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I. Ramos-Prieto

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

31 records · Page 2Linked to original sources
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↗
arXiv2023

Optical ladder operators in the Glauber-Fock oscillator array

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 optical ladder operators are straightforwardly constructed and shown to map eigensolutions into eigensolutions of the corresponding Hamiltonian operator, in pretty much the same manner as it is done for the quantum harmonic oscillator case. The ladder of the corresponding (eigen) supermodes is then easily established.

physics.optics↗
arXiv2023

Temporal factorization of a non-stationary electromagnetic cavity field

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 uniform motion (zero acceleration), we show that it is possible to factorize the entire temporal dependency and write its formal solution, i.e., the Hamiltonian becomes a product of a time-dependent function and a time-independent operator. With this factorization, we prove in detail that the photon production is proportional to the Planck factor involving a velocity-dependent effective temperature. This temperature significantly limits photon generation even for ultra-relativistic motion. The time-dependent unitary transformations we introduce to obtain temporal factorization help establishing connections with the shortcuts to adiabaticity of quantum thermodynamics and with the quantum Arnold transformation.

quant-ph↗
arXiv2023

Effects of squeezing on the power broadening and shifts of micromaser lineshapes

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. Furthermore, we show that when considering a superposition of squeezed coherent states with equal amplitude, the displacement of the transition lines depends significantly not only on the squeezing parameter but also on its sign.

quant-ph↗
arXiv2023

Discriminating coherent states superpositions by line shapes

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 ($|α|^2 <4$). Our research demonstrates that the changes in spectral line shape can be used to distinguish between Schrödinger cat states with opposite phases in $π$, namely, the states $|α\rangle + |-α\rangle$ and $|α\rangle - |-α\rangle$.

quant-ph↗
arXiv2023

Exact solution for the interaction of two decaying quantized fields

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, that allows us to rewrite the Lindblad master equation in terms of a von Neumann-like equation with an effective non-Hermitian Hamiltonian. This may be generalized to an arbitrary number of interacting fields. Finally, by applying an extra non-unitary transformation, we may diagonalize the effective non-Hermitian Hamiltonian to obtain the evolution of any input state in a fully quantum domain.

quant-ph↗
arXiv2021

Mathieu-Bragg photonic lattices

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.

quant-ph↗
arXiv2021

Exact solution of a non-stationary cavity with one intermode interaction

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. Such photon generation strongly depends on the number of modes in the cavity and their intermode couplings. Here, by using an algebraic approach, we show that for any set of functions parameterizing the effective Hamiltonian, the corresponding time-dependent Schrödinger equation admits an exact solution when the cavity has one intermode interaction. With the exact time evolution operator, written as a product of eleven exponentials, we obtain the average photon number in each mode, a few relevant observables and some statistical properties for the evolved vacuum state.

quant-ph↗
arXiv2021

Ion-laser-like interaction in optomechanical systems with Kerr nonlinearities

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.

quant-ph↗
arXiv2020

Approximate evolution for a hybrid system: An optomechanical Jaynes-Cummings model

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 JC Hamiltonian as an interaction. We transform the later with $\hat U_{opt}$ to obtain a generalized interaction picture Hamiltonian which can be linearized and whose time evolution operator is written in a product form. The analytic results are compared with purely numerical calculations using the full Hamiltonian and the agreement between them is remarkable.

quant-ph↗
arXiv2017

Quantum harmonic oscillator with time dependent mass

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 Schrödinger equation by using squeeze operators. Finally we give two examples of time dependencies: quadratically and hyperbolically growing masses.

quant-ph↗
arXiv2017

Dynamical Casimir effect in stochastic systems: photon-harvesting through noise

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-insulator phase transition---between an exponential growth and a low photon production. The low photon production is due to Bloch-like oscillations that produce a strong localization of the initial vacuum state, thus preventing higher generation of photons. To break localization of the vacuum state, and enhance the photon generation, we impose a dephasing mechanism, based on dynamic disorder, into the driving frequency of the mirror. Additionally, we explore the effects of finite temperature on the photon production. Concurrently, we propose a classical analogue of the dynamical Casimir effect in engineered photonic lattices, where the propagation of classical light emulates the photon generation from the quantum vacuum of a single-mode tunable cavity.

quant-ph↗