Narrow Results

The aim of this paper is the study of the generalized deformed quantum oscillators in the framework (q; α, β, γ; ν)-deformed of oscillator algebra. By selecting the special values of deformation parameters, we have separated a generalized deformed oscillator connected with generalized discrete Hermite II polynomials. By these means we have constructed Barut–Girardello type coherent states of this oscillator.

We have found the conditions on the (q; α, β, γ; ν)-deformation parameters at which the free (q; α, β, γ; ν)-deformed oscillator approximate the usual anharmonic oscillator in the homogeneous Kerr medium.

An analytical solution is obtained when the Kerr medium and Stark shift are considered as nonlinear interaction terms to the system containing two-qubit and two-mode electromagnetic field from the parametric amplifier. Dynamics of the population inversion, cavity–qubit and qubit–qubit entanglements are analyzed under the unitary cavity–qubit interaction, the Kerr medium and the Stark shift. The population inversion of a qubit presents periodic revivals and collapses. The results show that the entanglement and the population inversion as well as the inversion have the same stable intervals, that is, the collapse intervals. It is found that the Kerr medium and the Stark shift may lead to reduction of the periods and the amplitudes of the population inversion and the cavity–qubit/qubit–qubit entanglement. The deteriorated qubit–qubit/cavity–qubit entanglement and the population inversion, due to the Kerr medium, may be increased by increasing the Stark shift and vice versa.

We consider a generalized multi-photon interaction of two collectively two-level atoms with two-mode of electromagnetic field in the presence of Kerr medium and intensity-dependent coupling. We show that this atomic system possesses supersymmetric structure. We solved this system by virtue of supersymmetric unitary transformation. The supersymmetric generators of this atomic system are constructed. The diagonalization of the corresponding Hamiltonian is performed by introducing a supersymmetric unitary transformation. Accordingly, the eigenvalues and eigenfunctions of the Hamiltonian of the atomic system are obtained. The time evolution of the atom–field wave functions is derived in an exact form for two cases of the initial states of the atoms and the field modes. Some quantum effects such as the second-order correlation function, cross-correlation, purity and Husimi Q-function are investigated. The effects of the Kerr medium, detuning parameter, intensity-dependent coupling and multi-photon transition on the evolution of these quantum effects are examined. We conclude that the supersymmetric unitary transformation method is very simple and can be applied to a variety of atomic systems which possess a supersymmetric structure.

We consider a four-level double V-type atom with two closely-separated top levels and two closely-separated lower levels interacting with a single mode field via multi-photon processes and in the presence of Kerr medium. We show that this atomic system possesses supersymmetric structure and construct its supersymmetric generators. We diagonalize the Hamiltonian of this system using supersymmetric unitary transformation and obtain the corresponding eigenstates and eigenvalues. The atom–field wave functions are obtained when the atom and the field mode are initially in two different cases. The evolution of both the quasi-probability distribution Q-function and the Mandel Q-parameter of the field are studied when the input field is in a coherent state. The influence of the Kerr medium and the detuning parameters on the behavior of these quantum effects is analyzed. The results show that they play a prominent role on the Poissonian statistics of the field. Also, the Kerr medium changes the behavior of the quasi-probability distribution Q-function. We end with discussion and conclusions.

An analytical solution for a dissipative cavity field interacting with two qubits (TQs) in presence of Kerr-like medium is obtained. The super-operator method is used to obtaining the field density matrix elements under the dispersive approximation. Linear entropy is calculated to determine the entanglement between the cavity field and the TQs. Moreover, the Wehrl entropy and Wehrl phase distribution are discussed to discover the nonclassicality dynamics of a dissipative cavity field. It is found that the Kerr medium and the dissipation reduce the generated quantum coherence due to the qubit–cavity interactions. It is possible to control the ability of cavity–qubit interactions to generate quantum coherence by the mean photon number of the initial coherent cavity state. Moreover, the nonclassicality of the initial coherent state reduces the dissipative and the Kerr medium effects.

In this paper, the entanglement between two qubits that exist in two distinct cavities which are connected by an optical fiber is investigated by using the concurrence, while two-photon transitions and Kerr medium effect are also considered. Each cavity contains a qubit and a single-mode quantized field. The appearance of entanglement between the two qubits in the separate cavities originates from the presence of optical fiber. The obtained numerical results of the considered system show that, if the Kerr medium is large enough, the initial values of entanglement between the two qubits (which may have the maximum possible value, i.e. 1) can be approximately protected from the large amplitude fluctuations, so that acceptable stability is created. Also, qubit-field coupling and detuning effects are investigated and it is observed that symmetric coupling results in more stability of entanglement. Eventually, atomic population inversion is also studied and it is observed that it is controllable by considering different parameters.

We study the dynamics and quantum characteristics of a single two-level atom interacting with a single mode cavity field undergoing a multi-photon processes in the presence of a nonlinear Kerr-like medium. The wavefunctions of the multi-photon system are obtained when the atom starts in the excited and in the ground state. The atomic inversion, the squeezing of the radiation field and the quasiprobability distribution Q-function of the field are discussed. Numerical results for these characteristics are presented when the atom starts in the excited state and the field mode in a coherent state. The influence of the presence and absence of the number operator and the Kerr medium for the one- and two-photon processes on the evolution of these characteristics are analyzed.

We reveal that the intensity dependent coupling Hamiltonian via multi-photon interaction in a Kerr medium possesses a supersymmetric structure and therefore can be solved with the supersymmetric transform method. By selecting suitable supersymmetric generators, we derive its energy eigenvalues and eigenvectors.

In this paper we consider a four-level W-type atom interacting with a single-mode quantized electromagnetic field in the presence of the Kerr medium. The atom and the field are initially prepared in the excited state and coherent state, respectively. The influence of the Kerr medium on the N-order squeezing and Poissonian statistics is investigated. We found that the maximum value of squeezing decreases by increasing the order N. Also, we noticed that the Kerr-like medium decreases the amount of squeezing and increases the sub-Poissonian statistics.

In this work, we investigate a theoretical study of the stationary entanglement of an optomechanical system by adding a Kerr medium in the cavity where the mechanical resonator is perturbatively connected to an auxiliary qubit. The degree of entanglement between the cavity field and the mechanical system is measured by using the logarithmic negativity. We show that optomechanical entanglement is decreased by Kerr interaction due to photon blockage enhanced by mirror–qubit coupling, we also show that this enhancement is influenced by the temperature. In addition, we find that, in the presence of the mirror–qubit coupling, entanglement can arise with far weaker optomechanical coupling. The proposed scheme shows that the presence of the mirror–qubit coupling and Kerr medium is an effective control for an optomechanical system.

Enhancing and preserving the atomic correlation and entanglement is of significant utility in quantum information. To this aim, we study the temporal evolution of uncertainty-induced nonlocality (${𝒰}$) and logarithmic negativity (${ℒ}{𝒩}$) as measures of quantum correlations (QCs) and quantum entanglement (QE) between two effective atoms coupled to a bosonic reservoir in the absence of thermal fluctuations and in the presence of Kerr medium (KM) and Stark shift (SS) under which n-photon transitions are permitted. We explore how Markovian and non-Markovian regimes affect the temporal dynamics of atomic correlation and entanglement and its limitations. Our findings indicate that by adjusting the KM and SS parameters, the quantum correlations between the two atoms can be enhanced and maintained while displaying similar qualitative behavior. Notably, it was observed that the QCs and QE quantities are at their highest magnitudes in the non-Markovian regime when the strengths of both SS and KM are increased, implying that QCs and QE are well protected. In contrast to the typical view that protecting the QCs from decoherence that may be observed owing to environmental noise, we proposed a gainful way to reduce the atomic decoherence by adjusting the number of n-photon transitions. Our investigation reveals that in the non-Markovian regime, the considered system exhibits better resistance against decoherence in comparison to the Markovian regime, as evidenced by the significant amount of quantum correlations detected among the two effective atoms at a specific point in time.

In this paper, an attempt has been made to investigate a one-dimensional photonic crystal containing N-doped germanium semiconductor as a nonlinear defect layer with an intensity-dependent refractive index, silica (SiO₂) and zinc selenide (ZnSe) as crystal cells. Bistability of the TE polarization of the transmission spectrum due to the nonlinear property of the defect layer is investigated by the transfer matrix method (TMM). The refractive index of the germanium nonlinear semiconductor layer is simultaneously depending on the doping density and the intensity of the irradiated light. The changes in both factors are investigated. The impact on the transmission spectrum of the bistability threshold due to the change in the thickness of the defect layer, the thickness of other layers of crystal cells, and the angle of incident light are investigated. The nonlinear effect caused by light intensity as well as doped density effect on the germanium nonlinear semiconductor medium is used simultaneously. As a result, the nonlinear effect caused by the light intensity to create bistability is more than the doping density.

We study the interaction between a moving four-level rubidium atom and a single mode cavity field in the presence of a nonlinear Kerr-like medium. We derive the basic equations of motion for the atomic system and show that it is exactly solvable in the rotating wave approximation. The momentum increment, the momentum diffusion and the quasi-probability distribution Q-function of this system are studied. We investigate numerically the influence of the Kerr medium on the evolution of the previous statistical properties in the exact resonant and nonresonant cases where the atom is initially in the ground state and the field is in a coherent state. It is found that the Kerr medium has an important effect on their evolutions. Finally, conclusions and discussion are given.

In this paper, a model describing the interaction of a five-level (⁸⁵Rb) atom with one-mode cavity field including Kerr nonlinearity is discussed. Analytical solution for this model is presented when the atom is initially prepared in its upper state. The obtained results are then employed to examine the dynamical behavior of atomic inversion, field statistics and field squeezing when the input field is initially considered in a coherent state. It is found that the atom-field properties are influenced by the changing of the coupling constants, the detuning parameters and the Kerr medium.

Kerr media are applied in the photonic lattices and optical fibers, while optical fiber communication becomes one of the main pillars of modern communication. In this letter, we study a (3+1)-dimensional nonlinear Schrödinger equation with distributed coefficients for the spatiotemporal optical solitons or light bullets in a diffractive nonlinear Kerr medium with anomalous dispersion. The N-dark soliton solutions in terms of the Gramian is obtained via the Kadomtsev–Petviashvili hierarchy reduction, where N is a positive integer. Via the graphic analysis, we observe the interaction of the two dark solitons. Effects from the diffraction/dispersion coefficient $\beta (z)$ and gain coefficient $\gamma (z)$ are also discussed on the amplitudes and oscillations of the two dark solitons, as well as on the interaction of the two dark parabolic shape solitons.

We study the effect of Kerr type nonlinear medium in quantum state transfer (QST). We have investigated the effect of different coupling schemes and Kerr medium parameters $p$ and ${\omega }_K$. We found that the Kerr medium introduced in the connection channel can act like a controller for QST. The numerical simulations are performed without taking the adiabatic approximation. Rotating wave approximation is used in the atom–cavity interaction only in the lower coupling regime.

We discuss new aspects of the interaction between a cavity field and Kerr-like medium, focusing on Fisher Information. Here, we provide a new formula for marginal distributions of the Fisher Information and comparison with the Wehrl entropy for the system has been presented. The results show that, it is a correlation measure which is true for any quantum state, provided that it shows the same entropy behaviors of certain reduced states.

Entanglement properties of two uncoupled atoms embedded in a coherent field distribution through one quantum transition process are studied. A case of non-linear Hamiltonian of the problem is considered through which the effect of non-linear media is illustrated. Moreover, the effect of the frequency difference between the inter-atomic transition and the electromagnetic field is also analyzed. We show that, adjusting the considered parameters of the non-linear media and frequency difference leads to a strong control of the degree of entanglement where excellent periodicity of evolution with significant amplitudes maxima of entanglement can be obtained that is very important in predicting the behavior of transmitted information through the application of various information processing schemes. We present a detailed and comparative study of atom–atom entanglement for two cases corresponding to different injections of the two atoms one by one into the cavity field. In addition, we present an answer to the question: How is the quantum phase space structure for a composite system related to the entanglement characteristics of the corresponding quantum system? We demonstrate how can the entanglement in nonlinear tripartite systems be strongly associated with a delocalization in the phase space distribution.

In this paper, we investigate the geometric phase of the field interacting with a moving four-level atom in the presence of Kerr medium. The results show that the atomic motion, the field-mode structure and Kerr medium play important roles in the evolution of the system dynamics. As illustration, we examine the behavior of the geometric phase and entanglement with experimentally accessible parameters. Some new aspects are observed and discussed.

We investigate the effect of Kerr nonlinearity and optomechanical couplings on cavity field spectra in an optomechanical system driven by a pump field. In the mean-field approximation, the system exhibits optical bistability for a wide range of parameters. The spectra are numerically calculated for different initial states, which show that a single peak in the spectrum splits because of the presence of the optomechanical coupling and the increase of the number of phonon. In addition, the peak position in the cavity field spectra changes due to the Kerr nonlinearity, while the cavity detuning is modified. The strength of spectra determines the size of the photon-phonon conversion capabilities. These results provides a theoretical basis for optical communication.