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Optics and Spectroscopy

Diffusion Dynamics of Rydberg States in the Field of Radiation with Continuous Spectrum

Anastasia S. Chervinskaya, Dmitrii L. Dorofeev, B. A. Zon

Published Aug 1, 2021• 1 citation
Publisher

Abstract

Abstract Redistribution of population of Rydberg states and ionization of an atom as a result of multistep cascade transitions between states induced by radiation with continuous spectrum are analyzed. Analysis is carried out both by straightforward numerical solution of kinetic equations governing state populations and by using the diffusion approximation based on the Fokker–Planck equation. Using an example of a sodium atom exposed to radiation with rectangular spectrum as an example, we demonstrate good agreement between the diffusion approximation and numerical solution to kinetic equations. Estimates for state populations, ionization rate, and minimum spectral density of radiation required for achieving considerable ionization are obtained within the framework of the diffusion approximation.

DOI
10.1134/s0030400x21070055

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arXiv:0807.2535•New Journal of Physics•Jan 30, 2009•55 citations
Abstract Redistribution of population of Rydberg states and ionization of an atom as a result of multistep cascade transitions between states induced by radiation with continuous spectrum are analyzed. Analysis is carried out both by straightforward numerical solution of kinetic equations governing state populations and by using the diffusion approximation based on the Fokker–Planck equation. Using an example of a sodium atom exposed to radiation with rectangular spectrum as an example, we demonstrate good agreement between the diffusion approximation and numerical solution to kinetic equations. Estimates for state populations, ionization rate, and minimum spectral density of radiation required for achieving considerable ionization are obtained within the framework of the diffusion approximation.
Redistribution of population and ionization of atomic Rydberg states due to multistep cascade transitions between states under the influence of radiation with continuous spectrum is considered. Consideration is carried up both by simulation of kinetic equations for state populations and with the use of a diffusion approximation based on the Fokker-Planck equation. On the example of sodium atom under the influence of radiation with rectangular spectrum a good agreement between the diffusion approximation and the kinetic equation simulation is shown. In the frame of the diffusion approximation some estimations are derived for the state populations, ionization rates and minimal spectral density of radiation necessary for significant ionization.
A stochastic model of associative ionization in collisions of Rydberg atoms with ground-state atoms is presented. The conventional Duman–Shmatov–Mihajlov–Janev (DSMJ) model treats the ionization as excitation of Rydberg electron to the continuum by the electric-dipole field generated by exchange interaction within the quasi-molecular ion. The stochastic model essentially extends this treatment by taking into account redistribution of population over a range of Rydberg states prior to ionization, which is caused by non-adiabatic processes in overlapping multiple level crossings of quasi-molecular Rydberg states. The redistribution is modelled as diffusion of electrons in the Rydberg energy spectrum using a Fokker–Planck-type equation. The process of l -mixing of Rydberg states at large internuclear distances and twisting of the collision trajectories on attractive potentials are taken into account. The choice of the collision velocity distribution is also shown to be important. Associative ionization rates have been calculated for Na**( nl ) + Na collisions with n = 5–25 and l = 0, 1, 2, and compared with the available experimental data and the calculations performed using the nonlinear DSMJ model. At relatively low n the stochastic model yields a substantially better agreement with the experimental data than the DSMJ model, while the results of both models converge at large n .
Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for nSnSnS, nPnPnP, and nDnDnD states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers n=8−−65n=8--65n=8−−65 and at three ambient temperatures of 77, 300, and 600K600\phantom{\rule{0.3em}{0ex}}\mathrm{K}600K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show that these phenomena affect both the magnitude of measured ionization rates and shapes of their dependences on nnn. The calculated ionization rates are compared with the results of our earlier measurements of BBR-induced ionization rates of Na nSnSnS and nDnDnD Rydberg states with n=8−−20n=8--20n=8−−20 at 300K300\phantom{\rule{0.3em}{0ex}}\mathrm{K}300K. A good agreement for all states except nSnSnS with n>15n>15n>15 is observed. We also present the useful analytical formulas for the quick estimation of BBR ionization rates of Rydberg atoms.
The results of theoretical calculations of the blackbody ionization rates of lithium, potassium, and cesium atoms residing in Rydberg states are presented. The calculations are performed for nS , nP , and nD states in a wide range of principal quantum numbers, n = 8−65, for blackbody radiation temperatures T = 77, 300, and 600 K. The calculations are performed using the known quasi-classical formulas for the photoionization cross sections and for the radial matrix elements of transitions in the discrete spectrum. The effect of the blackbody-radiation-induced population redistribution between Rydberg states on the blackbody ionization rates measured under laboratory conditions is quantitatively analyzed. Simple analytical formulas that approximate the numerical results and that can be used to estimate the blackbody ionization rates of Rydberg atoms are presented. For the S series of lithium, the rate of population of high-lying Rydberg levels by blackbody radiation is found to anomalously behave as a function of n . This anomaly is similar to the occurrence of the Cooper minimum in the discrete spectrum.
We have studied ionization of alkali-metal Rydberg atoms by blackbody radiation (BBR). The results of theoretical calculations of ionization rates of Li, Na, K, Rb and Cs Rydberg atoms are presented. The calculations have been performed for n S, n P and n D states for principal quantum numbers n =8–65 at ambient temperatures of 77, 300 and 600 K. The calculations take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show that these phenomena affect both the magnitude of the measured ionization rates and their n dependence. A Cooper minimum for BBR-induced transitions between bound Rydberg states of Li has been found. The calculated ionization rates are compared with our earlier measurements of BBR-induced ionization rates of Na n S and n D Rydberg states with n =8–20 at 300 K. Good agreement for all states except n S with n >15 is observed. Useful analytical formulae for quick estimates of BBR ionization rates of Rydberg atoms are presented. Application of BBR-induced ionization signal to measurements of collisional ionization rates is demonstrated.