependent parameters in terms of the three basic operations provided by its underlying symmetry, rotation, displacement, and squeezing, using a Lie algebraic approach. Our factorization of the dynamics allows for the intuitive construction of protocols for state engineering, for example, creating and removing displacement and squeezing, as well as their combinations, optimizing squeezing, or more complex protocols that work for slow and fast rates of change in the oscillator parameters.

quant-ph↗

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

Para-particle oscillator simulations on a trapped ion quantum computer

Deformed oscillators allow for a generalization of the standard fermions and bosons, namely, for the description of para-particles. Such particles, while indiscernible in nature, can represent good candidates for descriptions of physical phenomena like topological phases of matter. Here, we report the digital quantum simulation of para-particle oscillators by mapping para-particle states to the state of a qubit register, which allow us to identify the para-particle oscillator Hamiltonian as an $XY$ model, and further digitize the system onto a universal set of gates. In both instances, the gate depth grows polynomially with the number of qubits used. To establish the validity of our results, we experimentally simulate the dynamics of para-fermions and para-bosons, demonstrating full control of para-particle oscillators on a quantum computer. Furthermore, we compare the overall performance of the digital simulation of dynamics of the driven para-Fermi oscillator to a recent analog quantum simulation result.

quant-ph↗

arXiv2022

Routes to chaos in a class-B laser coupled to a neutral resonator

We study the dynamics of a class-B semiconductor microring laser coupled to a neutral microring resonator for common fabrication parameters. For zero detuning between the resonators, we identify five dynamical regions controlled by the normalized pump rate of the laser and coupling strength between the resonators. These regions show stable lasing with phase locking for either sufficiently small or large coupling strength parameter values. Multistability and chaos arise in between these stable regions where at least one fixed point is attractive. The transition from stable to unstable lasing regions in the parameter space phase diagram is a crossover.

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↗