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Оптика и спектроскопия

Modeling of resonance fluorescence excitation spectra of two different two-level interacting nanoparticles

V. A. Morozov

Published Jan 1, 2022• 0 citations
Publisher

Abstract

Numerical simulations of the excitation spectra of resonant fluorescence bound by the dynamic interaction of two different two-level nanoparticles have been performed. We considered the excitation of one of the particles by monochromatic light with a frequency close to the transition frequency of this particle, at an irradiation intensity leading to a small population of its excited state. The formalism for the description of resonance fluorescence by the Heitler--Ma method was applied to a complete compound system of the marked particle pair and quantized emission field. The resulting expressions for the excitation spectrum reflect consideration of the absorption of the fluorescence photon without attributing it to the emission of any one particle. Expressions for the excitation spectra when taking into account such absorption of the fluorescence photon that allows us to attribute it to the radiation of one or another of the particles were obtained by solving a modified system of equations of the Heitler--Ma method, which reflects the addition of non-interfering amplitudes of the emission field states of each particle. It was found that the shape of the excitation spectra of the stationary resonance fluorescence of the particles in question is determined by the shape of the corresponding intensity spectra of the spontaneous fluorescence of these particles. Keywords: mathematical modeling, interacting two-level nanoparticles, resonant fluorescence, excitation spectrum.

DOI
10.21883/eos.2022.08.54775.3334-22

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Numerical simulations of the excitation spectra of resonant fluorescence bound by the dynamic interaction of two different two-level nanoparticles have been performed. We considered the excitation of one of the particles by monochromatic light with a frequency close to the transition frequency of this particle, at an irradiation intensity leading to a small population of its excited state. The formalism for the description of resonance fluorescence by the Heitler--Ma method was applied to a complete compound system of the marked particle pair and quantized emission field. The resulting expressions for the excitation spectrum reflect consideration of the absorption of the fluorescence photon without attributing it to the emission of any one particle. Expressions for the excitation spectra when taking into account such absorption of the fluorescence photon that allows us to attribute it to the radiation of one or another of the particles were obtained by solving a modified system of equations of the Heitler--Ma method, which reflects the addition of non-interfering amplitudes of the emission field states of each particle. It was found that the shape of the excitation spectra of the stationary resonance fluorescence of the particles in question is determined by the shape of the corresponding intensity spectra of the spontaneous fluorescence of these particles. Keywords: mathematical modeling, interacting two-level nanoparticles, resonant fluorescence, excitation spectrum.
The dynamic quenching of dual fluorescence is simulated based on solving a system of equations for matrix elements of the statistical operator of a five-level model molecule three levels of which belong to its excited states. It is assumed that one of the excited states is resonantly populated by monochromatic irradiation, while the other two states are populated as a result of subsequent relaxation processes. These two states are initial states for transitions that emit dual fluorescence photons. Expressions for the population of the excited molecular states in the case of steady-state fluorescence are obtained taking into account their decay (quenching) due to collisions with foreign molecules of the environment. As applied to molecules with intramolecular hydrogen bonds, the dual fluorescence quenching is described more completely and in more detail compared to the description given in the literature based on the molecular model with two excited levels.
Analytical expressions for describing the dynamics of the populations of the states of a five-level model molecule during fluorescence reflecting the quantum beats of the populations of its two excited degenerate states coupled by dynamic interaction are derived. The cases of excitation of the molecule by a short light pulse in a state with an energy higher than the energy of the degenerate states and into one of the degenerate states are considered. The populations of states are determined by solving the Schrödinger equation for the amplitudes of probability of populating the states of the composite system comprised of the molecule and a quantized radiation field. It was found that the resulting expressions satisfy the optical Bloch equations for the considered dynamics of the populations of the molecule’s states. Significant distinctions of the present results on the simulation of quantum beats from the corresponding simulation results reported in some works, performed based on different approaches, are revealed. The reasons for these differences are discussed.
The effect of collisions on the resonance fluorescence spectrum of two-level atoms excited by monochromatic resonance radiation is studied. Analysis is performed for systems where the Doppler broadening is small compared to the collision frequency (high buffer gas pressures) and for the general case where collisions arbitrarily change the phase of the radiation-induced dipole moment (from completely interrupted to completely unaffected phase of the dipole moment). Both at a relatively low and at a high excitation radiation intensity, the resonance fluorescence spectrum is shown to depend on whether the two-level system is closed or open. This is especially true for the narrow unshifted Rayleigh scattering line. It is shown that, although the absorption line is homogeneously broadened, the resonance fluorescence spectrum exhibits a clearly pronounced anisotropy. In a direction close to the direction of propagation of the excitation radiation, the Rayleigh scattering line is maximally narrowed. Under certain conditions (that can easily be created in experiments), the width of this line is proportional to the diffusion coefficient of atoms interacting with the radiation.
The effect of collisions on the resonance fluorescence spectrum of three-level atoms with a V-configuration of levels when excited by two monochromatic resonance fields has been theoretically investigated. The analysis has been carried out for the systems with a small Doppler broadening compared to the collision frequency (high buffer gas pressures) and for the general case of an arbitrary change (from complete failure to complete preservation) of the phase memory at any of the three transitions in the V-system. It has been shown that in the three-level V-type atoms excited by two monochromatic fields, the resonant fluorescence spectrum (the number of spectral lines and their widths) at one of the transitions strongly depends on the presence of resonant radiation at the adjacent transition. Under certain conditions, the line widths will be completely determined by the relaxation characteristics of the adjacent transition and, in particular, can be repeatedly narrowed with an increase in the radiation intensity at the adjacent transition. It has been shown that despite the homogeneous nature of the broadening of the absorption lines, the resonance fluorescence spectrum has a pronounced anisotropy with respect to the mutual orientation of the wave vectors of spontaneous and exciting radiation. It has been established that the line widths in the resonance fluorescence spectrum are proportional to the diffusion coefficient of the atoms interacting with radiation under certain conditions. This fact can serve as the basis for a spectroscopic method for measuring the transport frequencies of the collisions of the radiation-absorbing particles with the buffer ones. It has been shown that the effects of phase memory in the collisions lead to a strong qualitative and quantitative modification of the resonance fluorescence spectrum.
Resonance fluorescence of a two-level emitter displays persistently anti-bunching irrespective of the excitation intensity, but inherits the driving laser’s linewidth under weak monochromatic excitation. These properties are commonly explained in terms of two disjoined pictures, i.e., the emitter’s single photon saturation or passively scattering light. Here, we propose a unified model that treats all fluorescence photons as spontaneous emission, one at a time, and can explain simultaneously both the spectral and correlation properties of the emission. We theoretically derive the excitation power dependencies, measurable at the single-photon incidence level, of the first-order coherence of the whole resonance fluorescence and super-bunching of the spectrally filtered, followed by experimental confirmation on a semiconductor quantum dot micro-pillar device. Furthermore, our model explains peculiar coincidence bunching observed in phase-dependent two-photon interference experiments. Our work provides an intuitive understanding of coherent light-matter interaction and may stimulate new applications. Standard descriptions of resonance fluorescence consider either absorption and re-emission in a single-photon picture or passive scattering. This study shows that resonance fluorescence can be described by a pure quantum state of the emitter and photon, revealing a coherent superposition that challenges the conventional view of spontaneous emission as an incoherent process.
Abstract Mathematical modeling of the excitation dynamics of an isolated two-level particle under bichromatic irradiation is carried out on basis of solutions of the Schrödinger equation for the probability amplitudes of the states of the composite system of the particle and an interaction two-mode quantized radiation field, with the photons for each of which in a superposition state at the initial time. An analytical expression describing the change in the time of the population of the excited state of a particle in the adsorption of one of the irradiation photons in the simplest case when the irradiation is a sequence of identical pulses of a sinusoidal form is obtained. The obtained time dependence is compared with the time dependence of the diagonal matrix element of the statistical operator of the particle in the excited state found on the basis of the numerical solution of the system of the optical Bloch equations, with the corresponding irradiation described by the classical theory. Examples of significant differences in the type of these compared time dependences for a number of characteristic cases of irradiation are given.