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## Transitions between Highly Excited States of Alkali Atomsby
William A. Molander
When the fields which induce the transitions are generated by similarly excited atoms superfluorescence results. A general equation of motion for the atomic transition operators in multilevel superfluorescence is derived using the Markov approximation. When a small sample approximation is made, expectation values of this equation reduce to a simple intuitively appealing set of non-linear rate equations for the populations of the levels. Numerical solutions of these equations are presented for several interesting special cases. Several new phenomena are predicted including alteration of branching ratios, coherent trapping of population in an excited state, and relaxation oscillations in the decay. It is found that the non-linear decay tends to direct the population down a single decay route. Transitions between Rydberg states due to externally applied fields are also studied. Specifically the use of external fields to excite Rydberg atoms from states of low angular momentum to circular-orbit states is examined. The methods of Stark switching and microwave multiphoton resonance are found to be unable to excite circular-orbit states when the principle quantum number is greater than 15. A new method is proposed which overcomes this limitation. The method, which is simple to implement, is similar to Stark switching. The difference is that a microwave field rather than a d.c. field is used to split and mix the angular-momentum states.
As Rydberg atoms are pumped into circular orbits they enter the regime in which all quantum numbers are large. The Correspondence Principle suggests that the predictions of purely classical mechanics and those of quantum mechanics should converge in such a regime. This suggestion is examined by carrying out a classical calculation and a quantum mechanical calculation of the dynamics of the pumping of a hydrogen atom and an alkali atom by a d.c. or a.c. electric field from a state of low angular momentum to higher angular momentum. It is found that if one averages the classical predictions over a range of initial values consistent with the Uncertainty Principle limits the two theories agree rather well except that there remain some oscillations due to quantum inference in the quantum case.
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