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Physical Review A

Quantal and classical radiative cascade in Rydberg plasmas

M. Raymond Flannery, D. Vrinceanu

Published Sep 11, 2003• 38 citations
Publisher

Abstract

Atoms in high-$(n,\mathcal{l})$ states formed in cold Rydberg plasmas decay to the ground state in a succession of radiative transitions populating intermediate excited states. A classical treatment presents radiative cascade in a physically transparent way and reveals the ``trajectory'' in $n\mathcal{l}$ space obeyed by the cascade, scaling rules, and other aspects hidden within the quantal approach. Quantal-classical correspondence in radiative decay is directly demonstrated. Classical transition probabilities are also presented and are in excellent agreement with quantal transition probabilities, even for moderate quantum numbers.

DOI
10.1103/physreva.68.030502

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Cambridge University Press eBooks•Dec 31, 2015•0 citations
Atoms in high-(n,l)(n,\mathcal{l})(n,l) states formed in cold Rydberg plasmas decay to the ground state in a succession of radiative transitions populating intermediate excited states. A classical treatment presents radiative cascade in a physically transparent way and reveals the ``trajectory'' in nln\mathcal{l}nl space obeyed by the cascade, scaling rules, and other aspects hidden within the quantal approach. Quantal-classical correspondence in radiative decay is directly demonstrated. Classical transition probabilities are also presented and are in excellent agreement with quantal transition probabilities, even for moderate quantum numbers.
First Major Highlight: Collisional Stark Mixing at ultralow energies in Rydberg Plasmas. Atoms in high (n,l) states formed in cold Rydberg plasmas decay to the ground state in a succession of radiative transitions populating intermediate excited states. Which states are populated during cascading and with what probability can be obtained from known transition probabilities. Classical models simplify the calculation considerably, revealing the "trajectory" in nt space followed during the cascade, scaling rules and other aspects hidden within the quantal approach. Conserved Quantity (quantal analogue obscure): Quantal-Classical correspondence in radiative recombination and decay is directly demonstrated. Classical transition probabilities and radiative, recombination cross-section are in excellent agreement with quantal results. Cross section for three body collisional capture is formulated for arbitrary electron-energy distributions.
A steady-state cascade theory has been set up for radiative electron transitions. These are assumed to occur between a continuum and various excited states, as well as between any two excited states, of hydrogen-like atoms. The work contains two features which have not previously been fully taken into account: (1) Both spontaneous and induced transition probabilities have been included exactly. (2) In addition to the radiative transitions, the reverse transitions due to absorption of background radiation have also been included. The following graphical results are given: (a) The steady-state occupation probabilities of the excited states as a function of excess electron density. (b) A "sticking probability" Pn{P}_{n}Pn​ (for an electron from a level nnn to reach the ground state without leaving the atom) as a function of the principal quantum number nnn. (c) The effect of the cascade on the transition rate into the ground state. The calculation is valid for semiconductors and for the analogous astrophysical problem. Temperature dependences have also been studied. The graphs shown bear out quantitatively the expectation that Pn{P}_{n}Pn​ decreases as either the temperature or the principal quantum number increases.
In the last decade, ultracold plasmas have been created in the laboratory by photo-ionizing laser-cooled atoms. To understand the overall dynamics of ultracold plasmas, one needs to understand Rydberg collisional processes at ultracold temperatures. The two kinds of problems addressed in this thesis are: study of Rydberg atomic processes at ultracold temperatures, and a study of the overall dynamics of \nthe ultracold plasmas. \nTheoretical methods based on quantal-classical correspondence is used to understand Rydberg atomic processes such as radiative cascade, and radiative recombination. A simulation method suitable for ultracold collisions is developed and tested. \nThis method is then applied to study collisional-Stark mixing in Rydberg atoms. \nTo study the dynamics of the ultracold plasmas, a King model for the electrons in plasmas is proposed. The King model is a stationary, finite sized electron distribution for the electrons in a cloud of fixed ions with a Gaussian distribution. A Monte-Carlo method is developed to simulate the overall dynamics of the King distribution.
The past three decades have seen extraordinary progress in the manipulation of neutral atoms with laser light, to the point where it is now routine to trap and cool both individual atoms and entire atomic clouds to temperatures of only a few tens of nanoKelvin in a controlled and repeatable fashion. In this thesis we study several applications of Rydberg atoms – atoms with an electron in a highly excited state – within such ultracold atomic systems. Due to their highly-excited electron, Rydberg atoms have a number of exaggerated properties: in addition to being physically large, they have long radiative lifetimes, and interact strongly both with one another and with applied external fields. Rydberg atoms consequently find many interesting applications within ultracold atomic physics. We begin this thesis by analysing the way in which a rubidium atom prepared in an excited Rydberg state decays to the ground state. Using quantum defect theory to model the wavefunction of the excited electron, we compute branching ratios for the various decay channels that lead out of the Rydberg states of rubidium. By using these results to carry out detailed simulations of the radiative cascade process, we show that the dynamics of spontaneous emission from Rydberg states cannot be adequately described by a truncated atomic level structure. We then investigate the stability of ultra-large diatomic molecules formed by pairs of Rydberg atoms. Using quantum defect theory to model the electronic wavefunctions, we apply molecular integral techniques to calculate the equilibrium distance and binding energy of these molecular Rydberg states. Our results indicate that these Ryberg macro-dimers are predicted to show a potential minimum, with equilibrium distances of up to several hundred nanometres. In the second half of this thesis, we present a new method of symbolically evaluating functions of matrices. This method, which we term the method of path-sums, has applications to the simulation of strongly-correlated many-body Rydberg systems, and is based on the combination of a mapping between matrix multiplications and walks on weighted directed graphs with a universal result on the structure of such walks. After presenting and proving this universal graph theoretic result, we develop the path-sum approach to matrix functions. We discuss the application of path-sums to the simulation of strongly-correlated many-body quantum systems, and indicate future directions for the method.
Introduction Series of atomic spectral lines had been studied by emission from excited vapors even before Balmer described the regularity of the visible lines of hydrogen in 1884. However, direct excitation had been restricted to the few lowest-lying levels, particularly those accessible by electric dipole transitions from the ground state using classical light sources. The advent of tunable lasers in the 1970s changed such spectroscopic limitations enormonsly, allowing excitation to a very much larger number of states. Atoms in highly excited states, typically with principal quantum numbers n ≥ 10, are called Rydberg atoms. They are oversize, fragile states of significant intrinsic interest. They are very rare in nature because of their size and fragility, but they are found in interstellar space (H I regions). One of the best sources for comprehensive descriptions of Rydberg atoms and references to the literature describing their exploration is Ref. [120]. It describes their characteristic properties and behavior both classically and quantum mechanically, and especially their strongly enhanced interactions with external fields. The first thing to note is that Rydberg atoms are usually characterized by a single, highly excited electron while all the other electrons remain in their original states. Thus their properties are very nearly classical, and the atoms are much closer to the ideal hydrogen-like model of Chap. 7, along with appropriate quantum defects (see Chap. 10). The spectroscopy of such states is especially interesting because the active electron is much less perturbed by the other electrons in the atom than when it is in lower states. Moreover, there are some special circumstances in which the energy of a Rydberg state is degenerate with an atomic state having two electrons excited to lower levels, and such configurations yield further new information. Second, Rydberg atoms do not usually decay back to the ground state by emission of characteristic radiation, so their study is mediated by other techniques that reveal new and interesting properties. Such properties arise because Rydberg atoms have a huge dipole moment and very low binding energy resulting from the large average distance between the excited electron and the nucleus-plus-core of the rest of the atom with net charge e . Third, transitions between Rydberg states are quite different from those connecting to the ground state for at least three reasons.