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The Jaynes-Cummings quantum optics model allows us to understand the dialogue between light and matter at its most fundamental level, which is crucial for advancements in quantum science and technology. Several generalizations of the model have long been proposed, emphasizing their dynamic behavior but paying less attention to their spectroscopy. Here, we obtain analytical expressions of the time-dependent spectral response of a nonlinear Jaynes-Cummings model based on deformed field operators. We show that the long-time response of the resulting nonlinear cavity field resembles the one experimentally obtained in the strong-dispersive regime of circuit quantum electrodynamics. The spectrum is intrinsically asymmetric with the nonlinear coupling, a signature of the impossibility of getting resonant conditions for finite field excitations., Comment: 14 pages, 7 figures

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. Due to the forcing term, the interaction picture Hamiltonian contains the number operator in the exponents, and in order to deal with it, we approximate these exponentials by their average values taken between initial coherent states. Our approximation is justified when we compare our results with the numerical solution of the number of photons, phonons, Mandel parameter, and the Wigner function, showing an excellent agreement., Comment: 25 pages, 11 figures. Peer-reviewed version

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., Comment: 10 pages, 4 figures. Accepted in Phys. Rev. A

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 Schr\"odinger 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.

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.

We present an exact analytical solution of the anisotropic Hopfield model, and we use it to investigate in detail the spectral and thermometric response of two ultrastrongly coupled quantum systems. Interestingly, we show that depending on the initial state of the coupled system, the vacuum Rabi splitting manifests significant asymmetries that may be considered spectral signatures of the counterintuitive decoupling effect. Using the coupled system as a thermometer for quantum thermodynamics applications, we obtain the ultimate bounds on the estimation of temperature that remain valid in the ultrastrong coupling regime. Remarkably, if the system performs a quantum phase transition, the quantum Fisher information exhibits periodic divergences, suggesting that one can have several points of arbitrarily high thermometric precision for such a critical quantum sensor., Comment: 22 pages, 4 figures, Close to published version

In this work we study the generation of photons inside an ideal cavity with resonantly oscillating boundaries in the presence of a two-level atom. We make use of Lie algebraic techniques to obtain an approximate time-evolution operator and evaluate not only the resonant and dispersive regimes but also explore different regions of parameters. We have found a very good agreement between our approximate results and those obtained by numerical means., Comment: 11 pages, 5 figures

An effective toy model for an ideal one-dimensional nonstationary cavity is taken to be the starting point to derive a fitting markovian master equation for the corresponding leaky cavity. In the regime where the generation of photons via the dynamical Casimir effect is bounded, the master equation thus constructed allows us to investigate the effects of decoherence on the average number of Casimir photons and their quantum fluctuations through the second-order correlation function., Comment: 5 pages, 3 figures. Comments are welcome

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.

In this paper we show that the scattered field of a bichromatically driven V-type three-level atom exhibit asymmetry and large violation of classical bounds in amplitude-intensity correlations. These features result from the noncommutativity of amplitude and intensity field operators, and the strong non-Gaussian fluctuations in this system. The amplitude-intensity correlations of resonance fluorescence, with its large third-order fluctuations, describe the nonclassical features of the emitted field more accurately than the second-order measure related to squeezing. Spectra and variances of these correlations, along intensity-intensity correlations, provide a wealth of supporting information., Comment: 8 pages, 9 figures

Knowledge of the relationships among different features of quantumness, like entanglement and state purity, is important from both fundamental and practical viewpoints. Yet, this issue remains little explored in dynamical contexts for open quantum systems. We address this problem by studying the dynamics of entanglement and purity for two-qubit systems using paradigmatic models of radiation-matter interaction, with a qubit being isolated from the environment (spectator configuration). We show the effects of the corresponding local quantum channels on an initial two-qubit pure entangled state in the concurrence-purity diagram and find the conditions which enable dynamical closed formulas of concurrence, used to quantify entanglement, as a function of purity. We finally discuss the usefulness of these relations in assessing entanglement and purity thresholds which allow noisy quantum teleportation. Our results provide new insights about how different properties of composite open quantum systems behave and relate each other during quantum evolutions., Comment: 16 Pages, 10 Figures. One author added. Improved version with more references and comments

We study the dynamical Casimir effect in an electromagnetic cavity containing a Kerr medium. We obtain approximate expressions for the time evolution operator as well as for the number operator in the Heisenberg representation. We have found that the generation of photons from quantum vacuum is strongly affected by the presence of the Kerr medium, sharing physical features with the case of two two-level atoms in a cavity with oscillating walls. The nonlinear medium produces a saturation effect in the photon generation which shows strong oscillations whose frequency increases with the intensity of the nonlinear medium. We expect that these results could be relevant for any experimental study involving the dynamical Casimir effect that is willing to incorporate Kerr nonlinearities., Comment: 16 pages, 2 figures

On the basis of the f-deformed oscillator formalism, we propose to construct nonlinear coherent states for Hamiltonian systems having linear and quadratic terms in the the number operator by means of the two following definitions: i) as deformed annihilation operator coherent states (AOCS) and ii) as deformed displacement operator coherent states (DOCS). For the particular cases of the Morse and Modified P\"oschl-Teller potentials, modeled as f-deformed oscillators (both supporting a finite number of bound states), the properties of their corresponding nonlinear coherent states, viewed as DOCS, are analyzed in terms of their occupation number distribution, their evolution on phase space, and their uncertainty relations., Comment: 22 pages, 7 figures

In this work we make use of deformed operators to construct the coherent states of some nonlinear systems by generalization of two definitions: i) As eigenstates of a deformed annihilation operator and ii) by application of a deformed displacement operator to the vacuum state. We also construct the coherent states for the same systems using the ladder operators obtained by traditional methods with the knowledge of the eigenfunctions and eigenvalues of the corresponding Schr\"odinger equation. We show that both methods yield coherent states with identical algebraic structure., Comment: 13 pages

We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction picture representation and use an exact time evolution operator for the time independent part of the Hamiltonian. We approximate the interaction picture Hamiltonian in such a way as to make it a member of a Lie algebra. The corresponding time evolution operator behaves like a squeezing operator due to the temporal dependence of the oscillator's frequency. We analyze the probability amplitude and the auto correlation function for different Hamiltonian parameters and we find a very good agreement between our approximate results and converged numerical calculations., Comment: 11 pages, 3 figures

We construct Deformed Photon Added Nonlinear Coherent States (DPANCSs) by application of the deformed creation operator upon the Nonlinear Coherent States obtained as eigenstates of the deformed annihilation operator and by application of a deformed displacement operator upon the vacuum state. We evaluate some statistical properties like the Mandel parameter, Husimi and Wigner functions for these states and analyze their differences, we give closed analytical expressions for them. We found a profound difference in the statistical properties of the DPANCSs obtained from the two above mentioned generalizations., Comment: 8 pages, 7 figures, Accepted for publication in JOSAB