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Physical Review A

Simulating quantum interference in spontaneous decay near plasmonic nanostructures: Population dynamics

Sofia Evangelou, Vassilios Yannopapas, Emmanuel Paspalakis

Published May 26, 2011• 51 citations
Publisher

Abstract

It has been recently shown that the placement of a three-level $\mathsf{V}$-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.

DOI
10.1103/physreva.83.055805

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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 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.
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 present results on the controlled dynamics of an externally driven four-level quantum emitter coupled to a plasmonic metamaterial, specifically a periodic two-dimensional array of metal-coated dielectric nanospheres. For the study of the system's dynamics, we combine the density matrix approach for the quantum emitter with ab initio electromagnetic calculations for the plasmonic nanostructure. We then present results for the time evolution of the populations of the different levels of the quantum emitter in both the presence and the absence of the plasmonic nanostructure. The dependence of the population dynamics to different distances of the quantum emitter from the plasmonic nanostructure is also studied.
We investigate theoretically the non-Markovian dynamics of a degenerate V-type quantum emitter in the vicinity of a metallic nanosphere, a system that exhibits quantum interference in spontaneous emission due to the anisotropic Purcell effect. We calculate numerically the electromagnetic Green's tensor and employ the effective modes differential equation method for calculating the quantum dynamics of the emitter population, with respect to the resonance frequency and the initial state of the emitter, as well as its distance from the nanosphere. We find that the emitter population evolution varies between a gradual total decay and a partial decay combined with oscillatory population dynamics, depending strongly on the specific values of the above three parameters. Under strong-coupling conditions, coherent population trapping can be observed in this system. We compare our exact results with results when the flat continuum approximation for the vacuum modified by the metallic nanosphere is applied. We conclude that the flat continuum approximation is an excellent approximation only when the spectral density of the system under study is characterized by nonoverlapping plasmonic resonances.
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.
We investigate the incoherent resonance fluorescence spectrum emitted by a three-level V-type quantum emitter, under the influence of a two-dimensional plasmonic nanosphere array. The V-type quantum system is driven by a coherent electromagnetic field whilst quantum interference effects in the spontaneous emission due to the presence of the plasmonic nanostructure are accounted for. The characteristics of the incoherent resonance fluorescence spectrum are studied, for different sets of parameters, aiming at the specification of the conditions under which an outstanding spectral narrowing, or either, quenching effects are manifested.