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Introduction
Irán Ramos currently works at the Optics Coordination, Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE). Their most recent publication is 'Quantum harmonic oscillator with time dependent mass'.
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Publications
Publications (78)
In this study, we present an exact solution to the Lindblad master equation describing the interaction of two quantized electromagnetic fields in a decaying cavity coupled to a thermal reservoir at a finite temperature. The solution is obtained using the superoperator technique, leveraging commutation relations to factorize the exponential of the L...
We employ a squeeze operator transformation approach to solve the anisotropic quantum Rabi model that includes a diamagnetic term. By carefully adjusting the amplitude of the diamagnetic term, we demonstrate that the anisotropic Rabi model with the $A^2$ term can be exactly reduced to either a Jaynes-Cummings or an anti-Jaynes-Cummings model withou...
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 transit...
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...
We present examples where expressions for exp(A^+B^) can be derived even though operators (or superoperators) A^ and 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.
In this study, we provide an exact solution to the Lindblad master equation that describes the interaction of two quantized electromagnetic fields in a decaying cavity, coupled to a thermal reservoir at finite temperature. The solution is obtained using the superoperator technique, leveraging commutation relations to express the exponential of the...
We present a detailed derivation of the Poynting vector for Cauchy-Riemann beams propagating in free space considering a Gaussian modulation with $g \in \mathbb{C}$. The effect generated by this Gaussian modulation is a compression-expansion of the intensity distribution. It is shown that the parameter $g$ can reverse the direction of energy flux a...
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, a...
In this work, we detail a proposal for optical signals to be represented and analyzed in phase-space. Our proposal aims to integrate a series of operations in waveguide realization, as a compact all-together platform that takes an initial wavefield and returns a two-dimensional representation of the information. We show, step by step, that the quan...
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 w...
The similarity between the Schr\"odinger 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...
We explore the interaction between a three-level atom and a single-mode quantized cavity, known as the three-level ladder-type Jaynes-Cummings model. By employing the exact solution of the Schr\"odinger equation, we investigate how the initial conditions of the atom influence the occupation probabilities of the atomic energy levels, average photon...
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...
Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study introduces an innovative methodology aimed at reconstructing the Wigner distribution function of optical signals;...
We report explicit equations and matrix representations that allow simple calculation between three different media (free space, linear and quadratic refractive index distributions) for paraxial light propagation.
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 aver...
Leveraging operator techniques, we address the paraxial wave equation governing a field formed by the multiplication of a Gaussian function and an entire function; notably, the latter adheres to the Laplace equation, ∇⊥2f(x+iy)=0, a direct consequence of satisfying the Cauchy-Riemann equations. Our theoretical and experimental exploration brings to...
AC Stark shifts have an impact on the dynamics of atoms interacting with a near-resonant quantized single-mode cavity field, which is relevant to a single atom micromaser. In this study, we demonstrate that, when the field is in a squeezed coherent state, atomic lineshapes are highly sensitive to the squeezing parameter. Furthermore, we show that,...
In this study, we investigate the stationary states of the Glauber-Fock oscillator waveguide array. We begin by transforming the associated Hamiltonian into the form of a quantum harmonic oscillator Hamiltonian, allowing the implementation of a supersymmetric (SUSY) approach. By considering the simplest case for the intertwining operator, the optic...
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 an...
Este artículo investiga el efecto de niveles cercanos no resonantes en las líneas espectrales de los átomos que interactúan con un campo electromagnético. Específicamente, examinamos el efecto AC Stark que ocurre cuando la frecuencia del campo coincide con la frecuencia de transición entre dos niveles más bajos y el campo tiene un número promedio p...
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, $G/\omega_m$, is not negligible compared to one, i.e., the system operates in the strong-coupling regime. Due to the forcing term, the interaction pict...
Formas de Línea Atómicas en modelos de tipo Jaynes-Cummings Formas de Línea Atómicas En esta monografía se estudian las formas de línea atómicas en dos modelos de tipo Jaynes-Cummings. El primer modelo incluye la influencia de niveles cercanos no resonantes, que se identifican como un término de tipo AC Stark. El segundo modelo analiza cómo un camp...
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 exp...
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 perpendicular Laplacian with a zero eigenvalue, a consequence of the Cauchy-Riemann equations. We demonstrate, both theoretical...
We show that the Markovian dynamics of two coupled harmonic oscillators may be analyzed using a Schrödinger equation and an effective non-Hermitian Hamiltonian. This may be achieved by a non-unitary transformation that involves superoperators; such transformation enables the removal of quantum jump superoperators, which allows us to rewrite the Lin...
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,...
When an electromagnetic field is confined in a cavity of variable length, real photons may be generated from vacuum fluctuations due to highly nonadiabatic boundary conditions. The corresponding effective Hamiltonian is time-dependent and contains infinite intermode interactions. Considering one of the cavity mirrors fixed and the other describing...
When an electromagnetic field is confined in a cavity of variable length, real photons may be generated from vacuum fluctuations due to highly nonadiabatic boundary conditions. The corresponding effective Hamiltonian is time-dependent and contains infinite intermode interactions. Considering one of the cavity mirrors fixed and the other describing...
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 an...
It is well known that AC Stark shifts have an impact on the dynamics of atoms interacting with a near-resonant quantized single-mode cavity field, which is relevant for single-atom micromasers. In this study, we demonstrate that when the field is in a squeezed coherent state, the micromaser lines are highly sensitive to the squeezing parameter. Fur...
This article investigates the effect of near non-resonant levels on the spectral lines of atoms interacting with an electromagnetic field. Specifically, we examine the AC Stark effect that occurs when the field frequency matches the transition frequency between two lower levels and the field has a small average number of photons ($|\alpha|^2 <4$)....
We show that the Markovian dynamics of two coupled harmonic oscillators may be analyzed using a Schr\"odinger equation and an effective non-Hermitian Hamiltonian. This may be achieved by a non-unitary transformation that involves superoperators; such transformation enables the removal of quantum jump superoperators, that allows us to rewrite the Li...
Some of the distinctive features of a non-stationary one-dimensional electromagnetic cavity are its explicit time dependence, instantaneous frequency, intermode interactions, and the generation of real photons out of vacuum fluctuations under nonadiabatic changes of boundary conditions. Remarkably, considering that one of the cavity mirrors describ...
We present a new family of Bessel solutions of the paraxial equation. Such solutions keep their form during propagation due to a quadratic phase factor that makes them scaled propagation invariant fields. The Bessel beams we introduce have the particularity that the topological phase is twice the order of the Bessel function and the argument varies...
We show that the Kapitza–Dirac effect may be modeled by classical light propagation in photonic lattices having a square power law for the refraction index coefficient. The dynamics is shown to be fully soluble because both systems share the same time-independent Schrödinger equation: the angular Mathieu equation. We examine the trajectories of cla...
A non-stationary one-dimensional cavity can be described by the time-dependent and multi-mode effective Hamiltonian of the so-called dynamical Casimir effect. Due to the non-adiabatic boundary conditions imposed in one of the cavity mirrors, this effect predicts the generation of real photons out of vacuum fluctuations of the electromagnetic field....
We show that Bragg diffraction may be modeled by classical light propagation in photonic lattices having a square power law for the refraction index coefficient. The dynamics is shown to be fully integrable and therefore described in closed form. We examine the trajectories of classical light propagating in such structures.
A non-stationary one-dimensional cavity can be described by the time-dependent and multi-mode effective Hamiltonian of the so-called dynamical Casimir effect. Due to the non-adiabatic boundary conditions imposed in one of the cavity mirrors, this effect predicts the generation of real photons out of vacuum fluctuations of the electromagnetic field....
Introducing a Kerr medium in a cavity coupled to a harmonically moving mirror, we reproduce known and solvable interactions such as two-coupled harmonic oscillators and ion-laser like interactions for specific conditions. This is achieved by a unitary transformation allowing us to tune off the Kerr medium in order to simplify the Hamiltonian.
Introducing a Kerr medium in a cavity coupled to a harmonically moving mirror, we reproduce known and solvable interactions such as two-coupled harmonic oscillators and ion-laser like interactions for specific conditions. This is achieved by a unitary transformation allowing us to tune off the Kerr medium in order to simplify the Hamiltonian.
In this work, we start from a phenomenological Hamiltonian built from two known systems: the Hamiltonian of a pumped optomechanical system and the Jaynes-Cummings Hamiltonian. Using algebraic techniques we construct an approximate time evolution operator U^(t) for the forced optomechanical system (as a product of exponentials) and take the JC Hamil...
In this work we start from a phenomenological Hamiltonian built from two known systems: the Hamiltonian of a pumped optomechanical system and the Jaynes Cummings Hamiltonian. Using algebraic techniques we construct an approximate time evolution operator $\hat U_{opt}$ for the forced optomechanical system (as a product of exponentials) and take the...
We propose a trapped-ion platform to simulate a reconfigurable spin-spin Hamiltonian related to quantum thermodynamic processes. Starting from an experimental model describing two trapped ions under slightly off-resonant first sideband driving with individually controlled driving phases, we follow an operational quantum optics approach to show that...
Macedo and Guedes have shown how to solve a system of coupled harmonic oscillators with time dependent parameters [{Int. J. Mod. Phys.} {\bf 23}, 1450048 (2014)]. We show that the first transformation they did is not correct. We show how to solve the coupled harmonic oscillators for the cases they treat in their article, namely, $m_1(t)=m_2(t)=m_0...
We show how to generate quasi-rectangle-states of the vibrational motion of an ion, this is, states that have the same probability in a given position interval. We produce those states by repeated ion-laser interactions followed by conditional measurements that generate a superposition of squeezed states. The squeeze parameter of the initial state...
We show that two coupled time dependent harmonic oscillators with equal frequencies have an invariant that is a generalization of the Ermakov-Lewis invariant for the single time dependent harmonic oscillator.
We present an approximate Lie algebraic method to deal with a forced optomechanical Hamiltonian. We show that the approximations made in order to linearize the interaction Hamiltonian are fully justified by means of a comparison between a purely numerical calculation of the number of photons, phonons and linear entropy using the full Hamiltonian an...
In this work we construct an approximate time evolution operator for a system composed by two Jaynes-Cummings Hamiltonians. We express the full time evolution operator as a product of exponentials and we analyze the validity of our approximations contrasting our analytical results with those obtained by purely numerical methods.
We propose a trapped-ion platform to simulate a reconfigurable spin-spin Hamiltonian related to quantum thermodynamic processes. Starting from an experimental model describing two trapped-ions under slightly off-resonant first sideband driving with individually controlled driving phases, we follow an operational quantum optics approach to show that...
The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants , is presented. Finite circular and linear arrays are studied using classical arguments, and their proper solution is given using methods often found in...
In this paper, we show that the Pegg–Barnett formalism accepts coherent states constructed as eigenstates of the annihilation operator, considering both the number and the phase. These operators are defined within a $ (s + 1) $ ( s + 1 ) -dimensional Hilbert space $ {{\cal H}_s} $ H s and with periodic conditions. The coherent states that we find a...
This contribution has two main purposes. First, using classical optics we show how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we present classical analogs of coupled harmonic oscillators that correspond to anisotropic quadratic graded indexed media in a rotated reference frame, and we use operato...
The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants , is presented. Finite circular and linear arrays are studied using classical arguments, and their proper solution is given using methods often found in...
In this work we construct an approximate time evolution operator for a system composed by two coupled Jaynes-Cummings Hamiltonians. We express the full time evolution operator as a product of exponentials and we analyze the validity of our approximations contrasting our analytical results with those obtained by purely numerical methods.
We show how to generate quasi-rectangle-states of the vibrational motion of an ion, this is, states that have the same probability in a given position interval. We produce those states by repeated ion-laser interactions followed by conditional measurements that generate a superposition of squeezed states. The squeeze parameter of the initial state...
We show that by using the quantum orthogonal functions invariant, we found a solution to coupled time-dependent harmonic oscillators where all the time-dependent frequencies are arbitrary. This system may be found in many applications such as nonlinear and quantum physics, biophysics, molecular chemistry, and cosmology. We solve the time-dependent...
We show that, by using the quantum orthogonal functions invariant, we are able to solve a coupled of time dependent harmonic oscillators where all the time dependent frequencies are arbitrary. We do so, by transforming the time dependent Hamiltonian of the interaction by a set of unitary operators. In passing, we show that N time dependent and coup...
This contribution has two main purposes. First, we show using classical optics how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we use quantum mechanical techniques to solve, exactly, the propagation of light through a particular type of graded index medium. In passing, we show that the system pres...
The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants , is presented. Finite circular and linear arrays are studied using classical arguments, and their proper solution is given using methods often found in...
This contribution has two main purposes. First, we show using classical optics how to model two coupled quantum harmonic oscillators and two interacting quantized fields. Second, we use quantum mechanical techniques to solve, exactly, the propagation of light through a particular type of graded index medium. In passing, we show that the system pres...
We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schr\"odinger equation by using squeeze operators. Finally we give two examples of time dependencies: quadratically and hyperbolically growing masses.
Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville...
Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville...
We use the Fourier operator to transform a time dependent mass quantum harmonic oscillator into a frequency dependent one. Then we use Lewis-Ermakov invariants to solve the Schr\"odinger equation by using squeeze operators. Finally we give two examples of time dependencies: quadratically and hyperbolically growing masses.
We theoretically investigate the dynamical Casimir effect in a single-mode cavity endowed with a driven off-resonant mirror. We explore the dynamics of photon generation as a function of the ratio between the cavity mode and the mirror's driving frequency. Interestingly, we find that this ratio defines a threshold---which we referred to as a metal-...
We theoretically investigate the dynamical Casimir effect in a single-mode cavity endowed with a driven off-resonant mirror. We explore the dynamics of photon generation as a function of the ratio between the cavity mode and the mirror's driving frequency. Interestingly, we find that this ratio defines a threshold---which we referred to as a metal-...
We show that it is possible to find exact eigenstates in the interaction between a trapped ion oscillating in two dimensions and they will be entangled states. We also show that the Hamiltonian that describes this interaction may be mapped to a quantum Rabi interaction Hamiltonian (for a two-level atom and two quantized fields) by means of a unitar...
We show that it is possible to find exact eigenstates in the interaction between a trapped ion oscillating in two dimensions and they will be entangled states.We also show that the Hamiltonian that describes this interaction may be mapped to a quantum Rabi interaction Hamiltonian (for a two-level atom and two quantized fields) by means of a unitary...
Demostramos que es posible encontrar eigenestados exactos de la interacción de un ión atrapado oscilando en dos dimensiones y que cada uno de los eigenestados exactos son estados entrelazados.También demostramos que el hamiltoniano que describe dicha interacción puede ser mapeado a un escenario tipo Rabi cuántico (un átomo de dos niveles y dos camp...
We demonstrate that superpositions of coherent and displaced Fock states,
also referred to as generalized Schr\"odinger cats cats, can be created by
application of a nonlinear displacement operator which is a deformed version of
the Glauber displacement operator. Consequently, such generalized cat states
can be formally considered as nonlinear cohe...
We propose a class of nonlinear coherent states which are experimentally feasible in cavity or ion-trap quantum electrodynamics. These quantum field states arise from a new type of photon addition and subtraction based on London phase operators, also known as Susskind–Glogower operators, that just displaces the mean photon number without scaling th...