Nondegenerate Two-photon Transitions Research Articles

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.

Controlling the entanglement of a Λ-type atom in a bimodal cavity via atomic motion

In this paper, a model describing the interaction between a moving three-level atom and a two-mode cavity field with nondegenerate two-photon transitions is considered in the presence of intensity-dependent coupling and detuning parameters. In order to evaluate entanglement between subsystems, the exact time dependence of the state vector of the overall system is obtained. After studying the dynamics of the atom by considering atomic population inversion, entanglement of formation as a suitable measure of entanglement degree is discussed in detail. It is deduced from the numerical results that the domain and the maximum amount of the degree of entanglement can be suitably controlled by appropriately choosing the intensity-dependent nonlinearity function, the field-mode structure parameters, and detuning.

The influence of atomic coherence and dipole–dipole interaction on entanglement of two qubits with nondegenerate two-photon transitions

Considering two artificial identical atoms interacting with two-mode thermal field through non-degenerate two-photon transitions, this paper studies the influence of atomic coherence and dipole–dipole interaction on the entanglement of two qubits. It is found that the entanglement is greatly enhanced by these mechanisms.

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.

The dynamics of entanglement in two-atom Tavis–Cummings model with non-degenerate two-photon transitions for four-qubits initial atom-field entangled states

The influence of dipole–dipole interaction on the entanglement between two Δ-type artificial atoms interacting with two-mode field via non-degenerate two-photon transitions has been investigated. The atom-field system is assumed to be prepared in four-partite atom-field entangled state. The results show that the entanglement between two atoms can be increased by means of dipole–dipole interaction and for some initial states the entanglement sudden death effect can be weakened.

Effects of cavity-field statistics on atomic entanglement in a two-mode Jaynes–Cummings model with intensity-dependent coupling

We study the entanglement properties of a pair of two-level Rydberg atoms passing one after another into a lossless cavity with two modes. The atoms interact with the cavity field via an intensity-dependent, non-degenerate two-photon transition. The initial joint state of two successive atoms that enter the cavity is unentangled. Interactions mediated by the two-mode cavity photon field result in the final two-atom mixed entangled type state. The entanglement of formation of the joint two-atom state as a function of the Rabi angle, gt, is calculated for the two-mode Fock state field, coherent field, and thermal field, respectively, inside the cavity. The change in the magnitude of atomic entanglement with cavity photon number in two modes has been studied.

ENTANGLEMENT OF TWO DIPOLE-COUPLED ATOMS INTERACTING WITH TWO-MODE THERMAL FIELD IN THE CAVITY WITH HIGH TEMPERATURE

The entanglement of two dipole-coupled atoms with nondegenerate two-photon transitions interacting with two-mode field in lossless cavity has been investigated. The possibility of considerable growth of atomic entanglement is shown in the case of great mean values of thermal photons.

Exact Solutions for Jaynes-Cummings Models with Non-degenerate Two-Photon Transitions in the Ladder Configuration

In the present paper, the eigenfunctions and eigenvalues of the Hamiltonian of the interacting system have been obtained in two generalized Jaynes Cummings models separately, one in which the transition are mediated by two different modes of photon in the ladder configuration and the other involving two mode multi-photon interaction between the field and the atom. Effect of intensity dependent coupling between the field and the atom in both the above-mentioned cases have been investigated. Graphical features of the time dependence of population inversion have been analyzed when one of the field modes is prepared initially in a coherent state while the other one in a vacuum state. The unitary transformation method presented here for the special case of exact resonance not only solves the time-dependent problem but also provides the eigensolutions of the interacting Hamiltonian at the same time.

Atom-field entanglement in two-atom Jaynes–Cummings model with nondegenerate two-photon transitions

An exact solution of the problem of two two-level atoms with nondegenerate two-photon transitions and nondegenerate Raman transitions interacting with two-mode radiation field is presented. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom-field entanglement is investigated on the basis of the reduced atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process for both models is shown. Conditions and times of disentanglement are derived.

Dynamics of the two-atom Jaynes-Cummings model with nondegenerate two-photon transitions

An exact solution is found for the collective model of two identical two-level atoms that resonantly interact with a two-mode quantum electromagnetic field in an ideal cavity via two-photon nondegenerate transitions. In the case under study, at the initial moment, both field modes are in the coherent state and atoms are in the excited state. The time dependences of the atomic probabilities, the mean number of photons in the modes, and the statistics and squeezing of the photon modes are studied based on the exact solution.

Theory of the nondegenerate two-photon micromaser.

We present the theory of a microscopic maser operating on a nondegenerate two-photon transition between two states of same parity. We start from a three-level Hamiltonian, and discuss both the one-photon resonant cascade and the two-photon regime, when the intermediate state is far off resonance. In the semiclassical limit, we derive rate equations for the field intensities and get the corresponding steady-state values. The vacuum is stable in the two-photon regime but becomes unstable for zero detuning (a clear signature of a one-photon process). Solutions displaying true two-photon operation (intermediate state unpopulated) even with zero detuning are displayed. Using the full quantum density-matrix approach, we derive a master equation for the field and discuss both operating regimes, showing that the spontaneous emission may turn the vacuum unstable in the two-photon case. In the off-resonance two-photon regime, there is a strong correlation between the fluctuations of the intensities of the two modes. We find a squeezing factor of 50% for the fluctuations in the difference of intensities.