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arXiv:1902.06387 · Physical Review A

Level shift and decay dynamics of a quantum emitter around a plasmonic nanostructure

Meng Tian, Yong-Gang Huang, Shasha Wen, Xiaoyun Wang, Hong Yang, Jinzhang Peng, Heping Zhao

Published May 28, 2019• 16 citations
arXivHTMLPDF

Abstract

We put forward a general approach for calculating the energy level shift of a quantum emitter (QE) in arbitrary-shaped nanostructure. It is expressed by the sum of the real part and a simple integral of the imaginary part of the scattered photon Green's function (GF) in a rather narrow real frequency range without a principal value. Compared with the method of direct evaluation of the principal value integral along the positive frequency axis or the method of transferring the principal value into an integration along the imaginary frequency axis, our method avoids the principal value integral and the evaluation of the scattered GF with imaginary frequency. It is numerically demonstrated for a QE located around a nanosphere and in a gap plasmonic nanocavity. The decay dynamics of an excited QE is calculated using the time-domain method through solving the Schr\"odinger equation in the form of a Volterra integral of the second kind, and using the frequency-domain method based on the Green's function expression for the evolution operator. It is found that the frequency domain method requires much narrower band information of the scattered GF. These findings are instructive in the field of coherent light-matter interactions.

DOI
10.1103/physreva.99.053844

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We put forward a general approach for calculating the energy level shift of a quantum emitter (QE) in arbitrary-shaped nanostructure. It is expressed by the sum of the real part and a simple integral of the imaginary part of the scattered photon Green's function (GF) in a rather narrow real frequency range without a principal value. Compared with the method of direct evaluation of the principal value integral along the positive frequency axis or the method of transferring the principal value into an integration along the imaginary frequency axis, our method avoids the principal value integral and the evaluation of the scattered GF with imaginary frequency. It is numerically demonstrated for a QE located around a nanosphere and in a gap plasmonic nanocavity. The decay dynamics of an excited QE is calculated using the time-domain method through solving the Schr"odinger equation in the form of a Volterra integral of the second kind, and using the frequency-domain method based on the Green's function expression for the evolution operator. It is found that the frequency domain method requires much narrower band information of the scattered GF. These findings are instructive in the field of coherent light-matter interactions.
A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the excited QE will not relax completely to its ground state and is partially stabilized in its excited state after a long time. We develop some theoretical methods for investigating this problem and show how to form such a bound state and its effect on the non-Markovian decay dynamics. We put forward an efficient numerical approach for calculating the analytical part of the self-energy for frequency below the lower energy threshold. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range. With the above two quantities obtained, we show that the non-Markovian decay dynamics of an initially excited QE can be efficiently obtained by the method based on the Green's function expression for the evolution operator when a bound state exists. A general criterion for identifying the existence of a bound state is presented. The performances of the above methods are numerically demonstrated for a QE located around a metal nanosphere and in a gap plasmonic nanocavity. Numerical results show that these methods work well and the QE becomes partially stabilized in its excited state at a long time for the transition dipole moment beyond its critical value. In addition, it is also found that this critical value is heavily dependent on the distance between the QE and the metal surface, but nearly independent on the size of the nanosphere or the rod. Our methods can be utilized to understand the suppressed decay dynamics for a QE in an open quantum system and provide a general picture on how to form such a bound state.
Abstract The decay dynamic of an excited quantum emitter (QE) is one of the most important contents in quantum optics. It has been widely applied in the field of quantum computing and quantum state manipulation. When the electromagnetic environment is described by several pseudomodes, the effective Hamiltonian method based on the multi-mode Jaynes–Cummings model provides a clear physical picture and a simple and convenient way to solve the decay dynamics. However, in previous studies, only the resonant modes are taken into account, while the non-resonant contributions are ignored. In this work, we study the applicability and accuracy of the effective Hamiltonian method for the decay dynamics. We consider different coupling strengths between a two-level QE and a gold nanosphere. The results for dynamics by the resolvent operator technique are used as a reference. Numerical results show that the effective Hamiltonian method provides accurate results when the two-level QE is resonant with the plasmon. However, when the detuning is large, the effective Hamiltonian method is not accurate. In addition, the effective Hamiltonian method cannot be applied when there is a bound state between the QE and the plasmon. These results are of great significance to the study of the decay dynamics in micro-nano structures described by quasi-normal modes.
We study theoretically the statistics of photons generated by a quantum emitter located in the vicinity of a periodic plasmonic nanostructure. The presented formalism is based on a macroscopic QED formalism in conjunction with a density-matrix approach in order to obtain the second-order correlation function of the emitted photons accounting for the influence of the plasmonic environment. The metallic reservoir coupling is computed using Green's-function theory, which, for a periodic lattice of scatterers, is calculated by a multiple-scattering method. We show that the photon statistics and the antibunching of emitted photons depend very strongly on the orientation of the quantum emitter relative to the lattice, on the transition frequency of the emitter, on the intensity of the applied field, and on the geometrical parameters of the nanoparticles, such as the shell thickness.
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.
It is now well established that radiative decay of quantum emitters can be strongly modified by their environment. In this paper, we present an exact—within the weak-coupling approximation—multipole expression to compute the Lamb (frequency) shift induced by an arbitrary set of resonant scatterers on a nearby quantum emitter, using multiscattering theory. We also adopt a quasi-normal mode description to account for the line shape of the Lamb shift spectrum in the near field of a plasmonic nanosphere. It is then shown that the Lamb shift resonance can be blueshifted as the size of the nanoparticle increases, suggesting that nanoparticles may be used to tune this resonant interaction. Finally, a realistic calculation of the Lamb shift is made for a dimer configuration.
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.