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I. Ramos-Prieto

Publications and source records attributed to I. Ramos-Prieto.

At least 19 recordsLinked to original sources
arXiv2026

Lewis-Ermakov approach for the time-dependent two-level system

We construct an explicit Lewis-Ermakov-type dynamical invariant for time-dependent two-level systems by exploiting their algebraic correspondence with the time-dependent harmonic oscillator through the $su(2)$ and $su(1,1)$ algebras, which share the common complexification $sl(2,\mathbb{C})$. This invariant provides a closed-form evolution operator and an exact propagator for arbitrary time-dependent coupling $a(t)$ and detuning $b(t)$. We illustrate the method on representative scenarios, including Landau-Zener transitions, non-Hermitian dissipative processes, and adiabatic rapid passage, and we obtain inverse-engineered shortcuts to adiabaticity with fully explicit control fields when the auxiliary scaling function is taken to be real.

quant-ph↗
arXiv2026

From Rings to Top-Hat beams

We present the exact analytical paraxial propagation of structured light beams that transition from Ring annular profiles to top-hat intensity distributions. The initial field is defined as a superposition of a Gaussian-weighted power-law core and a singular inverse-quadratic modulation term, both carrying an azimuthal phase factor. By solving the Fresnel diffraction integral in cylindrical coordinates, we obtain exact closed-form expressions for the propagated field at arbitrary planes. The paraxial evolution is shown to be governed by a Cauchy-Riemann beam term and an infinite series of modified Bessel functions of the second kind weighted by an azimuthal phase factor. This analytical framework demonstrates how tuning the source parameters enables a continuous transition from ring-dominated annular profiles to uniform top-hat beams. For the fundamental mode ($l=0$), the singular component fills the central intensity null, producing a flat transverse plateau.

physics.optics↗
arXiv2026

The Dirac sea of phase: Unifying phase paradoxes and Talbot revivals in multimode waveguides

The quantum mechanical description of phase remains a fundamental challenge, with theoretical efforts tracing from the early works of London and Dirac to discrete formalisms. In this work, we extend the action-angle formalism to the Helmholtz-Schrödinger equation by introducing a phase-dependent wavefunction $ϕ(θ, t)$ residing in the Hardy space $H^2(\mathbb{D})$. This mathematical structure, defined by functions analytic on the unit disk with square-integrable boundary values, naturally ensures the positivity of the energy spectrum while providing a rigorous framework for wave dynamics in photonic systems. We demonstrate that establishing a self-adjoint phase operator requires extending the Hilbert space to $L^2$, a procedure that necessitates the admission of negative energy states. We interpret these states through an analogy with the Dirac sea, where the existence of antiphase or antiphoton modes provides a conceptual framework for understanding the fundamental limits of phase localization and quantum uncertainty. This formalism is applied to light propagation in multimode waveguides characterized by anharmonic refractive index profiles. By mapping modal dispersion to our phase representation, we show that the deviation of propagation constants from linear spacing governs the spatial evolution of the optical field. This approach offers a clear mechanism for the emergence of periodic self-imaging known as the Talbot effect, the generation of fractional revivals, and the formation of complex fractal interference patterns, providing a robust toolkit for the characterization and design of multimode interference devices.

quant-ph↗
arXiv2026

Paraxial beam propagation from Airy-type initial conditions via the Operator Method

We employ quantum mechanical operator techniques to solve the equations of $(1+1)D$ and $(2+1)D$ for paraxial waves with initial conditions defined by Airy-type functions. In the first part, we find the expressions of $(1+1)D$ optical beams, considering initial conditions such as Airy, Airy-truncated, and Airy-Gaussian functions. Subsequently, we extended the analysis to $(2+1)D$ optical beams with initial conditions generated by the product of two Airy, two Airy-truncated and two Airy-Gaussian functions, providing a comprehensive study of multidimensional Airy beam propagation. To validate our theoretical derivations, we present both theoretical and experimental intensity profiles, showing excellent agreement between the two, illustrating the physical characteristics of these beams. Although these solutions have previously been obtained via the diffraction integral and thoroughly studied, the primary goal here is to demonstrate that the optical fields can be derived using quantum mechanical operator methods. Finally, we remark that this alternative approach offers an elegant and powerful framework for analyzing paraxial wave propagation.

physics.optics↗
arXiv2025

Unitary transformation approach to the paraxial wave equation

We present a framework for the paraxial wave equation based on propagation-dependent unitary transformations closely related to the Lewis-Ermakov invariant. This approach establishes a formal equivalence between free-space propagation and the dynamics in a quadratic gradient index (GRIN) medium. In this context, the dynamical invariant and the free-space Hamiltonian do not commute at the initial propagation stage due to Gaussian modulation, which imposes an effective quadratic confinement. Exact commutativity would only be possible for an infinitely wide, nonsquare-integrable optical field; therefore, any finite-energy beam propagates as if it were subject to a quadratic GRIN-like potential. The unitary transformation approach reveals how the Gaussian envelope of physical beams leads to effective harmonic confinement and connects the propagation dynamics to oscillator-like invariants. This method enables the derivation of stationary solutions in different coordinate systems by mapping to an effective quadratic-like medium and establishes a direct link to the zero-frequency Ermakov equation and the Lewis-Ermakov invariants.

physics.optics↗
arXiv2025

An operator approach to the Madelung-Bohm continuity equation

We solve the probability continuity equation within the Madelung-Bohm framework, assuming a separable phase expressed as $S(x,t) = Q(x)\dotν(t) + μ(t)$. Using operator methods, we reformulate the wave function's amplitude into a form that is more practical for application to any given initial condition. This results in the function $F(x,t)$, which characterizes the wavefunction's amplitude, with $F$ being the transformation of the position operator via a squeeze-like operator. To demonstrate how this result can be applied, we examine two scenarios: one where the external potential is zero, causing the dynamics to originate only from the Bohm potential, and another where the form of $F$ mirrors the characteristics of wave propagation within optical waveguide arrays. In the second scenario, it is notable that the amplitude, phase, and potentials might become complex yet still comply with the Schrödinger equation.

quant-ph↗
arXiv2025

Waveguide arrays interaction to second neighbors: Exact solution

We provide an analytical framework for describing the propagation of light in waveguide arrays, considering both infinite and semi-infinite cases. The interaction up to second neighbors is taken into account, which makes for a more realistic setup. We show that these solutions follow a distinctive structural pattern. This pattern reflects a transition from conventional Bessel functions to the lesser-known one-parameter generalized Bessel functions, offering new insights into the propagation dynamics in these systems.

quant-ph↗
arXiv2024

Complete Rabi oscillations in the ion-laser interaction

We present the dynamics of a single harmonically trapped ion interacting with a laser, considering a linear combination of two eigenstates of the system as the initial state. The conditions on the physical parameters that allow for the evolution of the system are discussed. We are able to obtain analytical results even though no approximations are realized and are able to show Rabi oscillations for such initial states.

quant-ph↗
arXiv2024

Exact solution of the master equation for interacting quantized fields at finite temperature decay

We analyze the Markovian dynamics of a quantum system involving the interaction of two quantized fields at finite temperature decay. Utilizing superoperator techniques and applying two non-unitary transformations, we reformulate the Lindblad master equation into a von Neumann-like equation with an effective non-Hermitian Hamiltonian. Furthermore, an additional non-unitary transformation is employed to diagonalize this Hamiltonian, enabling us to derive an exact solution to the Lindblad master equation. This method provides a framework to calculate the evolution of any initial state in a fully quantum regime. As a specific example, we present the photon coincidence rates for two indistinguishable photons initially interacting within a cavity.

quant-ph↗
arXiv2024

Asymmetric Cauchy-Riemann Beams

We investigate, theoretically and experimentally, the evolution of a paraxial beam propagating in free space when its initial transverse structure is characterized by an asymmetric Gaussian modulation combined with an entire function. Utilizing a quantum optics operator approach, our study specifically examines the effects of parameter variations within the Gaussian modulation on two entire functions: the Bessel function and the Airy function. Through this investigation, we aim to elucidate how these parameter variations influence the beam's propagation dynamics and the role played by the asymmetry of the Gaussian modulation in the propagation of such paraxial beams. Additionally, we provide a comprehensive method for computing the propagated field under these conditions.

physics.optics↗
arXiv2024

Paraxial wave propagation: Operator techniques

The similarity between the Schrödinger equation and the paraxial wave equation permits numerous analogies linking these fields, which is pivotal in advancing both quantum mechanics and wave optics. In this study, we demonstrate the application of operator techniques to an electromagnetic field characterized by the function $f(x + ay)$, leveraging the structural analogies between these equations. Specifically, we employ initial conditions defined by Airy and Bessel functions to illustrate the practical implementation of these techniques.

physics.optics↗
arXiv2024

Some non-algebraic forms of $\exp(A+B)$

We present examples where expressions for $\exp(\hat{A}+\hat{B})$ can be derived even though the operators (or superoperators) $\hat{A}$ and $\hat{B}$ do not commute in a manner that leads to known factorizations. We apply our factorization to the case of a Lindblad operator modeling single photon decay and to a binary Glauber-Fock photonic lattice.

quant-ph↗
arXiv2024

Effects of classical drivings on the power broadening of atomic lineshapes

In the framework of the Jaynes-Cummings model, we investigate how atomic lineshapes are affected by coherently driving the atom-field interaction. We pay particular attention to the two-level atom interaction with a thermal cavity field, when both are influenced by external classical fields. Adopting a density matrix formalism, we calculate the average atomic inversion and demonstrate how the corresponding lineshapes vary as a function of the average number of thermal photons, and the atom-field classical coupling. Furthermore, we compare these results with those obtained from the standard Jaynes-Cummings model and validate our findings through numerical calculations.

quant-ph↗
arXiv2023

Temporal evolution of a driven optomechanical system in the strong coupling regime

We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, $G/ω_m$, is not negligible compared to one. Due to the forcing term, the interaction picture Hamiltonian contains the number operator in the exponents, and in order to deal with it, we approximate these exponentials by their average values taken between initial coherent states. Our approximation is justified when we compare our results with the numerical solution of the number of photons, phonons, Mandel parameter, and the Wigner function, showing an excellent agreement.

quant-ph↗
arXiv2023

Cauchy-Riemann beams in GRIN media

We investigate the propagation characteristics of Cauchy-Riemann beams in gradient-index media. Our study reveals two key findings: a) the preservation of their form during propagation, and b) surprisingly, the feasibility of obtaining the fractional Fourier transform for any arbitrary entire function. We provide an explicit and straightforward expression for this transform. Additionally, our results contribute to a deeper understanding of the behavior of Cauchy-Riemann beams in complex media, offering insights that may have implications for various applications in optics and wave propagation.

physics.optics↗
arXiv2023

Cauchy-Riemann beams

By using operator techniques, we solve the paraxial wave equation for a field given by the multiplication of a Gaussian function and an entire function. The latter possesses a unique property, being an eigenfunction of the {\it perpendicular} Laplacian with a zero eigenvalue, a consequence of the Cauchy-Riemann equations. We demonstrate, both theoretically and experimentally, the inherent rotation of this field during its propagation. The explanation for these rotations lies in the utilization of the quantum (Bohm) potential. The simplicity of this outcome reveals promising prospects: it enables the analytical deduction of the Fraunhofer or Fresnel diffraction pattern. In essence, this means that obtaining the Fresnel or Fourier transform of a function satisfying the Cauchy-Riemann equations becomes a straightforward task.

physics.optics↗
arXiv2023

Invariant approach to the Driven Jaynes-Cummings model

We investigate the dynamics of the driven Jaynes-Cummings model, where a two-level atom interacts with a quantized field and both, atom and field, are driven by an external classical field. Via an invariant approach, we are able to transform the corresponding Hamiltonian into the one of the standard Jaynes-Cummings model. Subsequently, the exact analytical solution of the Schrödinger equation for the driven system is obtained and employed to analyze some of its dynamical variables.

quant-ph↗