arXiv subjects

Antonio S. M. de Castro

Publications and source records attributed to Antonio S. M. de Castro.

11 recordsLinked to original sources

arXiv2026

Optical perspective on the time-dependent Dirac oscillator

The Dirac oscillator is a relativistic quantum system, characterized by its linearity in both position and momentum. Moreover, considering $(1{+}1)$ and $(2{+}1)$ dimensions, the system can be mapped onto the Jaynes-Cummings and anti-Jaynes-Cummings models, as illustrated in an exact manner by Bermudez \textit{et al.} [\href{ https://doi.org/10.1103/PhysRevA.76.041801}{Phys. Rev. A 76, 041801(R) (2007)}]. Using the optical counterparts of the Dirac oscillator, we analyze an extension of the model that incorporates a time-dependent frequency. We focus on the consequences of these time modulations on the angular momentum observables and spin-orbit entanglement. Noticeable changes in the \emph{Zitterbewegung} are found. We show that a specific choice of time dependence yields aperiodic evolution of the observables, whereas an alternative choice allows analytical solutions.

quant-ph↗

arXiv2026

Continuous limit of the square well problem in quantum mechanics

The free-particle and square-well potentials are two of the most emblematic problems in quantum mechanics, illustrating essential concepts such as matter waves, energy quantization, and bound states. It is therefore natural to consider how the free-particle solutions emerge from the square well as the width approaches infinity. In this work, we present a systematic procedure to demonstrate this transition by applying a Fourier transform to the wave equation.

quant-ph↗

arXiv2026

Non-Markovian Light-Matter Dynamics in the Time Fractional Jaynes-Cummings Model with Modulated Coupling

We investigate the fractional time description of a generalized quantum light-matter system modeled by a time-dependent Jaynes-Cummings (JC) interaction, with different coupling types: constant, linear, exponential, and sinusoidal. Two formulations of the time fractional Schrödinger equation (TFSE) are examined, with a focus on their impact on population inversion and entanglement. Our findings highlight that the introduction of fractional order introduces memory effects, associated with damped oscillations and asymptotic decay. Furthermore, we find that the time-dependent couplings, combined with distinct fractional formulations, influence how these effects occur, ultimately resulting in high or low entanglement. A key finding of our work is that, under sinusoidal coupling, non-periodic dynamics is preserved for both formulations of the TFSE; however, within a certain range, the fractional order can act as a control mechanism for the non-periodic evolution.

physics.gen-ph↗

arXiv2026

Fractional-Time Jaynes-Cummings Model: Unitary Description of its Quantum Dynamics, Inverse Problem and Photon Statistics

We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schrödinger equation. We examine how the fractional derivative order $α$ influences non-classical features under different initial conditions. For an initial Fock state, fractional evolution introduces transient dynamics and heightened sensitivity to coupling strength. Through an inverse problem approach, we interpret these effects as arising from an effective time-dependent coupling with a strong initial pulse. For an initial coherent state, the fractional order tunes the system between dynamical regimes, with a transition at $α= 0.50 $ where standard collapse-and-revival is replaced by stable, periodic evolution. This regime enhances non-classical field properties, including stronger sub-Poissonian statistics, periodic quadrature squeezing, and the formation of Schrödinger cat states.

quant-ph↗

arXiv2026

Quantum Resonator as a Directional Quantum Emitter

Single-photon sources are essential for testing fundamental physics and for the development of quantum technologies. In this work a single-photon source is investigated, based on a two-photon Jaynes-Cummings system, where the resonator works as the quantum emitter rather than the two-level system. This role reversal provides certain advantages, such as robustness against losses from the two-level system (e.g., dephasing), as it remains in its ground state throughout the entire dynamics. This provides higher efficiency, purity, and indistinguishability compared to sources based on the usual Jaynes-Cummings model under the same parameter conditions in both models. Another advantage of this system is the possibility of direct conversion of a coherent excitation pulse with one photon on average to a single-photon pulse with efficiency, purity, and indistinguishability above $90\%$. Since the entire excitation pulse is consumed in the generation of a single photon, the system also minimizes energy waste. The potential for implementing the two-photon JC model across different platforms expands the possibilities for controlled single-photon generation in applications in quantum information processing and computation.

quant-ph↗

arXiv2026

Building Block For Universal Continuous Variables Computation In Superconducting Devices

Continuous variable (CV) quantum computation offers an alternative to qubit-based computing by exploiting the infinite-dimensional Hilbert space of bosonic modes. Despite recent progress, superconducting platforms have yet to demonstrate a scalable architecture capable of universal computation. Here, we design and numerically simulate a two-layer superconducting architecture that implements all five interactions of the universal CV gate set (rotation, displacement, squeezing, Kerr, and beam splitter) within experimentally accessible regimes. To this end, we employ a DC-SQUID as the bosonic mode, a fluxonium qubit to mediate nonlinear interactions, and two ancillary qubits that enable Gaussian and multi-mode operations. By tuning fluxes and frequencies, we achieve high fidelities ($\geq 98\%$) across all gates within state-of-the-art parameter ranges. The modular nature of the design allows straightforward scaling, establishing a feasible pathway toward high-fidelity, universal CV quantum computation based on superconducting circuits.

quant-ph↗

arXiv2026

The Dirac equation: historical context, comparisons with the Schrödinger and Klein-Gordon equations, and elementary consequences

This paper offers educational insight into the Dirac equation, examining its historical context and contrasting it with the earlier Schrödinger and Klein-Gordon (KG) equations. The comparison highlights their Lorentz transformation symmetry and potential probabilistic interpretations. We explicitly solve the free-particle dynamics in Dirac's model, revealing the emergence of negative-energy solutions. This discussion examines the Dirac Sea Hypothesis and explores the solutions' inherent helicity. Additionally, we demonstrate how the Dirac equation accounts for spin and derive the Pauli equation in the non-relativistic limit. The Foldy-Wouthuysen transformation reveals how the equation incorporates spin-orbit interaction and other relativistic effects, ultimately leading to the fine structure of hydrogen. A section on relativistic covariant notation is included to emphasize the invariance of the Dirac equation, along with more refined formulations of both the KG and Dirac equations. Designed for undergraduate students interested in the Dirac equation, this resource provides a historical perspective without being purely theoretical. Our approach underscores the significance of a pedagogical method that combines historical and comparative elements to profoundly understand the role of the Dirac equation in modern physics.

physics.gen-ph↗

arXiv2025

Revisiting the Jaynes-Cummings model with time-dependent coupling

The Jaynes-Cummings (JC) model stands as a fully quantized, fundamental framework for exploring light-matter interactions, a timely reflection on a century of quantum theory. The time-dependent Jaynes-Cummings (TDJC) model introduces temporal variations in certain parameters, which often require numerical methods. However, under the resonance condition, exact solutions can be obtained, offering insight into a variety of physical scenarios. In this work, we study the resonant TDJC model considering different modulations of the atom-field coupling. The model is presented and an analytical solution derived in a didactic way, allowing us to examine how time-dependent couplings affect atomic population inversion and atom-field entanglement. We also consider an atom traversing a partially cooled cavity, which induces periodicity and reveals the combined effects of atomic motion and thermal fluctuations. The Bloch vector is used to analyze the dynamics of the system, including the atomic state purity, and reveals phenomena such as atomic dipole alignment with the field due to the oscillating coupling, as well as atomic population trapping, which arises by increasing the initial mean thermal photon number.

quant-ph↗

arXiv2025

Reproducing the effects of quantum deformation in the undeformed Jaynes-Cummings model

In the Jaynes-Cummings (JC) model, the time dependence in the coupling parameter allows changes in the forms of the Rabi oscillations. In the inverse problem approach (IPA), the time-dependent coupling parameter is obtained from the resulting population inversion. In this work, we employ the IPA to obtain a time-dependent coupling that reproduces the effects of $κ$-deformation in the population inversion of an undeformed JC. This is relevant because it may pave the way for simulating quantum deformation in the JC model and possibly enable an experimental verification in a setting where the coupling can be precisely controlled.

quant-ph↗

arXiv2025

High Efficiency Storage of Quasi-Classical and Quantum States in Coupled Resonators

We propose an optical model in which both quantum and quasi-classical states can be ideally stored using coupled resonators. The protocol is based on a time-dependent coupling between two cavities, carefully modulated to allow the complete transfer of an external propagating field from one cavity to another. The system maintains high storage efficiency (above $99.99\%$) even when error sources are introduced (up to $5\%$) in the coupling, such as amplitude deviation or a time delay between field propagation and coupling control. Furthermore, this procedure can be extended to store entangled states by considering either a pair of systems or bimodal cavities. Due to its high efficiency, this model may find application in current quantum technologies, such as quantum memories and quantum batteries, which rely on efficient quantum state storage.

quant-ph↗

arXiv2022

Quantum phase transitions for an integrable quantum Rabi-like model with two interacting qubits

A two-interacting-qubit quantum Rabi-like model with vanishing transverse fields on the qubit-pair is studied. Independently of the coupling regime, this model can be exactly and unitarily reduced to two independent single-spin quantum Rabi models, where the spin-spin coupling plays the role of the transverse field. This transformation and the analytical treatment of the single-spin quantum Rabi model provide the key to prove the integrability of our model. The existence of different first-order quantum phase transitions, characterized by discontinuous two-spin magnetization, mean photon number and concurrence, is brought to light.

quant-ph↗