Nonlinear Jaynes-Cummings Model Research Articles

Spectral response of a nonlinear Jaynes-Cummings model

Spectral response of a nonlinear Jaynes-Cummings model

A double Λ-five-level moving atom interacting with a two-mode field in the presence of damping and nonlinear Kerr medium

In this paper, we present the interaction between a five-level [Formula: see text]-configuration atom and a two-mode quantized field in the presence of the damping with the nonlinearity. According to the generalized nonlinear Jaynes–Cummings model (JCM) and the analytical solution of the Schrödinger equation, the general formula of the wave function for this system under special conditions, where the atom (the field) is initially prepared in the excited state (coherent state), has been found. Under some particular conditions, the five-level [Formula: see text]-type atom can be reduced to the three-level [Formula: see text]-type atom. Some physical aspects of the atom-field entangled state showing the entanglement degree, such as the field entropy. Moreover, we evaluate some of their non-classical statistical aspects such as atomic inversion. The effects of the physical parameters such as a Kerr medium, detuning parameter and the intensity-dependent coupling on the temporal behavior of the latter mentioned non-classical statistical aspects have been explored. We show that by choosing the evolved parameters in the interaction process, each of the above non-classical statistical features can be treated. We found that the parameters have an important influence on the properties of these phenomena.

The entanglement and second-order coherence function in a two-atom nonlinear Jaynes-Cummings model

The influence of the Kerr nonlinearity on the two two-level atoms entanglement is investigated in Jaynes–Cummings model (JCM), so that one of atoms is inside the cavity field and the other atom is outside it. We show that the entanglement of atoms increases with the decrease of the phase decoherence rate or Kerr coefficient, when considering the effect of external environment. Then due to the statistic properties of the anti-bunching effect of photons are related to entanglement, the nonlinear JCM is examined theoretically to analyze the bunching or anti-bunching effect by using the second-order coherence function. We find that the second-order coherence function decreases with the Kerr coefficient. Our results show that the field reflects the stronger bunching effect with the bigger average photon number.

Adiabatic sensing technique for optimal temperature estimation using trapped ions

We propose an adiabatic method for optimal phonon temperature estimation using trapped ions which can be operated beyond the Lamb-Dicke regime. The quantum sensing technique relies on a time-dependent red-sideband transition of phonon modes, described by the non-linear Jaynes-Cummings model in general. A unique feature of our sensing technique is that the relevant information of the phonon thermal distributions can be transferred to the collective spin-degree of freedom. We show that each of the thermal state probabilities is adiabatically mapped onto the respective collective spin-excitation configuration and thus the temperature estimation is carried out simply by performing a spin-dependent laser fluorescence measurement at the end of the adiabatic transition. We characterize the temperature uncertainty in terms of the Fisher information and show that the state projection measurement saturates the fundamental quantum Cram\'er-Rao bound for quantum oscillator at thermal equilibrium.

Interaction of a superconducting qubit and a nonlinear field under energy dissipative effect: entanglement and nonclassical properties

The present manuscript studies the temporal behavior of quantum entanglement and nonclassical properties for a superconducting-qubit ( $$\hbox {SC}_{ \text {qubit}}$$ )- field system in the framework of deformed f-oscillator formalism. We introduce the nonlinear Jaynes-Cummings model by using the deformation of the mode field operators. Such a generalization of the Jaynes Cummings model that considers the interaction of a $$\hbox {SC}_{\text {qubit}}$$ with an electromagnetic field in the presence of a nonlinear Kerr-like medium and energy dissipation. We examine the effect of the detuning and decay parameters on the degree of the quantum entanglement, population inversion and field photon statistics. Finally, the relationship among quantum quantifiers is explored according to the optimal choice of the main parameters of the physical model.

Dynamics of entanglement and non-classicality features of a single-mode nonlinear Jaynes–Cummings model

Abstract In this paper, we discuss a model of a nonlinear interaction between a λ-type four-level atom interacting with a cavity field. The analytical solution of the system under particular conditions has been obtained. Numerical treatments have been discussed and new features of the entanglement degree are obtained using entropy and Mandel Q-parameter. Moreover, we evaluate a few of their non-classical properties such as momentum increment, momentum diffusion, mean photon number and normal squeezing. The Kerr medium impact has been discussed through different phenomena. It is shown that Kerr-like medium parameter can be used as a controller parameter of the system dynamics.

Accessing the non-equal-time commutators of a trapped ion

The vibronic dynamics of a trapped ion in the resolved-sideband regime can be described by the explicitly time-dependent nonlinear Jaynes-Cummings model. It is shown that the expectation value of the interaction Hamiltonian and its non-equal-time commutator can be determined by measuring the electronic-state evolution. This yields direct insight into the time-ordering contributions to the unitary time evolution. In order to prove extraction of the quantities of interest works for possibly real data, we demonstrate the procedure by means of generated data.

Time ordering in the classically driven nonlinear Jaynes-Cummings model

Recently, in [Phys. Rev. A 97, 043806 (2018)], the detuned and nonlinear Jaynes-Cummings model describing the quantized motion of a trapped ion was introduced and its corresponding dynamics was solved via considering the driving laser in a quantized manner. In this work we reconsider this model and show that it can likewise be solved with a classical driving laser field. Using the exact solution we investigate the quantum time-ordering effects of the system with respect to nonclassicality of the motional states of the ion. Furthermore, we use the Magnus expansion to analyze the impact of certain orders of the time ordering and derive and exact radius of convergence beyond the established and only sufficient criterion. Finally, the differences of the solution derived here and the previously found one using a quantized pump, are discussed.

Optical nonreciprocity via the standard Jaynes–Cummings model in a gain microcavity

Optical nonreciprocal devices are essential to quantum information processing and communication. We proposed a scheme for optical nonreciprocity via the nonlinear Jaynes–Cummings model in a gain cavity. In addition, the gain cavity is coupled to two fibers with different coupling strengths. In the scheme, the nonlinearity, which is induced by the interaction between a two-level quantum emitter and the cavity field, is enhanced by the cavity gain. Our calculations show that the nonlossy optical nonreciprocity is achievable with high isolation ratio in proper parameter range. Especially, the analytic method further shows the reciprocity broken by the combination of the asymmetric coupling and enhanced nonlinearity.

Wigner function and entanglement dynamics of a two-atom two-mode nonlinear Jaynes–Cummings model

In this paper, a model in which two moving atoms interact with a two-mode field with nondegenerate two-photon transitions is studied in the presence of intensity-dependent coupling. To discuss the entanglement dynamics between subsystems as well as nonclassicality of the system, the time-dependent form of the state vector of the system is exactly obtained. The dynamics of entanglement between the atoms and the field is evaluated by the von Neumann entropy. To examine the degree of entanglement between the atoms, concurrence and negativity are obtained. Then, in order to understand the nonclassicality feature of the state vector of the system, the two-mode Wigner–Weyl quasi-probability distribution function is precisely derived. It is deduced from the numerical results that the domain and the maximum amount of the degree of entanglement and nonclassicality of the system can be appropriately tuned by suitably adopting the nonlinearity function and the field-mode structure parameters.

Nonlinear Jaynes–Cummings model for two interacting two-level atoms

In this work we examine a nonlinear version of the Jaynes–Cummings model for two identical two-level atoms allowing for Ising-like and dipole–dipole interplays between them. The model is said to be nonlinear in the sense that it can incorporate both a general intensity-dependent interaction between the atomic system and the cavity field and/or the presence of a nonlinear medium inside the cavity. As an example, we consider a particular type of atom-field coupling based upon the so-called Buck–Sukumar model and a lossless Kerr-like cavity. We describe the possible effects of such features on the evolution of some quantities of current interest, such as atomic excitation, purity, concurrence, the entropy of the field and the evolution of the latter in phase space.

Non-equilibrium dynamics of a nonlinear Jaynes–Cummings model in cavity arrays

We analyze in detail an open cavity array using mean-field description, where each cavity field is coupled to a number of three-level atoms. Such a system is highly tunable and can be described by a Jaynes–Cummings like Hamiltonian with additional nonlinear terms. In the single cavity case we provide simple analytic solutions and show, that the system features a bistable region. The extra nonlinear term gives rise to a rich dynamical behavior including occurrence of limit cycles through Hopf bifurcations. In the limit of large nonlinearity, the system exhibits an Ising like phase transition as the coupling between light and matter is varied. We then discuss how these results extend to the two-dimensional case.

Temporal Behavior of Rabi Oscillation in Nanomechanical QED System with a Nonlinear Resonator

In nanomechanical QED system, consisting of a charge qubit and a nanomechanical resonator with intrinsic nonlinearity, we study the temporal behavior of Rabi oscillation in the nonlinear Jaynes–Cummings model. Using microscopic master equation approach, we solve time evolution of the density operator describing this model. Also, the probability of excited state of charge qubit is calculated. These analytic calculations show how nonlinearity parameter and decay rates of two different excited states of the qubit-resonator system affect time-oscillating and decaying of Rabi oscillation.

Deformed photon-added entangled squeezed vacuum and one-photon states: Entanglement, polarization, and nonclassical properties

In this paper, after a brief review on the entangled squeezed states, we produce a new class of the continuous-variable-type entangled states, namely, deformed photon-added entangled squeezed states. These states are obtained via the iterated action of the f-deformed creation operator A = f (n)a† on the entangled squeezed states. In the continuation, by studying the criteria such as the degree of entanglement, quantum polarization as well as sub-Poissonian photon statistics, the two-mode correlation function, one-mode and two-mode squeezing, we investigate the nonclassical behaviors of the introduced states in detail by choosing a particular f-deformation function. It is revealed that the above-mentioned physical properties can be affected and so may be tuned by justifying the excitation number, after choosing a nonlinearity function. Finally, to generate the introduced states, we propose a theoretical scheme using the nonlinear Jaynes–Cummings model.

Entanglement analysis of a two-atom nonlinear Jaynes–Cummings model with nondegenerate two-photon transition, Kerr nonlinearity, and two-mode Stark shift

An entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of a detuning parameter and Stark effect. It is assumed that the atom–field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom–field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately.

Quantum Decoherence of Charge Qubit Coupled to Nonlinear Nanomechanical Resonator

When the nonlinearity of nanomechanical resonator is not negligible, the quantum decoherence of charge qubit is studied analytically. Using nonlinear Jaynes—Cummings model, one explores the possibility of being quantum data bus for nonlinear nanomechanical resonator, the nonlinearity destroys the dynamical quantum information-storage and maintains the revival of quantum coherence of charge qubit. With the calculation of decoherence factor, we demonstrate the influence of the nonlinearity of nanomechanical resonator on engineered decoherence of charge qubit.

Collapse revival behaviour of the entanglement between V-type three-level atoms and two-mode photons in nonlinear Jaynes–Cummings model

In this paper the time evolution of von Neumann entropy, as a measure of entanglement between V-type three-level atoms and the union of a two-mode field, is studied. The atom–field interaction is assumed to occur in a Kerr-type medium with an intensity-dependent coupling. Introducing a Casmir operator whose eigenvalues, N, give total excitations in the system and commutes with the governing Hamiltonian, it is concluded that the latter is block-diagonal with ever growing dimensions. As we shall show, however, each block consists of two 2 × 2 blocks while all the others, (N −1) in number, are 3 × 3. We then proceed to analytically calculate the time-evolution operator which is also block-diagonal, each block with the same properties as that of the Hamiltonian. Our calculations show that, as expected, the atom–field entanglement oscillates which, depending upon the initial state, exhibits the phenomenon of collapse revivals. It is further shown that collapse revivals occur whenever both 2 × 2 blocks are involved in the time evolution of the system. Properties of such behaviour in the entanglement are also discussed in detail.

The f-deformed Jaynes–Cummings model and its nonlinear coherent states

Based on the f-oscillator formalism, we introduce a nonlinear Jaynes–Cummings model (NJCM) which is constructed from the standard JCM by deforming the single-mode field operators. Such a generalization of the JCM describes the interaction of a two-level atom with a single mode of the electromagnetic field in the presence of a nonlinear Kerr-like medium. Since the medium is modelled as an f-oscillator, it is possible to consider the field f-coherent states (nonlinear coherent states) and their evolution.

Evolution properties of the field quantum entropy in the nonlinear Jaynes-Cummings model of a trapped ion

The time evolution properties of the field quantum entropy in the system of a trapped ion interacting resonantly with a standing-wave laser field is studied by utilizing the Von Neumann reduced quantum entropy theory, and our attention focuses on the discussion of the influence of the Lamb-Dick parameter, the position of the ion in the standing-wave laser field and the initial state of the trapped ion on the evolution properties of the field quantum entropy. The results obtained from the numerical calculation indicate that: the value of the Lamb-Dick parameter effect the oscillation frequency and amplitude of the quantum entanglement between the trapped ion and the standing-wave laser field, the larger the Lamb-Dick parameter is, the weaker the average entanglement level between the ion and the field will be. When moving the tapped ion from the node of the standing-wave laser to the loop, the vibration frequency of the quantum entanglement between the field and the ion becomes slow gradually, and the entanglement degree gets weaker and weaker. With the decrease of the probability of the trapped ion being in the excited state, the quantum entanglement between the trapped ion and the stanging-wave laser field shows the tendency of increase first and then decrease. These properties have certain reference value for the preparation of entangled states and for the quantum communications with the thapped ion, and so on.

Output entanglement from SU(1, 1) coherent states under nonlinear dissipation in the dispersive limit

An analytical solution is found for the master equation of a system described by a nonlinear Jaynes–Cummings model, in the presence of nonlinear quantum dissipation at zero temperature in the large detuning approximation. We study the influence of nonlinear quantum dissipation on the output entanglement dynamics of the atom–field system, considering the field to be initially in SU(1, 1) coherent states. It is found that in the presence of the nonlinear quantum dissipation, the amplitude of the output entanglement between the field and the atom decreases with time, however the entanglement between the field–atom system and the environment increases with time.