arXiv subjects

Thiago T. Tsutsui

Publications and source records attributed to Thiago T. Tsutsui.

8 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

Discrete-time quantum walks with energy-dependent coins

In this work, we extend the scattering quantum walk (SQW) framework to a lattice of energy-dependent point interactions. This yields, within the coined quantum walk (CQW) formalism, a coin operator that is directly related to the scattering matrix of zero-range potentials. The model thus provides a discrete-time quantum-walk (DTQW) analog of a periodic array of point interactions of the Kronig-Penney type, where the walker's wavenumber serves as a continuous, physically transparent control parameter for the coin operation. We analyze the spectra and the dynamics of position probability and entanglement, yielding distinct results for specific energies and point interactions. We relate the spectral structure to the spatial probability distribution and explicitly characterize the long-time entanglement behavior for each point interaction. The transmission modulus determines the quasienergy gap, bandwidth, and maximum group velocity, while also controlling the long-time coin-position entanglement for the initial state considered. The four families of one-dimensional point interactions ($δ$, $δ'$, crossed and asymmetric) realize qualitatively distinct transmission profiles and span the full range of behavior, including enhanced or strongly suppressed spreading and oscillatory entanglement.

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

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↗