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Photonics

Anisotropic Purcell Effect and Quantum Interference in Fractal Aggregates of Nanoparticles

Vassilios Yannopapas, Emmanuel Paspalakis

Published Aug 3, 2023• 0 citations
Publisher

Abstract

We study theoretically the emergence of an anisotropic Purcell factor in random two-dimensional fractal aggregates of nanoparticles. These nanoparticles can either be metallic nanoparticles made of silver, which exhibit surface plasmon resonances, or high-index dielectric nanoparticles like silicon, which possess optical Mie resonances. To calculate the spontaneous emission rates of a quantum emitter, we utilize the electromagnetic Green’s tensor within the framework of the coupled-dipole method. Our findings reveal that the Purcell factor exhibits spatial variations, with certain regions, referred to as hot spots, displaying high values for dipoles oriented within the plane of the fractal aggregate, while dipoles oriented vertically to the aggregate have values close to unity. This anisotropy in the Purcell factor leads to significant quantum interference effects in the spontaneous emission paths of multi-level quantum emitters. As a consequence of this quantum interference, we demonstrate the occurrence of population trapping in a V-type quantum emitter embedded within a fractal aggregate of nanoparticles which cannot otherwise take place if the emitter is placed in vacuum.

DOI
10.3390/photonics10080898

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We study theoretically the emergence of an anisotropic Purcell factor in random two-dimensional fractal aggregates of nanoparticles. These nanoparticles can either be metallic nanoparticles made of silver, which exhibit surface plasmon resonances, or high-index dielectric nanoparticles like silicon, which possess optical Mie resonances. To calculate the spontaneous emission rates of a quantum emitter, we utilize the electromagnetic Green’s tensor within the framework of the coupled-dipole method. Our findings reveal that the Purcell factor exhibits spatial variations, with certain regions, referred to as hot spots, displaying high values for dipoles oriented within the plane of the fractal aggregate, while dipoles oriented vertically to the aggregate have values close to unity. This anisotropy in the Purcell factor leads to significant quantum interference effects in the spontaneous emission paths of multi-level quantum emitters. As a consequence of this quantum interference, we demonstrate the occurrence of population trapping in a V-type quantum emitter embedded within a fractal aggregate of nanoparticles which cannot otherwise take place if the emitter is placed in vacuum.
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 investigate the phenomenon of quantum interference in spontaneous emission for a three-level V-type quantum emitter placed between two bismuth-chalcogenide (Bi2Te3, Bi2Se3) microspheres. In particular, we find that the degree of quantum interference can become as high as 0.994, a value which is attributed to the strong dependence of the spontaneous emission rate on the orientation of an atomic dipole relative to the surfaces of the microspheres, at the excitation frequencies of phonon-polariton states of the bismuth-chalcogenide microspheres (anisotropic Purcell effect). As a consequence of the high degree of quantum interference, we observe the occurrence of strong population trapping in the quantum emitter. To the best of our knowledge, the reported values of the degree of quantum interference are record values and are obtained for a relatively simple geometrical setup such as that of a microparticle dimer.
We investigate the phenomenon of quantum interference in spontaneous emission pathways for a quantum emitter embedded in a two-dimensional photonic crystal composed of a square lattice of dielectric cylindrical rods. Using a V-type three-level system as a model, we demonstrate that the anisotropic Purcell effect inherent in such photonic structures can amplify quantum interference to its theoretical maximum, where the degree of interference p reaches unity. This results in the complete suppression of spontaneous emission for one polarization (directional suppression) and the emergence of coherent population trapping without the need for external coherent fields. By employing density matrix formalism, we derive analytical expressions for the population dynamics and identify conditions for indefinite or long-lived excited-state population. Our findings can find application in quantum technologies, including high-precision atomic clocks, magnetometry, and quantum information processing.
The mechanism of using the anisotropic Purcell factor to control the spontaneous emission linewidths in a four-level atom is theoretically demonstrated; if the polarization angle bisector of the two dipole moments lies along the axis of large/small Purcell factor, destructive/constructive interference narrows/widens the fluorescence center spectral lines. Large anisotropy of the Purcell factor, confined in the subwavelength optical mode volume, leads to rapid spectral line narrowing of atom approaching a metallic nanowire, nanoscale line width pulsing following periodically varying decay rates near a periodic metallic nanostructure, and dramatic modification on the spontaneous emission spectrum near a custom-designed resonant plasmon nanostructure. The combined system opens a good perspective for applications in ultracompact active quantum devices.
The theoretical method to study strong coupling between an ensemble of quantum emitters (QEs) and surface plasmons excited by the nanoparticle cluster has been presented by using a rigorous first-principles electromagnetic Green's tensor technique. We have demonstrated that multi-qubit entanglements for two-level QEs can be produced at different coupling resonance frequencies, when they locate in the hot spots of the metallic nanoparticle cluster. The duration of quantum beats for such an entanglement can reach two orders longer than that for the entanglement in a photonic cavity. The phenomenon originates from collective coupling resonance excitation of the cluster. At the frequency of single scattering resonance, the entanglement cannot be produced although the single QE spontaneous decay rate is very big.
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.