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Quantum Electronics

Numerical modelling of emission of a two-level atom near a metal nanoparticle with account for tunnelling of an electron from an atom into a particle

S. V. Fedorovich, Игорь Евгеньевич Проценко

Published Jan 31, 2016• 0 citations
Publisher

Abstract

We report the results of numerical modelling of emission of a two-level atom near a metal nanoparticle under resonant interaction of light with plasmon modes of the particle. Calculations have been performed for different polarisations of light by a dipole approximation method and a complex multipole method. Depending on the distance between a particle and an atom, the contribution of the nonradiative process of electron tunnelling from a two-level atom into a particle, which is calculated using the quasi-classical approximation, has been taken into account and assessed. We have studied spherical gold and silver particles of different diameters . The rates of electron tunnelling and of spontaneous decay of the excited atomic state are found. The results can be used to develop nanoscale plasmonic emitters, lasers and photodetectors.

DOI
10.1070/qe2016v046n01abeh015806

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 19, 2010•0 citations
We report the results of numerical modelling of emission of a two-level atom near a metal nanoparticle under resonant interaction of light with plasmon modes of the particle. Calculations have been performed for different polarisations of light by a dipole approximation method and a complex multipole method. Depending on the distance between a particle and an atom, the contribution of the nonradiative process of electron tunnelling from a two-level atom into a particle, which is calculated using the quasi-classical approximation, has been taken into account and assessed. We have studied spherical gold and silver particles of different diameters . The rates of electron tunnelling and of spontaneous decay of the excited atomic state are found. The results can be used to develop nanoscale plasmonic emitters, lasers and photodetectors.
The photon-number statistics from resonance fluorescence of a two-level atom near a metal nanosphere driven by a laser field with finite bandwidth is studied theoretically. Our analysis shows that all interesting physics here takes place in a small area around the nanosphere where the near field and the atom-nanosphere coupling essentially affect the radiative properties of the atom. Computer modeling estimates this area roughly as $r\ensuremath{\le}2a$ (r(r(r is the distance from the center of the nanosphere to the atom), with aaa being the radius of the nanosphere. At the larger distances, the influence of the nanoparticle vanishes and the atom tends to behave similarly to that in free space. It is shown that the distribution function p(n,T)p(n,T)p(n,T) of the emission probability of nnn photons in a given time interval TTT in steady-state resonance fluorescence drastically depends on the atom location around the nanosphere for $r\ensuremath{\le}2a$, featuring a characteristic twist in the ridgelike dependence and a convergence time of up to $9\ensuremath{\mu}\text{s}$, two orders of magnitude slower than for the atom in free space. At large distances, the distribution converges to a Gaussian one, as for the atom in free space. The typical convergence time scale at large distances r>2ar>2ar>2a tends to the convergence time of the atom in free space. There are also two areas symmetrical around the nanosphere in which $\ensuremath{\Omega}\ensuremath{\sim}\ensuremath{\gamma}$ and the convergence time goes to zero. This behavior is determined by the interplay of the radiative and nonradiative decay rates of the atom due to the coupling with the metal nanosphere and by the near-field intensity. Additional parameters are the normalized laser frequency detuning from the atomic resonance and the bandwidth of the incoming laser field.
This review is devoted to the study of effects of quantum optics in nanostructures. The mechanisms by which the rates of radiative and nonradiative decay are modified are considered in the model of a two-level quantum emitter (QE) near a plasmonic nanoparticle (NP). The distributions of the intensity and polarization of the near field around an NP are analyzed, which substantially depend on the polarization of the external field and parameters of plasmon resonances of the NP. The effects of quantum optics in the system NP + QE plus external laser field are analyzed-modification of the resonance fluorescence spectrum of a QE in the near field, bunching/antibunching phenomena, quantum statistics of photons in the spectrum, formation of squeezed states of light, and quantum entangled states in these systems.
Abstract It is demonstrated that the interaction of a two-level quantum emitter (atom, molecule, etc) with a plasmonic nanoparticle (prolate nanospheroid) in an external laser field features either an essential increase (up to a few orders of magnitude) or reduction (up to a few times) of the total decay rate of the emitter in specific areas around the nanoparticle in contrast to its decay rate in a vacuum. It is also shown that the resonance fluorescence spectrum of the emitter in close proximity to a plasmonic nanoparticle is very sensitive to both the location of the emitter around the nanoparticle and to polarization of the near-field, which depends in turn on the polarization of the incident laser field. This can be used in engineering potential quantum optics experiments with quantum emitters in the near-field, as well as for 3D nanoscopy of the near-field by registering the resonance fluorescence spectra of quantum emitters scattered in the vicinity of a plasmonic nanoparticle.
We develop a theory of cooperative emission of light by an ensemble of emitters, such as fluorescing molecules or semiconductor quantum dots, located near a metal nanostructure supporting surface plasmon. The primary mechanism of cooperative emission in such systems is resonant energy transfer between emitters and plasmons rather than the Dicke radiative coupling between emitters. We identify two types of plasmonic coupling between the emitters, (i) plasmon-enhanced radiative coupling and (ii) plasmon-assisted nonradiative energy transfer, the competition between them governing the structure of system eigenstates. Specifically, when emitters are removed by more than several nanometers from the metal surface, the emission is dominated by three superradiant states with the same quantum yield as a single emitter, resulting in a drastic reduction of ensemble radiated energy, while at smaller distances cooperative behavior is destroyed by nonradiative transitions. The crossover between two regimes can be observed in distance dependence of ensemble quantum efficiency. Our numerical calculations incorporating direct and plasmon-assisted interactions between the emitters indicate that they do not destroy the plasmonic Dicke effect.
Abstract This review is devoted to studies of quantum optics effects for quantum emitters (QEs) in the near field of nanoparticles (NPs). In the simple model of a two-level QE located near a plasmon NP, we analyze the mechanisms for modifying the radiative and nonradiative decay rates and discuss the distribution of the near-field intensity and polarization around the NP. This distribution has a complex structure, being significantly dependent on the polarization of the external radiation field and on the parameters of NP plasmon resonances. The quantum optics effects in the system (NP + QE + external laser field) are analyzed, including the near-field modification of the resonance fluorescence spectrum of a QE, the bunching/antibunching effects and photon quantum statistics effects in the spectrum, the formation of squeezed light states, and quantum entangled states in such systems.
We develop a theory of cooperative emission of light by an ensemble of emitters, such as fluorescing molecules or semiconductor quantum dots, located near a metal nanostructure supporting surface plasmon. The primary mechanism of cooperative emission in such systems is resonant energy transfer between emitters and plasmons rather than the Dicke radiative coupling between emitters. We identify two types of plasmonic coupling between the emitters, (i) plasmon-enhanced radiative coupling and (ii) plasmon-assisted nonradiative energy transfer, the competition between them governing the structure of system eigenstates. Specifically, when emitters are removed by more than several nm from the metal surface, the emission is dominated by three superradiant states with the same quantum yield as a single emitter, resulting in a drastic reduction of ensemble radiated energy, while at smaller distances cooperative behavior is destroyed by nonradiative transitions. The crossover between two regimes can be observed in distance dependence of ensemble quantum efficiency. Our numerical calculations incorporating direct and plasmon-assisted interactions between the emitters indicate that they do not destroy the plasmonic Dicke effect.