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Herald of the Bauman Moscow State Technical University Series Natural Sciences

Influence of a Scattering Medium Consisting of Potassium Atoms on the Luminescent Signal Decay Time: Theoretical Investigation by Monte Carlo Method

V.M. Yamshchikov

Published Jun 1, 2022• 1 citation
Publisher

Abstract

The study solves the problem of the luminescent photons propagation in a resonantly absorbing medium consisting of atoms of the studied substance and a buffer inert gas. The Monte Carlo method was used in numerical experiments carried out to simulate real processes that occur in a chamber designed to determine the lifetime of an individual atom in an excited state by the method of measuring the luminescence intensity decay time. Findings of the research show that when luminescent photons are repeatedly scattered (scattering means the process of absorption and re-emission of a photon by an atom) in a medium, the luminescence decay time noticeably increases, reaching a value greater than the average lifetime of an individual atom in an excited state. The reflection of photons from the walls that make up the chamber can lead to errors in measuring the lifetime. The process of luminescence decay is studied theoretically for various detunings of the laser frequency from the resonant transition frequency. A three-level model of the atom and a model of complete frequency redistribution were applied. The study describes an algorithm based on the Monte Carlo method, which is used to model the three-level population kinetics, laser radiation transfer, radiation trapping, and frequency redistribution

DOI
10.18698/1812-3368-2022-3-69-85

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Optics and Spectroscopy•Dec 1, 2021•1 citation
The study solves the problem of the luminescent photons propagation in a resonantly absorbing medium consisting of atoms of the studied substance and a buffer inert gas. The Monte Carlo method was used in numerical experiments carried out to simulate real processes that occur in a chamber designed to determine the lifetime of an individual atom in an excited state by the method of measuring the luminescence intensity decay time. Findings of the research show that when luminescent photons are repeatedly scattered (scattering means the process of absorption and re-emission of a photon by an atom) in a medium, the luminescence decay time noticeably increases, reaching a value greater than the average lifetime of an individual atom in an excited state. The reflection of photons from the walls that make up the chamber can lead to errors in measuring the lifetime. The process of luminescence decay is studied theoretically for various detunings of the laser frequency from the resonant transition frequency. A three-level model of the atom and a model of complete frequency redistribution were applied. The study describes an algorithm based on the Monte Carlo method, which is used to model the three-level population kinetics, laser radiation transfer, radiation trapping, and frequency redistribution
The method of numerical simulation was used to study the effective deexcitation time of the resonance transition in lithium vapor at the wavelength λ = 670.776 nm. Taking into account the partial frequency redistribution and the cylindrical geometry of the medium, the rate equations of the population balance of a two-level atom were solved along with the equation of radiation transfer. The light scattering by an atom was simulated by a linear combination of the angle-averaged frequency distribution functions R II and R III. The Biberman-Holstein escape factor was calculated as a function of the optical thickness of lithium vapor for different geometries of the luminescing gas and different models of the frequency redistribution functions.
In this work, a stationary problem analytical solution of the non-monochromatic directional radiation transfer through a medium filled with alkali metal atoms and a buffer gas is obtained. The three-level atom approximation was used to describe the level population kinetics. The processes of absorption and stimulated emission of photons, collisional mixing of the levels of the alkali metal atom fine structure, and spontaneous transitions were taken into account. The absorption of spontaneous radiation by the medium was not taken into account. Using the example of a medium consisting of potassium vapor and a helium buffer gas, the analytical and numerical solutions are compared.
Time dependent description of resonance Raman scattering is performed for a general system, by a density matrix reformulation of damping theory originally used for resonance fluorescence of atom. Radiative damping in the intermediate states can be described in terms of "damping operator" in realistic situations. In large ergodic systems, the scattering reduces to luminescence if the relaxation time within the excited states is much shorter than the radiative lifetime. In a typical case, time resolved emission spectra consist of various stages (i) scattering complex where absorption and emission are inseparable, (ii) dynamical and then (iii) kinetic relaxations giving rise to the hot luminescence, which finally converges to (iv) the ordinary luminescence from relaxed excited states. Hot luminescence does not appear within a motionally narrowed line. The interpretation of spectra depends also on the method of observation.
The method of numerical simulation was used to study the effective lifetime of the excited level of the resonance transition in sodium and lithium vapour. Taking into account the partial frequency redistribution and the cylindrical geometry of the medium, the rate equations of the population balance of a two-level atom were solved with the equation of radiation transfer. The Biberman–Holstein escape factor was calculated as a function of the optical thickness of vapour for different geometries of the luminescing gas and different models of the frequency redistribution functions. The dependence of the escape factor on the optical thickness investigated experimentally by Romberg and Kunze (J. Quant. Spectrosc. Radiat. Transfer. 1988 39 99) is discussed.
When a resonant photon traverses a sample of absorbing atoms, how much time do atoms spend in the excited state? Does the answer depend on whether the photon is ultimately scattered vs. transmitted? In particular, if it is not scattered, meaning that it emerges in the direction it entered, does it cause atoms to spend any time in the excited state, and if so, how much? In this thesis, I report an experimental measurement of the time a transmitted photon causes atoms to spend in the excited state. The experiment is carried out in an ultra-cold gas of Rubidium 85 atoms and involves simultaneously recording changes to the excited state occupation number induced by incident ("signal") photons and whether those photons are transmitted. The time atoms spend in the excited state, which is defined in terms of the time integral of the average excited state occupation number, is measured weakly using a separate, off-resonant “probe” laser to monitor the index of refraction of the sample—that is, I measure the nonlinear phase shift written by a signal pulse on this probe beam—and direct detection is used to isolate the effect of a single transmitted photon. For short pulses (10 ns, to be compared to the 26 ns atomic lifetime) and an optically thick medium (peak OD = 4, leading to 60% absorption given our broad bandwidth), I report that the average time atoms spend in the excited state due to one transmitted photon is not zero, but rather (77 +/- 16)% of the time the average incident photon causes them to spend in the excited state. This observation of “excitation without loss” is attributed to coherent forward emission, which arises, for instance, due to the sign-flip the instantaneous Rabi frequency (pulse envelope) picks up when a broadband pulse propagates through an optically thick medium with highly frequency-dependent absorption [1]. The results of this thesis reveal the complex history of photons as they propagate through an absorbing medium and illustrate the power of utilizing post-selection to experimentally investigate the past behaviour of observed quantum systems.
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.