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Journal of the Optical Society of America B

Entanglement transfer from entangled nonlinear coherent states to separable qubits

Azam Anbaraki, Davood Afshar, Mojtaba Jafarpour

Published Jun 6, 2017• 4 citations
Publisher

Abstract

We study entanglement transfer from even and odd two-mode nonlinear coherent states to two separable qubits. The separable qubits are assumed to be in the following three states: both of the qubits are in the ground state, one qubit is in the ground state and the other is in a mixed state, and both of them are in a mixed state. The interaction between the field states and the system of qubits is considered under the Jaynes–Cummings model. We use negativity to evaluate the entanglement transfer to the system of qubits after interaction with the field states. The conditions for the production of the maximum amount of entanglement between qubits will be discussed. We observe that the maximum value of entanglement transfer is related to the interaction of odd nonlinear coherent states with the qubits when both of the latter are in the ground state.

DOI
10.1364/josab.34.001366

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We study entanglement transfer from even and odd two-mode nonlinear coherent states to two separable qubits. The separable qubits are assumed to be in the following three states: both of the qubits are in the ground state, one qubit is in the ground state and the other is in a mixed state, and both of them are in a mixed state. The interaction between the field states and the system of qubits is considered under the Jaynes–Cummings model. We use negativity to evaluate the entanglement transfer to the system of qubits after interaction with the field states. The conditions for the production of the maximum amount of entanglement between qubits will be discussed. We observe that the maximum value of entanglement transfer is related to the interaction of odd nonlinear coherent states with the qubits when both of the latter are in the ground state.
Abstract In this paper, using an entangled three-mode field state, we study the production of entanglement in a three- qubit system. The entangled three-mode field state is defined as superposed three-mode nonlinear coherent state, which is shown to be entangled as an increasing function of the coherency parameter. The interaction between the field state and a system of three separable qubits is considered under Jaynes–Cummings model. Our study reveals that the three-qubit system becomes entangled after the interaction and the entanglement can be tuned by changing the coherency parameter of the initial field state. In addition, we show how population inversion is affected by the interaction.
Entanglement transfer from the superposition states of the pair coherent states or the SU(1,1) coherent states to two initially separable qubits is investigated. The entropy of the superposition states has a novel property: there exists a maximum value when the phase difference between the two 2-mode coherent states is π. In the process of entanglement transfer from these superposition states to qubits, it is found that the qubits have the largest possible entanglement at the maximum of the entropy of the initial field, which shows a relationship between the entanglement of the initial field and that of the qubits. The concurrence of the qubits can periodically approach unity when the parameters of the initial field are properly chosen and the two qubits are initially at the ground states.
We consider the entanglement of two remote qubits induced by local interaction with the two-mode nonclassical state fields. We investigate the transfer of entanglement from different two-mode nonclassical state fields to a pair of separable and mixed qubits. We find that no matter what state the qubit subsystem is initially prepared in, at the specific time $gt\ensuremath{\simeq}11.07$ the entanglement of the Bell state fields can be almost completely transferred to the qubit subsystem, i.e., the Bell state fields can drive an initially separable and very mixed state of qubits into an almost pure highly entangled state suitable for quantum information processing. For the entangled coherent state fields $\ensuremath{\mid}u⟩={N}_{1}(\ensuremath{\mid}\ensuremath{\alpha},\ensuremath{-}\ensuremath{\alpha}⟩+\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha},\ensuremath{\alpha}⟩)$ and $\ensuremath{\mid}{u}^{\ensuremath{'}}⟩={N}_{2}(\ensuremath{\mid}\ensuremath{\alpha},\ensuremath{-}\ensuremath{\alpha}⟩\ensuremath{-}\ensuremath{\mid}\ensuremath{-}\ensuremath{\alpha},\ensuremath{\alpha}⟩)$ we find that when $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ is small, the dynamic behaviors of the entanglement between two qubits are quite different. For $\ensuremath{\mid}u⟩$ there is almost no entanglement between two qubits while for $\ensuremath{\mid}{u}^{\ensuremath{'}}⟩$ the dynamic behavior of the entanglement between two qubits is very similar to that of the Bell state field. For large $\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}$ we find that the dynamic behaviors of entanglement between two qubits are almost the same for these two fields, and when $gt\ensuremath{\sim}\ensuremath{\mid}\ensuremath{\alpha}\ensuremath{\mid}\ensuremath{\pi}$ the entanglement between two qubits reaches its maximum and is almost independent of initial mixedness of the qubit subsystem. For the two-mode squeezed vacuum state field we find that when $r\ensuremath{\sim}0.86$ and $gt\ensuremath{\simeq}11.07$ the entanglement transfer reaches its maximum which also almost does not depend on the initial mixedness of the qubit subsystem.
For nonlinear interactions with different forms of intensity-dependent coupling, entanglement transfer from the correlated two-mode SU(1,1) coherent states (SCS) to the initially separable and mixed atoms is investigated. It is found that suitable intensity-dependent coupling can enhance the entanglement transfer and make the atomic entanglement evolve periodically especially for the initially mixed atomic states. For SCS, the entanglement between the two modes is strengthened with the increase of the photon number difference (PND) between the two modes of the fields. When PND is odd, the entanglement between the atoms is less than that when PND is even.
We study the interaction between a single-mode quantized field and a quantum system composed of two qubits. We suppose that two qubits initially be prepared in the mixed and separable state, and study how entanglement between two qubits arises in the course of evolution according to the Jaynes–Cummings type interaction with nonclassical radiation field. We also investigate the relation between entanglement and purity of qubit subsystem. We show that different photon statistics have different effects on the dynamical behavior of the qubit subsystem. When the qubits are initially prepared in the maximally mixed and separable state, for coherent state field we cannot find entanglement between two qubits; for squeezed state field entanglement between two qubits exists in several short period of time; for even and odd coherent state fields of large photon number, the dynamical behavior of the entanglement between two qubits shows collapse and revival phenomenon. For odd coherent state field of small photon number, the entanglement with both qubits initially prepared in maximally mixed state can be stronger than that with both qubits initially prepared in pure states. For fields of small photon number, the entanglement strongly depends on the states they are initially prepared in. For coherent state field, and odd and even coherent state fields of large photon number, the entanglement only depends on the purity of the initial state of qubit subsystem. We also show that during the evolution the unentangled state may be purer than the entangled state, and the maximum degree of entanglement may not occur at the time when the qubit subsystem is in the purist state.
We investigate the process of entanglement transfer from a three-mode quantized field to a system of three spatially separated qubits, each one made of a two-level atom resonantly coupled to a cavity mode. The optimal conditions for entanglement transfer, evaluated by atomic tripartite negativity, are derived for radiation prepared in qubitlike and Gaussian entangled states in terms of field parameters, atom-cavity interaction time, cavity mirror losses, and atomic preparation. For qubitlike states we find that for negligible cavity losses some states may completely transfer their entanglement to the atoms and/or be exactly mapped to the atomic state, whereas for Gaussian states we find a range of field parameters needed to obtain a large entanglement transfer. The purity of the three-qubit states and the entanglement of two-qubit subsystems are also discussed in some detail.