Transferring entanglement to the steady state of flying qubits

Yanqiang Guo, Jie Li, Tiancai Zhang, and Mauro Paternostro

Phys. Rev. A 86, 052315 – Published 12 November 2012

Abstract

The transfer of entanglement from optical fields to qubits provides a viable approach to entangling remote qubits in a quantum network. In cavity quantum electrodynamics, the scheme relies on the interaction between a photonic resource and two stationary intracavity atomic qubits. However, it might be hard in practice to trap two atoms simultaneously and synchronize their coupling to the cavities. To address this point, we propose and study entanglement transfer from cavities driven by an entangled external field to controlled flying qubits. We consider two exemplary non-Gaussian driving fields: NOON and entangled coherent states. We show that in the limit of long coherence time of the cavity fields, when the dynamics is approximately unitary, entanglement is transferred from the driving field to two atomic qubits that cross the cavities. On the other hand, a dissipation-dominated dynamics leads to very weakly quantum-correlated atomic systems, as witnessed by vanishing quantum discord.

Received 15 June 2012

DOI:https://doi.org/10.1103/PhysRevA.86.052315

Authors & Affiliations

Yanqiang Guo¹, Jie Li², Tiancai Zhang¹, and Mauro Paternostro^2,3

¹State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
²Centre for Theoretical Atomic, Molecular and Optical Physics, School of Mathematics and Physics, Queen's University, Belfast BT7 1NN, United Kingdom
³Institut für Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, D-89069 Ulm, Germany

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Vol. 86, Iss. 5 — November 2012

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Images

Figure 1
Scheme of the protocol: Two remote and identical cavities are driven by a two-mode quantum correlated field, which is coupled to each cavity via a leaky mirror. Two qubits are then sent to pass simultaneously through the cavities along the vertical ( $x$ ) direction from the tops of the geometrical centers.Reuse & Permissions
Figure 2
(a) Entanglement transfer for free-falling atoms and a single-photon entangled driving field (i.e., NOON states with $N = 1$ ), $x (t) = x_{0} + g t^{2} / 2$ , where $x_{0} = - 4 ω_{0}$ , $g = 9.82$ m/s $^{2}$ , and for $Ω_{0} = 4$ kHz (dashed line) and $Ω_{0} = 5.9$ kHz (solid line). (b) Entanglement of atomic qubits crossing the cavities under conditions of uniform motion [ $x (t) = x_{0} + V t$ with $x_{0} = - 4 ω_{0}$ and $V = 0.001$ m/s] and with the same driving field used in (a). We have taken $Ω_{0} = 155$ Hz (dashed line) and $Ω_{0} = 365$ Hz (solid line). (c) Comparison between the unitary (solid line) and dissipation-affected (dashed line) entanglement-transfer performance for free-falling motion of the atomic qubits with $Ω_{0} = 5.9$ kHz. In the dissipation-affected simulation, we have taken $Ω_{0} / Γ ≃ 10^{2}$ . In all our calculations we have taken the cavity mode $Ψ_{2, 0} (x, 0)$ (i.e., the ${TEM}_{20}$ mode), $ω_{0} = 10$ $μ$ m, and $T = 0.9$ , and the qubits are prepared in ${| 00 〉}_{12}$ .Reuse & Permissions
Figure 3
(a) Entanglement transfer for free-falling atoms and ECS external driving with $x_{0} = - 4 ω_{0}$ , $α = 1.1$ , and $Ω_{0} = 6.1$ kHz. (b) Entanglement for atomic qubits crossing the cavities under uniform motion ( $x_{0} = - 4 ω_{0}$ , $V = 0.005$ m/s) and $Ω_{0} = 850$ Hz, under the same driving as in (a). The atomic steady-state entanglement at the exit of the cavities for both motions is comparable. (c) Comparison between the unitary (solid line) and dissipation-affected (dashed line) entanglement-transfer behavior for uniform motion of the atomic qubits ( $V = 0.005$ m/s), $Ω_{0} = 340$ Hz, and $α = 0.9$ . We have taken $Ω_{0} / Γ ≃ 10^{2}$ . For all plots, we take the cavity mode $Ψ_{2, 0} (x, 0)$ , $ω_{0} = 30$ $μ$ m, $T = 0.9$ , and initial atomic ground state.Reuse & Permissions
Figure 4
(a) Temporal behavior of the elements of the two-qubit density matrix for the case of an entangled single-photon driving field (solid lines). The dashed lines are the corresponding steady-state values. We have used the notation ${(ρ_{12})}_{i j, k l} = 〈 i j | ρ_{12 s s} | k l 〉$ . The initial state of the atoms is taken to be ${|00〉}_{12}$ . (b) Quantum discord versus dimensionless interaction time $γ t$ for the case addressed in (a). (c) Atomic steady-state discord against the amplitude $α \in R$ in an ECS driving the entanglement-transfer process. Dynamically, the two-atom state is always separable with discord following a trend (at a set value of $α$ ) very similar to what is shown in (b) for an entangled single-photon driving field.Reuse & Permissions

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