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.
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 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 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.
In this paper, a scheme for the generation of long-living entanglement between two distant Λ-type three-level atoms separately trapped in two dissipative cavities is proposed. In this scheme, two dissipative cavities are coupled to their own non-Markovian environments and two three-level atoms are driven by the classical fields. The entangled state between the two atoms is produced by performing Bell state measurement (BSM) on photons leaving the dissipative cavities. Using the time-dependent Schördinger equation, we obtain the analytical results for the evolution of the entanglement. It is revealed that, by manipulating the detunings of classical field, the long-living stationary entanglement between two atoms can be generated in the presence of dissipation.
This thesis is an exploration of quantum repeaters from a practical point of view. Quantum repeaters are devices which help improve the quantum communication capacity of a lossy bosonic channel (which include photonic channels such as optical fiber) beyond what is possible using a purely lossy channel. The analyses in this thesis involve modeling the experimental imperfections inherent in the various devices which comprise a quantum repeater, then combining these models to calculate various quantities of interest. \n \nTwo systems are analyzed in this thesis. One is a simple quantum repeater, while the other is a potential building block for more complex quantum repeaters. \n \nThe simple quantum repeater scheme can be implemented with currently available technology. In it, two parties perform quantum key distribution (QKD) by exchanging photons with two quantum memories placed between them. Its secret key rate ideally scales as the square root of the transmittivity of the optical channel, which is superior to QKD schemes based on direct transmission because key rates for the latter scale at best linearly with transmittivity. Taking into account imperfections in the setup, such as detector efficiency and dark counts, we present parameter regimes in which our protocol outperforms protocols based on direct transmission. We find that implementing our scheme with trapped ions is a promising way to reach the necessary parameter regimes, and that the regimes are easier to reach if the optical channels are very lossy. \n \nThe creation of entanglement between two quantum memories is an important building block in some quantum repeater schemes. We consider a specific quantum memory consisting of an atom trapped in a cavity. The system allows a CNOT operation to be performed between an atom and a photon. We study three methods for taking advantage of this to entangle two atoms: (1) interacting a coherent pulse with each atom, then performing an entangling measurement on the pulses; (2) interacting a single coherent pulse with each atom sequentially; (3) emitting an entangled photon from one atom and interacting it with the other atom. The success probability of each method is compared, as well as the quality of the entangled states produced by each one, taking into account imperfections which appear in a specific experimental implementation of such memories. We find that there is a tradeoff between success probability and entangled state quality when coherent states are used, and that method 3 provides higher-quality entangled states than is possible with the other two methods.
The entanglement between two identical two-level atoms successively passing a vacuum or a thermal cavity has been investigated taking into account the detuning. The cases when atoms are initially prepared in the separable two-atom or Bell type entangled atomic states have been considered. It has been shown that thermal field can produce the entanglement between Rydberg atoms successively passing a cavity for all considered initial atomic states. For separable initial atomic states and vacuum state of the cavity the presence of detuning leads to decreasing of the degree of atomic entanglement. For entangled initial atomic states and vacuum state of the cavity the presence of detuning leads to decreasing of the entanglement amplitude oscillations. We have also derived that for thermal field the increasing of the mean photon number leads to decreasing of the entanglement, but the entanglement increases as the detuning increases. For thermal field and small detuning we have established that the effect of sudden death and birth of entanglement takes place and that for large detuning such effect vanishes. Results of the computer simulation are presented.
In this paper, the dynamics of a system consisting of a three-level atom, which interacts with a single-mode quantized field in a lossy cavity, is studied in the presence of the dependence of atom–field coupling and third-order nonlinear susceptibility on the intensity of light. The system contains a Λ -type atom coupled to a single-mode radiation field, with a degenerate multi-photon transition in the intensity-dependent regime. Also, the nonlinearity of the medium due to Kerr and intensity-dependent Kerr effects, and the detuning parameters are considered. Furthermore, to see the effects of dissipation such as photon absorption and scattering by the cavity mirrors and spontaneous emission of the atom, a non-Hermitian Hamiltonian is introduced, which results in obtaining the state vector of the whole system by applying the time-dependent Schrödinger equation. Thereupon, the dynamics of entanglement, coherence, photon statistics, and quadrature squeezing are numerically investigated. In each case, the roles of the intensity-dependent nonlinearity function, Kerr and intensity-dependent Kerr nonlinearity, different sources of dissipation, and detuning parameters are discussed. The numerical results indicate that the nonclassicality can remarkably be revealed, and can appropriately be controlled via the above-mentioned effects. It can be found that the presence of dissipation not only does not weaken the physical properties but also can enhance and protect the nonclassicality of the system.