In this paper we study the production of entanglement between two atoms which are far from each other. We consider a system including eight two-level atoms (1, 2, ⋯, 8) such that any atom with its adjacent atom is in an atomic Bell state, so that we have four separate pairs of maximally entangled states where . Our purpose is to produce entanglement between the atomic pair (1, 8), while these two distant atoms have no interaction. By performing the interaction between adjacent non-entangled atomic pairs (2, 3) as well as (6, 7), each pair with a two-mode quantized field, the entanglement is produced between atoms (1, 4) and (5, 8), respectively. Finally, by applying an appropriate Bell state measurement (BSM) on atoms (4, 5) or performing an interaction between them with a single-mode field (quantum electrodynamic: QED method), the qubit pair (1, 8) becomes entangled and so the quantum repeater is successfully achieved. This swapped entanglement is then quantified via concurrence measure and the effects of coupling coefficients and detuning on the concurrence and success probability are numerically investigated. The maxima of concurrence and success probability and the corresponding time periods have been decreased by increasing the detuning in asymmetric condition in the BSM method. Also, the effects of detuning, initial interaction time and coupling coefficient on the produced entanglement by the QED method are considered. Increasing (decreasing) of the detuning (interaction time) has a destructive effect on the swapped entanglement in asymmetric condition.
In this paper we study the production of entanglement between two atoms which are far from each other. We consider a system including eight two-level atoms (1, 2, ⋯, 8) such that any atom with its adjacent atom is in an atomic Bell state, so that we have four separate pairs of maximally entangled states where . Our purpose is to produce entanglement between the atomic pair (1, 8), while these two distant atoms have no interaction. By performing the interaction between adjacent non-entangled atomic pairs (2, 3) as well as (6, 7), each pair with a two-mode quantized field, the entanglement is produced between atoms (1, 4) and (5, 8), respectively. Finally, by applying an appropriate Bell state measurement (BSM) on atoms (4, 5) or performing an interaction between them with a single-mode field (quantum electrodynamic: QED method), the qubit pair (1, 8) becomes entangled and so the quantum repeater is successfully achieved. This swapped entanglement is then quantified via concurrence measure and the effects of coupling coefficients and detuning on the concurrence and success probability are numerically investigated. The maxima of concurrence and success probability and the corresponding time periods have been decreased by increasing the detuning in asymmetric condition in the BSM method. Also, the effects of detuning, initial interaction time and coupling coefficient on the produced entanglement by the QED method are considered. Increasing (decreasing) of the detuning (interaction time) has a destructive effect on the swapped entanglement in asymmetric condition.
Abstract In this paper we want to investigate the possibility of transferring entanglement to two three-level separable atomic states over long distance using the quantum repeater protocol. In detail, our model consists of eight Λ-type three-level atoms where only the pairs (1, 2), (3, 4), (5, 6) and (7, 8) are prepared in maximally entangled states. Performing suitable interaction between non-entangled three-level atoms (2, 3) and (6, 7) in two-mode cavities with photon leakage rates κ , κ ′ in the presence of spontaneous emission leads to producing entanglement between atoms (1, 4) and (5, 8), separately. Finally, the entanglement between atoms (1, 8) is successfully produced by performing interaction between atoms (4, 5) while spontaneous emission is considered in a dissipative cavity. In the continuation, the effects of detuning, dissipation sources and initial interaction time are evaluated on the negativity and success probability of the processes. It is shown that, the maxima of negativity are decreased by increasing the detuning, in most cases. Also, the time evolution of negativity is non-periodic in the presence of dissipation. In addition, increasing the initial interaction time has a constructive effect on the negativity in all considered cases. The oscillations of negativity are destroyed as time goes on and the produced entanglement becomes stable. The success probability of entangled state of atoms (1, 8) is tunable by controlling the detuning and dissipation. We show that via justifying the involved parameters one can arrive at conditions in which the decoherence effects are fully disappeared; as a result, an ideal quantum repeater can be properly achieved while atomic and field dissipations are taken into account.
In this paper, we consider the quantum repeater protocol for distributing the entanglement to two distant three-level atoms. In this protocol, we insert six atoms between two target atoms, such that the eight considered atoms are labeled by 1,2,⋯8, while only each two adjacent atoms (i,i+1) with i=1,3,5,7 are entangled. Initially, the separable atomic pair states (1,4) and (5,8) become entangled by performing interaction between atoms (2,3) and (6,7) in two optomechanical cavities, respectively. Then, via performing appropriate interaction between atoms (4,5) in an optical cavity quantum electrodynamics approach, the target atoms (1,8) finally become entangled. Throughout this investigation, the effects of mechanical frequency and optomechanical coupling strength to the field modes on the produced entanglement and the related success probability are evaluated. It is shown that the time period of produced entanglement can be developed by increasing the mechanical frequency. Also, the maximum of the success probability of atoms (1,8) is increased by decreasing the optomechanical coupling strength to the field modes in most cases.
Considering the dipole-dipole coupling intensity between two atoms and the field in the Fock state, the entanglement dynamics between two atoms that are initially entangled in the system of two two-level atoms coupled to a single mode cavity in the presence of phase decoherence has been investigated. The two-atom entanglement appears with periodicity without considering phase decoherence, however, the phase decoherence causes the decay of entanglement between two atoms, with the increasing of the phase decoherence coefficient, the entanglement will quickly become a constant value, which is affected by the two-atom initial state. Meanwhile the two-atom quantum state will forever stay in the maximal entangled state when the initial state is proper even in the presence of phase decoherence. On the other hand, the Bell violation and the entanglement do not satisfy the monotonous relation, a large Bell violation implies the presence of a large amount of entanglement under certain conditions, while a large Bell violation corresponds to a little amount of entanglement in certain situations. However, the violation of Bell-CHSH inequality can reach the maximal value if two atoms are in the maximal entangled state, or vice versa.
A detailed treatment of the entanglement dynamics of two distant but non-identical systems is presented. We study the entanglement evolution of two remote atoms interacting independently with a cavity field, as in the double Jaynes–Cummings model. The four-qubit pairwise concurrences are studied, allowing for asymmetric atom–cavity couplings and off-resonant interactions. Counter to intuition, imperfect matching can prove advantageous to entanglement creation and evolution. For two types of initial entanglement, corresponding to spin-correlated and anti-correlated Bell states Φ and Ψ, a full, periodic and directed transfer of entanglement into a specific qubit pair is possible, for resonant interactions, depending on the choice of relative couplings. Furthermore, entanglement transfer and sudden death (ESD) can be prevented using off-resonant interactions, although for some initial states, detunings will trigger an otherwise frozen entanglement, to allow a full entanglement transfer.
Abstract Entanglement between two identical two-level atoms (qubits) that interact nonresonantly with the thermal field of a single-mode ideal resonator via effective degenerate two-photon transitions is studied. Based on an exact solution for the time-dependent density matrix, negativity is calculated as a measure of atom entanglement. The effect detuning between the atomic frequencies and the doubled frequency of the resonator field has on the dynamics of qubit entanglement in cases of separable and entangled initial atomic states is investigated.
We consider two non interacting two-atoms Tavis-Cummings systems and examine the entanglement among four two-state atoms. For our purpose, we assume that one atom from each system are entangled initially and we obtain time-dependent concurrence among atoms. There are six pairwise concurrences among atoms and in this paper, we focus on remote atoms. We show that initially non-entangled atoms and becomes entangled by passing time, the process which may be interpreted as entanglement transfer between the cavities.