arXiv subjects

A. Kunold

Publications and source records attributed to A. Kunold.

At least 19 recordsLinked to original sources

arXiv2026

Polarization-controlled effective Rabi dynamics in driven Graphene: A Floquet-Magnus approach

Polarization ellipticity $\beta$ and the relative angle $\Delta$ between electron momentum and driving field act as independent control parameters for coherent dynamics in periodically driven Dirac systems. In this work, we analyze the dynamics of resonantly driven Dirac electrons in graphene under elliptically polarized electromagnetic radiation using the Floquet-Magnus expansion. Working in the interaction picture and applying a rotating-wave-type transformation, we derive an effective two-level Hamiltonian that governs the macromotion at resonance ($\omega = \Omega/2$). The resulting quasienergy splitting depends nontrivially on $\beta$ and $\Delta$ through interference between the Bessel harmonics $J_0(\zeta)$ and $J_2(\zeta)$. Circular polarization ($\beta = \pm 1$) restores rotational symmetry and yields a $\Delta$-independent effective Rabi frequency, whereas elliptical and linear polarizations produce anisotropic responses with a $\pi$-periodic angular modulation. Beyond spectral properties, we identify a polarization-induced phase that acts as an effective initial Floquet kick, shifting the effective initial conditions and producing measurable shifts in the timing of occupation oscillations, whose sign depends on both helicity and relative orientation. Through an explicit Fourier decomposition of the time-evolution operator, we separate macromotion from micromotion contributions and validate the zeroth-order Magnus approximation via numerical simulations, achieving root-mean-square errors of $\sim 1\%$ over 100 driving periods in the weak-field regime. These results establish polarization ellipticity and relative orientation as tunable and experimentally accessible knobs for quantum control in two-dimensional Dirac materials, with direct implications for time-resolved spectroscopy.

cond-mat.mes-hall↗

arXiv2026

The thermodynamics of liquid-vapor coexistence for a van der Waals fluid. Analytical solution of the Clausius-Clapeyron equation

This work presents a pedagogical derivation of the thermodynamics of a van der Waals fluid by explicitly incorporating pairwise molecular interactions and the finite size of particles into the statistical-mechanical description. Starting from the Lennard-Jones potential, we evaluate the second virial coefficient to infer the virial expansion of the equation of state and recover the van der Waals equation using only its leading correction. The corresponding partition function allows us to obtain all thermodynamic potentials for both monoatomic and diatomic fluids in a transparent and instructive manner. Building on this framework, we formulate and solve analytically the Clausius-Clapeyron equation in the vicinity of the critical point, obtaining the liquid-vapor coexistence curve in closed form. This approach not only clarifies the microscopic origin of van der Waals thermodynamics but also complements-and in several aspects improves upon-traditional treatments that rely heavily on numerical methods or heuristic arguments. In addition, because the van der Waals equation naturally predicts the liquid-vapor equilibrium, the existence of critical points, and the functional form of the saturation curve of the pressure as a function of temperature, it provides an analytically tractable framework for studying a 150-year-old problem that has historically been addressed using graphical constructions or numerical solutions. As such, the formulation developed here offers a coherent, accessible, and conceptually unified route for students and instructors to understand phase coexistence in simple fluids from first principles.

cond-mat.stat-mech↗

arXiv2024

Collective coupling of driven multilevel atoms and its effect on four-wave mixing

Microscopic models based on multilevel atoms are central to optimizing non-linear optical responses and the coherent control of light. These models are traditionally based on single-atom effects that are parametrically extrapolated to include collective effects, such as an enhanced response or propagation within atomic media. In this work we present a systematic analysis of the cooperative effects arising in driven systems composed of multilevel atoms coupled via a common electromagnetic environment. The analysis is based on an interplay between dressed states induced by the driving field and photon exchanges, and collective decay channels. This theory is applied to the case of four-wave mixing induced by a pair of lasers acting on an atomic pair with internal levels in the diamond configuration. The effect of inter-atomic correlations and collective decay over the photons created in this nonlinear process is then explored. The dependence of single and two-photon correlations are studied in detail for each region by varying atomic orientations and laser parameters { consistent with current experiments involving atomic gases.}Photonic correlation functions are shown to exhibit a transition from a Lorentz-like dependence on the two-photon detuning -- with general features that can be obtained in an isolated atom scheme -- to a two-peaked distribution when the dipole-dipole interactions become relevant. For weak Rabi frequencies whose value is smaller than the highest collective decay rate, the atoms are trapped inside their ground state as they approach each other. It is found that the anisotropy of the dipole-dipole interaction and its wave nature are essential to understand the behavior of the photons correlations. Signatures of these processes are identified for existing experimental realizations.

quant-ph↗

arXiv2021

Dirac materials under linear polarized light: quantum wave function evolution and topological Berry phases as classical charged particles trajectories under electromagnetic fields

The response of electrons under linearly polarized light in Dirac materials as borophene or graphene is analyzed in a continuous wave regime for an arbitrary intense field. Using a rotation and a time-dependent phase transformation, the wave function evolution is shown to be governed by a spinor-component decoupled Whittaker-Hill equation. The numerical solution of these equations enables to find the quasienergy spectrum. For borophene it reveals a strong anisotropic response. By applying an extra unitary transformation, the wave functions are proven to follow an Ince equation. The evolution of the real and imaginary parts of the wave function is interpreted as the trajectory of a classical charged particle under oscillating electric and magnetic field. The topological properties of this forced quantum system are studied using this analogy. In particular, in the adiabatic driving regime, the system is described with an effective Matthieu equation while in the non-adiabatic regime the full Whittaker-Hill equation is needed. From there, it is possible to separate the dynamical and Berry phase contributions to obtain the topological phase diagram due to the driving. Therefore, a different path to perturbation theory is developed to obtain time-driven topological phases.

cond-mat.mes-hall↗

arXiv2021

Machine learning assisted GaAsN circular polarimeter

We demonstrate the application of a two stage machine learning algorithm that enables to correlate the electrical signals from a GaAs$_x$N$_{1-x}$ circular polarimeter with the intensity, degree of circular polarization and handedness of an incident light beam. Specifically, we employ a multimodal logistic regression to discriminate the handedness of light and a 6-layer neural network to establish the relationship between the input voltages, the intensity and degree of circular polarization. We have developed a particular neural network training strategy that substantially improves the accuracy of the device. The algorithm was trained and tested on theoretically generated photoconductivity and on photoluminescence experimental results. Even for a small training experimental dataset (70 instances), it is shown that the proposed algorithm correctly predicts linear, right and left circularly polarized light misclassifying less than $1.5\%$ of the cases and attains an accuracy larger than $97\%$ in the vast majority of the predictions ($92\%$) for intensity and degree of circular polarization. These numbers are significantly improved for the larger theoretically generated datasets (4851 instances). The algorithm is versatile enough that it can be easily adjusted to other device configurations where a map needs to be established between the input parameters and the device response. Training and testing data files as well as the algorithm are provided as supplementary material.

cond-mat.other↗

arXiv2021

Chiral photodetector based on GaAsN

The detection of light helicity is key to several research and industrial applications from drugs production to optical communications. However, the direct measurement of the light helicity is inherently impossible with conventional photodetectors based on III-V or IV-VI semiconductors, being naturally non-chiral. The prior polarization analysis of the light by a series of often moving optical elements is necessary before light is sent to the detector. A method is here presented to effectively give to the conventional dilute nitride GaAs-based semiconductor epilayer a chiral photoconductivity in paramagnetic-defect-engineered samples. The detection scheme relies on the giant spin-dependent recombination of conduction electrons and the accompanying spin polarization of the engineered defects to control the conduction band population via the electrons' spin polarization. As the conduction electron spin polarization is, in turn, intimately linked to the excitation light polarization, the light polarization state can be determined by a simple conductivity measurement. This effectively gives the GaAsN epilayer a chiral photoconductivity capable of discriminating the handedness of an incident excitation light in addition to its intensity. This approach, removing the need of any optical elements in front of a non-chiral detector, could offer easier integration and miniaturisation. This new chiral photodetector could potentially operate in a spectral range from the visible to the infra-red using (In)(Al)GaAsN alloys or ion-implanted nitrogen-free III-V compounds.

physics.app-ph↗

arXiv2021

Polarization sensitive photodectector based on GaAsN

We propose and numerically simulate an optoelectronic compact circular polarimeter. It allows to electrically measure the degree of circular polarization and light intensity at room temperature for a wide range of incidence angles in a single shot. The device, being based on GaAsN, is easy to integrate into standard electronics and does not require bulky movable parts nor extra detectors. Its operation hinges mainly on two phenomena: the spin dependent capture of electrons and the hyperfine interaction between bound electrons and nuclei on Ga$^{2+}$ paramagnetic centers in GaAsN. The first phenomenon confers the device with sensitivity to the degree of circular polarization and the latter allows to discriminate the handedness of the incident light.

cond-mat.mes-hall↗

arXiv2020

Floquet spectrum and electronic transitions of tilted anisotropic Dirac materials under electromagnetic radiation: monodromy matrix approach

We analyze the quasienergy-spectrum and the valence to conduction-band transition probabilities of a tilted anisotropic Dirac material subject to linearly and circularly polarized electromagnetic fields. The quasienergy-spectrum is numerically calculated from the monodromy matrix of the Schrödinger equation via the Floquet theorem for arbitrarily intense electromagnetic fields. To asses the valence to conduction-band transition times we deduced a Rabi-like formula in the rotating wave approximation. In the strong-field regime the spectrum as a function of the momentum components divides into two very distinctive regions. In the first, located around the Dirac point, the quasi-spectrum is significantly distorted by the field as the electronic parameters are renormalized by electronic-dressing. In the second, all the characteristics of the free carrier spectrum are retained. Linearly polarized light anisotropically deforms the spectrum according to the field polarization direction. Dirac-like points form around the original Dirac point. The quasi spectrum of circularly polarized light, instead, exhibits a gap formation in the Dirac point and has elliptical symmetry. We show that, in contrast to the single-photon resonant transitions that characterize the weak-field regime, the strong-field regime is dominated by multiphoton resonances.

cond-mat.mes-hall↗

arXiv2020

Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities

The Floquet spectrum in an anisotropic tilted Dirac semimetal modulated by linearly polarized light is addressed through the solution of the time-dependent Schrödinger equation for the two-dimensional Dirac Hamiltonian via the Floquet theorem. The time-dependent wave functions and the quasienergy spectrum of the two-dimensional Dirac Hamiltonian under the normal incidence of linearly polarized waves are obtained for an arbitrarily intense electromagnetic radiation. We applied a set of unitary transformations to reduce the Schrödinger equation to an ordinary second-order differential Hill equation with complex coefficients. Through the stability analysis of this differential equation, the weak and strong field regimes are clearly distinguished in the quasi-spectrum. In the weak electric field regime, above a certain threshold given by the field parameters, the spectrum mostly resembles that of free electrons in graphene. Below this threshold, in the strong electric field regime, the spectrum abruptly becomes highly anisotropic and a gap opens up. As an example, we apply the results to the particular case of borophene.

cond-mat.mes-hall↗

arXiv2019

Electron-nucleus spin correlation conservation of the spin dependent recombination in Ga$^{2+}$ centers

Spin dependent recombination in GaAsN offers many interesting possibilities in the design of spintronic devices mostly due to its astounding capability to reach conduction band electron spin polarizations close to 100% at room temperature. The mechanism behind the spin selective capture of electrons in Ga$^{2+}$ paramagnetic centers is revisited in this paper to address inconsistencies common to most previously presented models. Primarily, these errors manifest themselves as major disagreements with the experimental observations of two key characteristics of this phenomenon: the effective Overhauser-like magnetic field and the width of the photoluminescence Lorentzian-like curves as a function of the illumination power. These features are not only essential to understand the spin dependent recombination in GaAsN, but are also key to the design of novel spintronic devices. Here we demonstrate that the particular structure of the electron capture expressions introduces spurious electron-nucleus correlations that artificially alter the balance between the hyperfine and the Zeeman contributions. This imbalance strongly distorts the effective magnetic field and width characteristics. In this work we propose an alternative recombination mechanism that preserves the electron-nucleus correlations and, at the same time, keeps the essential properties of the spin selective capture of electrons. This mechanism yields a significant improvement to the agreement between experimental and theoretical results. In particular, our model gives results in very good accord with the experimental effective Overhauser-like magnetic field and width data, and with the degree of circular polarization under oblique magnetic fields.

cond-mat.mes-hall↗

arXiv2019

Dynamical band gap tuning in Weyl semi-metals by intense elliptically polarized normal illumination and its application to $8-Pmmn$ borophene

The Dynamical-gap formation in Weyl semimetals modulated by intense elliptically polarized light is addressed through the solution of the time-dependent Schrödinger equation for the Weyl Hamiltonian via the Floquet theorem. The time-dependent wave functions and the quasi-energy spectrum of the two-dimensional Weyl Hamiltonian under normal incidence of elliptically polarized electromagnetic waves are obtained using a non-perturbative approach. In it, the Weyl equation is reduced to an ordinary second-order differential Mathieu equation. It is shown that the stability conditions of the Mathieu functions are directly inherited by the wave function resulting in a quasiparticle spectrum consisting of bands and gaps determined by dynamical diffraction and resonance conditions between the electron and the electromagnetic wave. Estimations of the electromagnetic field intensity and frequency, as well as the magnitude of the generated gap are obtained for the $8-Pmmn$ phase of borophene. We provide with a simple method that enables to predict the formation of dynamical-gaps of unstable wave functions and their magnitudes. This method can readily be adapted to other Weyl semimetals.

cond-mat.mes-hall↗

arXiv2018

Method for finding the exact effective Hamiltonian of time driven quantum systems

Time-driven quantum systems are important in many different fields of physics like cold atoms, solid state, optics, etc. Many of their properties are encoded in the time evolution operator which is calculated by using a time-ordered product of actions. The solution to this problem is equivalent to find an effective Hamiltonian. This task is usually very complex and either requires approximations, or in very particular and rare cases, a system-dependent method can be found. Here we provide a general scheme that allows to find such effective Hamiltonian. The method is based in using the structure of the associated Lie group and a decomposition of the evolution on each group generator. The time evolution is thus always transformed in a system of ordinary non-linear differential equations for a set of coefficients. In many cases this system can be solved by symbolic computational algorithms. As an example, an exact solution to three well known problems is provided. For two of them, the modulated optical lattice and Kapitza pendulum, the exact solutions, which were already known, are reproduced. For the other example, the Paul trap, no exact solutions were known. Here we find such exact solution, and as expected, contain the approximate solutions found by other authors.

quant-ph↗

arXiv2017

Electron-nuclear coherent spin oscillations probed by spin dependent recombination

We demonstrate the detection of coherent electron-nuclear spin oscillations related to the hyperfine interaction and revealed by the band-to-band photoluminescence (PL) in zero external magnetic field. On the base of a pump-probe PL experiment we measure, directly in the temporal domain, the hyperfine constant of an electron coupled to a gallium defect in GaAsN by tracing the dynamical behavior of the conduction electron spin-dependent recombination to the defect site. The hyperfine constants and the relative abundance of the nuclei isotopes involved can be determined without the need of electron spin resonance technique and in the absence of any magnetic field. Information on the nuclear and electron spin relaxation damping parameters can also be estimated from the oscillations damping and the long delay behavior.

cond-mat.mes-hall↗

arXiv2016

Electron-nuclear spin dynamics of Ga$^{2+}$ paramagnetic centers probed by spin dependent recombination: A master equation approach

Similar to nitrogen-vacancy centers in diamond and impurity atoms in silicon, interstitial gallium deep paramagnetic centers in GaAsN have been proven to have useful characteristics for the development of spintronic devices. Among other interesting properties, under circularly polarized light, gallium centers in GaAsN act as spin filters that dynamically polarize free and bound electrons reaching record spin polarizations (100\%). Furthermore, the recent observation of the amplification of the spin filtering effect under a Faraday configuration magnetic field has suggested that the hyperfine interaction that couples bound electrons and nuclei permits the optical manipulation of its nuclear spin polarization. Even though the mechanisms behind the nuclear spin polarization in gallium centers are fairly well understood, the origin of nuclear spin relaxation and the formation of an Overhauser-like magnetic field remain elusive. In this work we develop a model based on the master equation approach to describe the evolution of electronic and nuclear spin polarizations of gallium centers interacting with free electrons and holes. Our results are in good agreement with existing experimental observations. In regard to the nuclear spin relaxation, the roles of nuclear dipolar and quadrupolar interactions are discussed. Our findings show that, besides the hyperfine interaction, the spin relaxation mechanisms are key to understand the amplification of the spin filtering effect and the appearance of the Overhauser-like magnetic field. Based on our model's results we propose an experimental protocol based on time resolved spectroscopy. It consists of a pump-probe photoluminescence scheme that would allow the detection and the tracing of the electron-nucleus flip-flops through time resolved PL measurements.

cond-mat.other↗

arXiv2016

Singularities and internal rotational dynamics of electron beams

We study the internal rotational dynamics of electronic beams in relation to the phase singularities of their wave functions. Given their complex singularity structure, Hermite-Gaussian beams and other superpositions of Laguerre-Gaussian modes are studied here. We show that by inspecting the lowest non-vanishing terms of the wave function near the singularity it is possible to infer the structure of the Bohmian streamlines. Conversely, starting from a map of the electron's Bohmian velocities, we demonstrate that it is possible to derive the form of the electron's wave function near the singularity. We outline a procedure that could yield an experimental method to determine the main parameters of the electron's wave function close to a singularity.

quant-ph↗

arXiv2016

Time evolution of two-dimensional quadratic Hamiltonians: A Lie algebraic approach

We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach presented here is mainly motivated by the two-dimensional quadratic Hamiltonian, it may be applied to investigate the evolution operators of any Hamiltonian having a dynamical algebra with a large number of elements. We illustrate the method by finding the propagator and the Heisenberg picture position and momentum operators for a two-dimensional charge subject to uniform and constant electro-magnetic fields.

math-ph↗

arXiv2015

Lie algebraic approach to quadratic Hamiltonians and the bi-dimensional charged particle in time-dependent electromagnetic field

We discuss the one-dimensional, general quadratic Hamiltonian and the bi-dimensional charged particle in time-dependent electromagnetic fields through the Lie algebraic approach. Such method consists in finding a set of generators that form a closed Lie algebra in terms of which it is possible to express the Hamiltonian and the therefore the evolution operator. The evolution operator is then the starting point to obtain the propagator as well as the explicit form of the Heisenberg picture position and momentum operators. First, the set of generators forming a closed Lie algebra is identified for the general quadratic Hamiltonian. This algebra is later extended to study the the Hamiltonian of a charged particle in electromagnetic fields, given the similarities between the terms of these two Hamiltonians.

quant-ph↗

arXiv2014

Unitary approach to the quantum forced harmonic oscillator

In this paper we introduce an alternative approach to studying the evolution of a quantum harmonic oscillator subject to an arbitrary time dependent force. With the purpose of finding the evolution operator, certain unitary transformations are applied successively to Schrödinger's equation reducing it to its simplest form. Therefore, instead of solving the original Schrödinger's partial differential equation in time and space the problem is replaced by a system of ordinary differential equations. From the obtained evolution operator we workout the propagator. Even though we illustrate the use of unitary transformations on the solution of a forced harmonic oscillator, the method presented here might be used to solve more complex systems. The present work addresses many aspects regarding unitary transformations and the dynamics of a forced quantum harmonic oscillator that should be useful for students and tutors of the quantum mechanics courses at the senior undergraduate and graduate level.

quant-ph↗