Double Jaynes-Cummings Model Research Articles

The role of thermal and squeezed photons in the entanglement dynamics of the double Jaynes–Cummings model

The effects of squeezed photons and thermal photons on the entanglement dynamics of atom-atom, atom-field and field-field subsystems are studied for the double Jaynes–Cummings model. For this purpose, squeezed coherent states and Glauber-Lachs states of radiation are chosen as field states. For the atomic states, we choose one of the Bell state as pure state and a Werner-type state as mixed state. Werner-type state is used to understand the effects of mixedness on entanglement. To measure the entanglement between the two atoms, Wootters’ concurrence is used; whereas for the atom-field and field-field subsystems, negativity is chosen. The squeezed photons and thermal photons create, destroy and transfer entanglement within various subsystems. Also, the addition of squeezed photons and thermal photons either lengthens or shortens the duration of entanglement sudden deaths (ESD) associated with atom-atom, atom-field and field-field entanglement dynamics in a complementary way. The effects of Ising-type interaction, detuning and Kerr-nonlinearity on the entanglement dynamics are studied. Each of these interactions removes the ESDs associated with various subsystems. We show that new entanglements are created in this atom-field system by introducing Ising-type interaction between the two atoms. With proper choice of the parameters corresponding to Ising-type interaction, detuning and Kerr-nonliearity, entanglement can be transferred among various subsystems.

Dynamics of a multipartite hybrid quantum system with beamsplitter, dipole–dipole, and Ising interactions

The possibility of exploiting heterogeneous quantum systems to high precision, for storing, processing, and transmitting information, makes them ideal candidates for multitasking purposes in quantum communication. Appropriate quantum systems involving a judicious choice of interactions that augment each other are potentially useful for probing deep into quantum regimes. Here, we use one such hybrid bipartite quantum model, with one subsystem made of a pair of qubits and another comprising a pair of oscillators, to study the entanglement dynamics and the entanglement transfer between discrete and continuous variables. The basic model is the standard double Jaynes–Cummings model, which, under suitable conditions, is known to support both entanglement transfer and entanglement sudden death. In this work, we generalize this model to include further experimentally relevant interactions, such as the beamsplitter-type exchange interaction between the oscillators, and dipole–dipole and Ising-type interactions between the qubits. The way various interactions and initial oscillator states affect the entanglement dynamics is examined theoretically for generic experimental conditions. Using exact analytical solutions, we show that, compared to the beamsplitter or dipole–dipole interaction, the Ising interaction can have a significant positive impact on entanglement sudden death and birth, and the postponement of the onset of these phenomena, apart from producing a substantial reduction in the time duration of the death.

The interplay of symmetry with the Rabi oscillation in the non-Hermitian double Jaynes–Cummings model

We study the dynamical evolution and symmetry breaking of the non-Hermitian double Jaynes–Cummings model with symmetry. The results indicate that there exist symmetry maintained and breaking phase in this model, and the non-Hermitian terms lead to different behaviors in two phases. In the symmetry phase, there exists stable Rabi oscillation caused by the interaction between photons and atoms. At the exceptional point, the system shows critical property that the probabilities in each state over time tend to be equal. The system will undergo a transition from the symmetry phase to the symmetry breaking phase, as increasing the coupling constant. In the symmetry breaking phase, complex eigenvalues appear, and the probability in each state increases monotonically in an exponential form. This study can help us to understand the effect of symmetry on the interaction between photons and atoms in non-Hermitian systems.

Dynamic behavior of the quantum correlations of two cavity fields in the double Jaynes–Cummings model

The influence of the atom’s spatial degrees of freedom and the purity of the initial state on the dynamics of Bell non-locality, entanglement, geometric measure of quantum discord (GMQD) and quantum discord in a double Jaynes–Cummings model are investigated. We study the above four quantum correlations for an initial Werner-like state between the electronic states of the two atoms and between the two cavities respectively and find that all these quantum correlations are sensitive to the wave packet width and the purity of the initial state. For Bell non-locality, we find the phenomenon of sudden death and sudden birth, whereas the other three quantum correlations decay to zero asymptotically. We find that both the wave packet width and the purity of the initial state affect the GMQD and quantum discord in a similar way and we also notice that GMQD and quantum discord always exist, except where the purity of the initial state is zero, while Bell non-locality and entanglement can occur only when the purity meets certain conditions.

Influence of detuning and Kerr nonlinearity on atom-atom entanglement in the double two-photon Jaynes–Cummings model

In this work, the authors investigated the dynamics of entanglement of two identical two-level atoms (qubits) in the framework of the two-photon double Jaynes–Cummings model, taking into account the detuning between atoms and the double frequency of the field modes of the resonators, as well as the Kerr medium in both resonators. The authors derived the time dependence of the negativity parameter for the Bell initial states of the atoms and the vacuum states of the resonator fields. The results showed that detuning and Kerr nonlinearity leads to stabilization of the entanglement for all initial Bell-type atomic states. For some initial atomic entanglement states, the detuning and Kerr environment in the resonators can prevent the effect of sudden death of the atom-atom entanglement.

Thermal entanglement in a double Jaynes–Cummings model

In this paper, we have investigated the entanglement dynamics between two initially entangled qubits interacting with two independent thermal cavities modes in the framework of resonant double Jaynes–Cummings model. We obtain the exact solution for the model under consideration and derive the time dependence of the atom-atom negativity. Results reveal that for entangled atoms the initial atomic quantum correlations can partially restore its original values for a finite interval of time, even for relatively high cavity temperatures.

Population inversion and entanglement in single and double glassy Jaynes-Cummings models

We find that a suppression of the collapse and revival of population inversion occurs in response to insertion of Gaussian quenched disorder in atom-cavity interaction strength in the Jaynes-Cummings model. The character of suppression can be significantly different in the presence of non-Gaussian disorder, which we uncover by studying the cases when the disorder is uniform, discrete, and Cauchy-Lorentz. Interestingly, the quenched averaged atom-photon entanglement keeps displaying nontrivial oscillations even after the population inversion has been suppressed. Subsequently, we show that disorder in atom-cavity interactions helps to avoid sudden death of atom-atom entanglement in the double Jaynes-Cummings model. We identify the minimal disorder strengths required to eliminate the possibility of sudden death. We also investigate the response of entanglement sudden death in the disordered double Jaynes-Cummings model in the presence of atom-atom coupling.

Tomographic entanglement indicators in multipartite systems

We assess the performance of an entanglement indicator which can be obtained directly from tomograms, avoiding state reconstruction procedures. In earlier work, we have examined this tomographic entanglement indicator, and a variant obtained from it, in the context of continuous variable systems. It has been shown that, in multipartite systems of radiation fields, these indicators fare as well as standard measures of entanglement. In this paper, we assess these indicators in the case of two generic hybrid quantum systems, the double Jaynes-Cummings model and the double Tavis-Cummings model using, for purposes of comparison, the quantum mutual information as a standard reference for both quantum correlations and entanglement. The dynamics of entanglement is investigated in both models over a sufficiently long time interval. We establish that the tomographic indicator provides a good estimate of the extent of entanglement both in the atomic subsystems and in the field subsystems. An indicator obtained from the tomographic indicator as an approximation, however, does not capture the entanglement properties of atomic subsystems, although it is useful for field subsystems. Our results are inferred from numerical calculations based on the two models, simulations of relevant equivalent circuits in both cases, and experiments performed on the IBM computing platform.

Entanglement Between Two Dipole-Coupled Qubits Interacting with Two Independent Slightly Detuned Cavity Modes

Considering the generalized double Jaynes-Cummings model, we examine the entanglement between two non-identical dipole-dipole coupled qubits interacting with two independent detuned vacuum cavity modes. We calculate the negativity as a measure of qubits entanglement. We find that entanglement parameter evolve periodically with time and the period are affected by the model parameters and initial states of qubits. For unentangled initial states the detuning and dipole-dipole interaction affect only the period of entanglement oscillations, not the maximum value of entanglement. For entangled states the detuning stabilizes the entanglement parameter oscillations. According to choice of initial entangled state the dipole-dipole strength is greatly enhances or weakens the oscillations of the entanglement parameter.

Collapse and revival oscillation in Double Jaynes–Cummings model

We develop a systematic method of solving two non-interacting Jaynes-Cummings models by using the dressed state formalism in Hilbert space $\mathcal{H}_{AB}^{(2\otimes2)}$. It is shown that such model, called Double Jaynes-Cummings model (D-JCM), can be exactly solved if we take the initial bare state as the linear superposition of two Bell states. The collapse and revival oscillation, which is the standard trait of typical Jaynes-Cummings model, can be recovered if we make measurement at each local sites. Some consequence of the entanglement-induced dressing is discussed.

Effects of cavity–cavity interaction on the entanglement dynamics of a generalized double Jaynes–Cummings model

We consider a generalized double Jaynes–Cummings model consisting of two isolated two-level atoms, each contained in a lossless cavity that interact with each other through a controlled photon-hopping mechanism. We analytically show that at low values of such a mediated cavity–cavity interaction, the temporal evolution of entanglement between the atoms, under the effects of cavity perturbation, exhibits the well-known phenomenon of entanglement sudden death (ESD). Interestingly, for moderately large interaction values, a complete preclusion of ESD is achieved, irrespective of its value in the initial atomic state. Our results provide a model to sustain entanglement between two atomic qubits, under the adverse effect of cavity induced perturbation, by introducing a non-intrusive inter-cavity photon exchange that can be physically realized through cavity-QED setups in contemporary experiments.

Analytical solution and entanglement swapping of a double Jaynes–Cummings model in non-Markovian environments

Analytical solution and entanglement swapping of a double Jaynes-Cummings model in non-Markovian environments are investigated by the timeconvolutionless master equation method. We obtain the analytical solution of this model and discuss in detail the influence of atom-cavity coupling, non-Markovian effect and initial state purity on entanglement dynamics. The results show that, in the non-Markovian environments, the entanglement between two cavities can be swapped to other bipartite subsystems by interaction between an atom and its own cavity. Due to the dissipation of environment, the entanglements of all bipartite subsystems will eventually decay to zero when the atom couples weakly to its cavity and the non-Markovian effect is also weak. All bipartite subsystems can tend to steady entanglement states if and only if there is the strong atom-cavity coupling or the strong non-Markovian effect. The steady state of the subsystem composed of an atom and its own cavity is independent on the purity but the steady states of other bipartite subsystems are dependent on the purity.

The Collapse and Revival of Bell-nonlocaliy for Continuous Variables

We study the quantum nonlocality dynamics of pair coherent states in the double Jaynes-Cummings model. It is shown that the Bell-inequality violation can be fully destroyed in a finite time and then recovered. The inequality violation can obtain better recovery when only one atom couples to either of the cavity fields. Besides, the correlation property of cavity fields is more feasible affected when the atom interacts resonantly with the second cavity field. The difference in the number of photons of the two modes may play an important role in the case of resonant interaciton especially.

Geometry in the Entanglement Dynamics of the Double Jaynes–Cummings Model

We report on the geometric character of the entanglement dynamics of two pairs of qubits evolving according to the double Jaynes–Cummings model. We show that the entanglement dynamics for the initial states | ψ 0〉 = cos α | 10〉 + sin α | 01〉 and | ϕ 0〉 = cos α | 11〉 + sin α | 00〉 cover three-dimensional surfaces in the diagram C ij × C ik × C il , where C mn stands for the concurrence between qubits m and n, varying 0 ≤ α ≤ π / 2. In the first case, projections of the surfaces on a diagram C ij × C kl are conics. In the second case, curves can be more complex. We relate those conics with a measurable quantity, the predictability. We also derive inequalities limiting the sum of the squares of the concurrence of every bipartition and show that sudden death of entanglement is intimately connected to the size of the average radius of a hypersphere.

Quantum correlations between two non-interacting atoms under the influence of a thermal environment

By considering a double Jaynes—Cummings model, we investigate the dynamics of quantum correlations, such as the quantum discord and the entanglement, for two atoms in their respective noisy environments, and study the effect of the purity and the cavity temperature on the quantum correlations. The results show that the entanglement suffers sudden death and revival, however the quantum discord can still reveal the quantum correlations between the two atoms in the region where the entanglement is zero. Moreover, when the temperature of each cavity is high the entanglement dies out in a short time, but the quantum discord still survives for quite a long time. It means that the quantum discord is more resistant to environmental disturbance than the entanglement at higher temperatures.

Effect of the Stark shift on entanglement in a double Jaynes-Cummings model in thermal environment

Considering a double two-photon Jaynes-Cummings (J-C) model, we study the effects of Stark shift and mean photon number on entanglement between two two-level atoms when the atoms are initially in a maximally entangled state and the fields are in the single-mode thermal fields. The results show that the two atoms evolve periodically into a disentangled separable state when Stark shift is not considered. However, in the presence of Stark shift, the two two-level atoms are no longer disentangled and long-lived entanglement can be obtained. For a larger value of the Stark shift parameter and a smaller mean photon number, the two atoms can remain in a stationary entangled state. These properties show that the Stark shift can be used to control entanglement in the double two-photon J-C model under the influence of thermal environment.

Entanglement Dynamics of the Double Intensity-Dependent Coupling Jaynes-Cummings Models

We consider entanglement dynamics of double intensity-dependent coupling Jaynes-Cummings models with two different initial light fields, which one is in the squeezed vacuum state and another is in the coherent state. The results show that, when the compressibility factor and the mean photon number are smaller, the concurrence of atoms exhibits phenomenon of dead and revival periodically, and the entanglement perfectly transferres between the atoms and the fields. As the value of them grow larger, the entanglement sudden death and sudden revival come out. Comparing with the normal double Jaynes-Cummings model, we notice that the concurrence of the atoms which in the normal double Jaynes-Cummings models evolves irregularly. And it is find that periodical entanglement pulse can be generated by using double intensity-dependent coupling Jaynes-Cummings models. This result might be useful in quantum information processes.

Tunable Entanglement Sudden Death and Birth in Cavity QED with Nonlinear Kerr-Like Medium

The influence of nonlinear Kerr-like medium on the phenomenon of entanglement sudden death and birth in a double Jaynes–Cummings model is investigated. It is shown that the entanglement sudden death and birth phenomenon may appear in this system and the duration of entanglement sudden death and birth can be controlled by the nonlinear Kerr-like medium. Particularly, the phenomenon of entanglement sudden death and birth disappears one after another if we increase the value of the Kerr coefficient χ continuously, and all disappears if the value of the Kerr coefficient χ is large enough.

Evolution of Bell-nonlocality of two cavity fields in the double Jaynes-Cummings model

The Bell-nonlocality of two initially entangled macroscopic fields in the double Jaynes-Cummings model is investigated. Moreover, the process by which detuning between the atomic transition frequency and the field frequency affects the evolution of the Bell-nonlocality of two macroscopic fields is studied. The effect of the disparity between the two coupling strengths is discussed.

Exact solution of entanglement of the double Jaynes–Cummings model without rotating wave approximation

This paper investigates the influences of atom-field coupling and dipole–dipole coupling for atoms on the entanglement between two atoms by means of concurrence. The results show that the sudden death occurs when the atom-field coupling is strong enough, and the collapse and the revival appear when the dipole–dipole interaction is strong enough.