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arXiv:1112.0144 · Physical Review B

Dissipation-driven generation of two-qubit entanglement mediated by plasmonic waveguides

Diego Martín-Cano, Alejandro González-Tudela, Luis Martín-Moreno, Francisco José García-Vidal, C. Tejedor, Esteban Moreno

Published Dec 5, 2011• 191 citations
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Abstract

We study the generation of entanglement between two distant qubits mediated by the surface plasmons of a metallic waveguide. We show that a V-shaped channel milled in a flat metallic surface is much more efficient for this purpose than a metallic cylinder. The role of the misalignments of the dipole moments of the qubits, an aspect of great importance for experimental implementations, is also studied. A careful analysis of the quantum dynamics of the system by means of a master equation shows that two-qubit entanglement generation is essentially due to the dissipative part of the effective qubit-qubit coupling provided by the surface plasmons. The influence of a coherent external pumping, needed to achieve a steady-state entanglement, is discussed. Finally, we pay attention to the question of how to get information experimentally on the degree of entanglement achieved in the system.

DOI
10.1103/physrevb.84.235306

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We study the generation of entanglement between two distant qubits mediated by the surface plasmons of a metallic waveguide. We show that a V-shaped channel milled in a flat metallic surface is much more efficient for this purpose than a metallic cylinder. The role of the misalignments of the dipole moments of the qubits, an aspect of great importance for experimental implementations, is also studied. A careful analysis of the quantum dynamics of the system by means of a master equation shows that two-qubit entanglement generation is essentially due to the dissipative part of the effective qubit-qubit coupling provided by the surface plasmons. The influence of a coherent external pumping, needed to achieve a steady-state entanglement, is discussed. Finally, we pay attention to the question of how to get information experimentally on the degree of entanglement achieved in the system.
Entanglement between two qubits (two level atoms) mediated by surface plasmons in three-dimensional plasmonic waveguides is studied using a quantum master equation formalism. Two types of waveguides, a nanowire and a V-shaped channel cut in a flat metal plane, are considered. The Green functions for the waveguides, which rigorously describes the dissipative qubit environment, are calculated numerically using a direct finite-difference time-domain (FDTD) solution of Maxwell's equations. Finite-length effects are shown to play a crucial role in enhancing entanglement, and resonant-length plasmonic waveguides can provide higher entanglement between qubits than infinite-length waveguides. It is also shown that coupling slots can improve entanglement via stronger qubit-waveguide coupling, for both the infinite- and finite-waveguide cases. The formalism used in the paper can be applied to a wide range of plasmonic waveguides.
A dissipative-driven system can generate steady-state entanglement robust to control parameters, while a quantum plasmonic system has the advantages of being strongly coupled to qubits and manipulation of electromagnetic waves in the subwavelength regime. We propose an effective multiqubit dissipative-driven entanglement model for a plasmonic system which takes into account coupling of the plasmonic cavity and qubits as well as the direct coupling between any two qubits and develop a numerical solution of the effective model on a scalable composite plasmonic structure. In this structure, the multiqubit entanglement under asymmetric detuning, especially for those combinations containing pairs of antisymmetric detuning qubits, achieves stronger steady-state entanglement measured by negativity and pairwise concurrence. The robustness of multiqubit entanglement against variations of the control parameters is also presented. In addition, the phenomenon of entanglement sudden death caused by the driving field in entanglement dynamics is investigated. Our model shows evidence that quantum plasmonics has great potential in multiqubit entanglement.
We investigate the dynamics of quantum coherence and quantum correlation of two qubits mediated by a one-dimensional plasmonic waveguide. The analytical expression of the dissipative dynamics of the two qubits is obtained for the initial X state. The dynamical behaviors of the quantum coherence and quantum correlation are shown to be largely dependent on the parameters of the initial state. Starting from a product state, quantum coherence and quantum correlation can be induced by the plasmonic waveguide. Under continuous drivings, steady quantum correlation can be obtained at specific distance larger than the operating wavelength and large values of steady quantum coherence are attainable at arbitrary distance. The detuning effect on the dissipation-driven generation of steady quantum coherence and quantum correlation is also explored.
We theoretically study the dissipative dynamics of a quantum emitter placed near the planar surface of a metal supporting surface-plasmon excitations. The emitter-metal coupling regime can be tuned by varying some control parameters such as the qubit-surface separation and/or the detuning between characteristic frequencies. By using a Green's-function approach jointly with a time-convolutionless master equation, we analyze the non-Markovian dissipative features on the qubit time evolution in two cases of interest: (i) an undriven qubit initially prepared in its excited state and (ii) the evolution toward a steady state for a system driven by a laser field. For weak to moderate qubit-metal coupling strength, and on time scales large compared to the surface plasmon oscillation time, a Markovian approximation for the master-equation results to be adequate to describe the qubit main optical properties: surface enhancements of rate emission, optical spectra, and time-dependent photon-photon correlation functions. The qubit decay shows a crossover passing from being purely dissipative for small qubit-surface distances to plasmon emission for larger separations.
We investigate relaxation dynamics in the system of two identical quantum dipole emitters (QDEs) located near a metal nanoparticle (MNP) exhibiting a dipolar localized surface plasmon (LSP) resonance at the frequency of the QDE radiative transition. Considering one QDE to be brought into an optically active excited state and weakly coupled to the resonant LSP, we show that a stable superposition state of two QDEs is formed during the transition time, which is much shorter than the QDE spontaneous decay time and determined by the efficiency of resonant interaction between the QDEs and induced LSP. It is elucidated that the superposition state is established as a result of redistribution of the energy of the initially excited QDE so that the corresponding steady-state QDE fields induced at the MNP site cancel each other. The degree of steady-state entanglement characterized by the concurrence is found dependent only on the ratio of distances between the QDEs and the MNP, reaching its maximum value of $\ensuremath{\sim}0.65$, when the separation between the MNP and the initially excited QDE is larger by $\ensuremath{\sim}20%$ than the distance from the other QDE to the MNP.