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Physical review. B./Physical review. B

Prolonging entanglement dynamics near periodic plasmonic nanostructures

Nikos Iliopoulos, Andreas Terzis, Vassilios Yannopapas, Emmanuel Paspalakis

Published Aug 4, 2017• 27 citations
Publisher

Abstract

We study the dynamics of two initially entangled qubits, where each one interacts locally and independently of the other, with a plasmonic nanostructure. By considering two different cases for the qubits, two identical two-level systems and two identical V-type quantum systems, where one two-level transition plays the role of the qubit while the third level acts as an ``umbrella level'', we study the corresponding entanglement dynamics for several pure and mixed initial states. As the plasmonic nanostructure we take a two-dimensional lattice of metal-coated dielectric nanoparticles. The presence of this nanostructure leads to highly suppressed spontaneous emission rates of the individual quantum systems, as well as to highly anisotropic spontaneous decay rates for orthogonal dipole matrix elements due to the anisotropic Purcell effect, leading to quantum interference in spontaneous emission. Both of the effects can be used for significantly prolonging the time evolution of entanglement for several system parameters.

DOI
10.1103/physrevb.96.075405

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We study the dynamics of two initially entangled qubits, where each one interacts locally and independently of the other, with a plasmonic nanostructure. By considering two different cases for the qubits, two identical two-level systems and two identical V-type quantum systems, where one two-level transition plays the role of the qubit while the third level acts as an ``umbrella level'', we study the corresponding entanglement dynamics for several pure and mixed initial states. As the plasmonic nanostructure we take a two-dimensional lattice of metal-coated dielectric nanoparticles. The presence of this nanostructure leads to highly suppressed spontaneous emission rates of the individual quantum systems, as well as to highly anisotropic spontaneous decay rates for orthogonal dipole matrix elements due to the anisotropic Purcell effect, leading to quantum interference in spontaneous emission. Both of the effects can be used for significantly prolonging the time evolution of entanglement for several system parameters.
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).
In this paper is made a detailed study of the dynamic behavior of total quantum correlations near periodic plasmonic nanostructures. The complex system we are examining consists of two quantum subsystems, each of which interacts locally and independently with a corresponding plasmonic nanostructure. Dynamic study is done for both pure and mixed quantum states. Our quantum system in the first case consists of two subsystems of two-level systems (or else qubits). In the second case it consists of two identical three-level V-type quantum systems, where one two-level transition plays the role of the qubit while the third level acts as an umbrella level. As a plasmonic nanostructure we take a two-dimensional lattice of metal-coated dielectric nanoparticles. The presence of nanostructure leads to a highly suppressed spontaneous emission rates due to the anisotropic Purcell effect, which increases the quantum interference of spontaneous emission. This phenomenon is useful for prolonging the time evolution of quantum correlations in the system.
It has been recently shown that the placement of a three-level V\mathsf{V}V-type quantum emitter in the proximity of metallic nanostructures can create dynamics similar to that of quantum interference in spontaneous emission. Here we continue this work and present results on the population dynamics of a three-level V-type quantum emitter for various initial conditions in the presence of a two-dimensional array of metal-coated dielectric nanospheres.
We show that the quantum interference between two spontaneous emission channels can be greatly enhanced when a three-level V-type atom is placed near plasmonic nanostructures such as metallic slabs, nanospheres, or periodic arrays of metal-coated spheres. The spontaneous emission rate is calculated by a rigorous first-principles electromagnetic Green's tensor technique. The enhancement of quantum interference is attributed to the strong dependence of the spontaneous emission rate on the orientation of an atomic dipole relative to the surface of the nanostructure at the excitation frequencies of surface plasmons.
We analyze the two-time intensity correlation function of the fluorescent field emitted by a three-level V-type quantum emitter located in the vicinity of a two-dimensional periodic plasmonic nanostructure. Due to the interaction of the quantum emitter with an electromagnetic field, the ground state population is excited to the upper levels, presenting decay due to spontaneous emission. The distinctive characteristic of this system is that the decay rates for a quantum emitter with dipole orientation perpendicular and normal to the surface of the nanostructure array exhibit large differences which vary with the distance between the quantum emitter and the two-dimensional nanoparticle array. This leads to simulation of quantum interference effects in spontaneous emission. By studying the dependence of the two-time intensity correlation function on specific physical parameters of the hybrid structure, including the intensity of the applied field, the detuning from resonance, the distance between the quantum emitter and the plasmonic nanostructure, as well as the spacing between the upper levels, we demonstrate a strong modification of the two-time intensity correlation functions. We also identify the conditions under which the two-time intensity correlation function is maximized, an effect which is associated to the bunching to antibunching transition of the emitted photons.
We study theoretically the effects of the presence of a plasmonic nanostructure on free-space spontaneous emission in a four-level quantum system, where one V\mathsf{V}V-type transition is influenced by the interaction with surface plasmons and the other V\mathsf{V}V-type transition occurs in free space. The plasmonic nanostructure that we consider is a two-dimensional array of metal-coated dielectric nanospheres. We show that the spectrum of spontaneous emission in the free-space modes is strongly influenced by the presence of the plasmonic nanostructure, and we explore the dependence of the spectrum on different initial conditions of the quantum system and on the distance from the nanostructure.