Degenerate Two-photon Transitions Research Articles

Dynamics of entanglement of atoms with two-photon transitions induced by a thermal field

In this paper, we investigate the entanglement between two two-level atoms non-resonantly in-teracting with a thermal field of a lossless one-mode resonator via degenerate two-photon transi-tions. On the basis of the exact solution of the time-dependent density matrix we calculate the negativity as a measure of atomic entanglement. We show that for separable initial atomic states a slight atom-field detuning may generate the high amount of atom-atom entanglement. The re-sults also show that for non-resonant atom-field interaction the entanglement induced by nonlin-ear two-photon interaction is smaller than that induced by one-photon interaction in contrast to the resonant interaction situation. For a Bell-type entangled initial atomic state we obtain that if the detuning increases, there is an appreciable decrease in the amplitudes of the negativity oscilla-tions. The results also show that elimination of the sudden death of entanglement for non-resonant two-photon atom-field interaction may take place.

The entanglement of atoms with two-photon transitions in the presence of ac Stark shift of energy levels

In this paper, we investigated the dynamics of atomic entanglement in a quantum system consisting of two identical two-level atoms (qubits) resonantly interacting with a mode of a thermal cavity field through degenerate two-photon transitions, in the presence of a Stark energy level shift. An analytical expression is obtained for the atom entanglement (negativity) parameter for separable and entangled initial states of atoms. The influence of the Stark shift on the degree of atom-atom entanglement is considered. It is established that the Stark shift leads to a significant increase in the degree of atom entanglement in the case of separable initial states of atoms and to stabilization of atomic entanglement in the case of entangled initial states of atoms.

Atom-atom entanglement in a not-resonant two-photon Tavis-Cummings model

The entanglement between two two-level atoms (qubits) interacting not-resonantly with a one mode of thermal field in a lossless cavity via effective degenerate two-photon transitions is investigated. Based on the exact solution for the time-dependent density matrix of the system under consideration, negativity is calculated as a measure of the entanglement of atoms. The influence of a detuning on the dynamics of entanglement of atoms for separable and entangled initial atomic states and thermal cavity state is investigated.

Influence of Stark shift on entanglement of two atoms with degenerate two-photon transitions for entangled and disentangled initial states

Considering two-atom degenerate two-photon Jaynes–Cummings model, we investigate the atom–atom entanglement when (a) atoms and field are prepared initially in the entangled atom-field W- or GHZ state, (b) two atoms are prepared initially in the coherent disentangled state and the cavity field is prepared in a few-photon Fock state, and study the effect of the Stark shift on entanglement. The results show that the atom–atom negativity evolves periodically with time and the periods are affected by the Stark shift and the degree of the initial atomic coherence. Considering different initial states we derived that the atom–atom entanglement can be greatly increased or decreased due to the presence of the Stark shift. In addition, the entanglement sudden death effect vanishes due to the presence of Stark shift for some initial states.

ENTANGLEMENT OF ATOMS SUCCESIVELY PASSING A CAVITY TAKING INTO ACCOUNT THE STARK SHIFT

In the article we consider the influence of dynamical Stark shift on entanglement degree of two atoms with degenerate two-photon transitions successively passing an ideal one-mode cavity. We suppose that the field be prepared in vacuum state and the atoms be prepared in coherent superposition of excited and ground states. Thus it was also supposed that atoms fly by the cavity for identical time. On the basis of exact expression of evolution operator we carried out atom-atom entanglement for different values of two-atom coherence parameters and different values of cavity flight time. It is shown that Stark shift of energy levels can be used for effective control on a degree of atomic entanglement.

The influence of the dipole-dipole interaction and atomic coherence on the entanglement of two atoms with degenerate two-photon transitions

Entanglement of two artificial two-level atoms with degenerate two-photon transitions is considered in the case in which the atoms interact with the thermal single-mode field in an ideal cavity. The possibility of controlling the atomic entanglement degree in such a system due to the induction of atomic coherence and direct dipole-dipole interaction of atoms is shown.

Entanglement and sudden death of two two-level atoms interacting with a cavity field in presence of degenerate parametric amplifier

In the presence of degenerate two-photon transitions the problem of the interaction between two two-level atoms and a single-mode is considered. Near resonance case, a closed form of the analytic solution for the wave function is obtained. The entanglement between an atom and field in the interacting system is studied by using the change in atomic and field entropies. The relationship between entropy changes and concurrence entanglement is discussed. Our results show that the behavior of the entropy change in agreement with the behavior of the concurrence to measure the entanglement between two subsystem structures.

INFLUENCE OF STARK SHIFT ON ENTANGLEMNT OF TWO ATOMS WITH DEGENERATE TWO-PHOTON TRANSITIONS

The influence of dynamical Stark shift on the entanglement between two atoms prepared in initial W-like states in Tavis — Cummings model with degenerate two-photon transitions has been investigated. The results show that effect of sudden death of entanglement the effect can be weakened for some initial states with taking into account the Stark shift.

Entangled two two-level atoms interacting with a cavity field in the presence of the stark shift terms

The general solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a cavity single-mode radiation field in the presence of the Stark shift terms is obtained. The temporal evolution of the atomic inversion for the single-atom case, the entropy squeezing and the atomic variances squeezing are studied. We use the linear entropy and von Neumann entropy to measure the degree of entanglement between the atoms and the field. It has shown that an increase in the value of the Stark shift parameter leads to an increase in the degree of entanglement. These aspects are sensitive to changes in the Stark shift parameter.

Two coupled oscillators in the form of a frequency converter in interaction with a single atom via two-photon processes

We consider the problem of a two-level atom with degenerate two-photon transitions interacting with a single-mode radiation field in the presence of a parametric frequency-converter term. A Hamiltonian representing such a system contains three time-dependent coupling parameters. We obtain an exact solution of the wave function in the Schrodinger picture, using the canonical transform and under a certain choice of the coupling parameters. We use the results obtained to discuss the atomic inversion as well as the linear entropy in addition to both the variance and entropy squeezing. We show that the system at a certain time is sensitive to variations in both the detuning parameter Δ and the ratio of the coupling parameter g.

Entanglement for two-atom Tavis–Cummings model with degenerate two-photon transitions in the presence of the Stark shift

The dynamics of atom–field entanglement for two two-level atoms with degenerate two-photon transitions interacting with one-mode radiation field with taking into account the Stark shift is investigated. Asymptotic solutions for system state vectors are obtained in the approximation of large initial coherent fields. The atom–field entanglement is investigated also on the basis of the linear atomic entropy dynamics. The possibility of the system being initially in a pure disentangled state to revive into this state during the evolution process is shown. Conditions and times of disentanglement are derived.

THE INFLUENCE OF DIPOLE-DIPOLE INTERACTION ON THE SUDDEN DEATH OF ENTANGLEMENT OF TWO ATOMS WITH DEGENERATE TWO-PHOTON TRANSITIONS

The influence of dipole-dipole interaction on the entanglement between twoatoms with different initial W-like states in Tavis-Cummings model with degenerate two-photon transitions has been investigated. The results show that theentanglement between two atoms can be increased by means of dipole-dipoleinteraction and for some initial states the sudden death effect can be weakened.

Entanglement in the degenerate two-photon Tavis–Cummings model

An exact solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a one-mode coherent 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 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 the model considered is shown. The conditions and times of disentanglement are derived.

Entropic uncertainty in two two-level atoms interacting with a cavity field in presence of degenerate parametric amplifier

The analytical solution of the problem of two two-level atoms with degenerate two-photon transitions interacting with a single-mode radiation field in the presence of a parametric amplifier term is presented. The purity of the atomic state has been used to measure the degree of entanglement between the atom and the field. The temporal evolution of variance and entropy squeezing as well as atomic inversion for the single-atom case are studied. It has been shown that maximum squeezing for the variance and entropy squeezing occurs when the ratio between the amplifier coupling λ3 and the field frequency ω equals 0.26. Increasing the value of the ratio λ3/ω further leads to the vanishing of squeezing from the system. It is also noted that the existence of the coupling parameter results in the system never reaching the pure state except at the points of revival times. The Q function has been also considered to give more information in the phase space about the system. These aspects are sensitive to changes in the amplifier parameter.