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Prolonging the Qubits Entanglement via Local Surface Plasmon Modes

Chia-Yi Ju, Wan-Yu Liu, Shuo-Yen Chen, Guang-Yin Chen

Published Jul 11, 2023• 0 citations
Publisher

Abstract

A key to achieving quantum computing is the qubit-entanglement. Nevertheless, real-life qubits cannot be isolated from the environment completely. As a result, the entanglement between qubits decoheres via their interaction with the environment. Therefore, it is essential to understand how the qubit-entanglement changes over time. In this work, we study the entanglement between qubits when placed in a bulk of dielectric material embedded with a nanosized metal particle. Most importantly, we focus on the effects of the unavoidable localized surface plasmons induced at the surface of the metal particle. We discuss how the distance between the metal particles affects the entanglement of the qubits and how various entangled states are affected by the localized surface plasmons.

DOI
10.1142/s2010324723400179

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A key to achieving quantum computing is the qubit-entanglement. Nevertheless, real-life qubits cannot be isolated from the environment completely. As a result, the entanglement between qubits decoheres via their interaction with the environment. Therefore, it is essential to understand how the qubit-entanglement changes over time. In this work, we study the entanglement between qubits when placed in a bulk of dielectric material embedded with a nanosized metal particle. Most importantly, we focus on the effects of the unavoidable localized surface plasmons induced at the surface of the metal particle. We discuss how the distance between the metal particles affects the entanglement of the qubits and how various entangled states are affected by the localized surface plasmons.
In the field of quantum information and quantum computing, entanglement plays an essential role. Entanglement preservation is an important issue as realistic quantum systems are affected by decoherence and entanglement losses due to the interaction with their environment. For example, in spite of an exponential decay of a single qubit, the entanglement between two qubits may completely disappear at a finite time; a phenomenon known as “entanglement sudden death” [1]. Recently, interest has been given in cases that qubits can be strongly coupled to plasmonic nanostructures, like, for example, an one-dimensional plasmonic waveguide [2] or a two-dimensional lattice of metal-coated dielectric nanoparticles [3]. In such systems the strong interaction with the surface plasmons leads to significant entanglement between the two qubits. Here, we consider the interaction of two initially entangled qubits interacting individually with a two-dimensional lattice of metal-coated dielectric nanoparticles. We consider two cases for the qubits, a pair of regular two-level systems and a pair of V-type systems where one transition is the qubit and the other level acts as an umbrella level [4]. We consider the entanglement dynamics for different initial conditions of the qubits. The specific plasmonic nanostructure leads to strongly modified spontaneous emission rates of individual quantum systems (strong suppression in certain cases) and, in addition, to strongly anisotropic Purcell effect for orthogonal dipoles, that in turn can be used for simulating quantum interference in spontaneous emission [5]. We use these effects for significantly prolonging entanglement dynamics near the plasmonic nanostructure in both cases, in comparison to the cases that the qubits are in free space. 1. T. Yu and J. H. Eberly, Phys. Rev. Lett. 93, 140404 (2004). 2. A. Gonzalez-Tudela, D. Martin-Cano, E. Moreno, L. Martin-Moreno, C. Tejedor, and F. J. Garcia-Vidal, Phys. Rev. Lett. 106, 020501 (2011). 3. N. Iliopoulos, A. F. Terzis, V. Yannopapas, and E. Paspalakis, Ann. Phys. 365, 38 (2016). 4. S. Das and G. S. Agarwal, Phys. Rev. A 81, 052341 (2010). 5. V. Yannopapas, E. Paspalakis, and N. V. Vitanov, Phys. Rev. Lett. 103, 063602 (2009).
The generation of quantum entanglement is important for a wide range of quantum technology protocols. In nanophotonics, a promising platform for quantum technologies, entanglement generation via plasmon-mediated coupling in quantum dot qubits is often modeled within the dipole limit, where only dipolar plasmons of the mediating nanoparticle are considered, and the local response approximation, where nonlocal corrections are ignored. However, multipolar effects manifest strongly at coupling distances less than the nanoparticle size, while nonlocal optical effects stem from a size-induced dielectric response. We investigated these two important effects in the generation of two-qubit entanglement mediated by plasmonic coupling. A cavity quantum electrodynamic approach is employed, where the induced plasmonic effects lead to modified transition rates in the dynamics of the coupled quantum dot qubits. We find that multipolar modes and size-dependent damping lead to entanglement decay at small coupling distances and limit mediated entanglement with certain particle sizes. We discuss potential implications of multipolar modes in entanglement-based quantum sensing.
Metals can sustain traveling electromagnetic waves at their surfaces supported by the collective oscillations of their free electrons in unison. Remarkably, classical electromagnetism captures the essential physics of these 'surface plasma' waves using simple models with only macroscopic features, accounting for microscopic electron–electron and electron–phonon interactions with a single, semi-empirical damping parameter. Nevertheless, in quantum theory these microscopic interactions could be important, as any substantial environmental interactions could decohere quantum superpositions of surface plasmons, the quanta of these waves. Here we report a measurement of path entanglement between surface plasmons with 95% contrast, confirming that a path-entangled state can indeed survive without measurable decoherence. Our measurement suggests that elastic scattering mechanisms of the type that might cause pure dephasing in plasmonic systems must be weak enough not to significantly perturb the state of the metal under the experimental conditions we investigated.
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.