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Journal of Physics B Atomic Molecular and Optical Physics

Multiphoton transition probabilities for potassium in strong parallel microwave and static fields

Jianguo Rao, Baiwen Li, K T Taylor

Published Sep 27, 1999• 2 citations
Publisher

Abstract

We refine an earlier method for calculating the spectra of atoms and molecules in a strong microwave or laser field plus a static electric field. Results are reported for microwave resonance transition spectra of potassium for transitions from the 19s state at five choices of fixed microwave field strength (38, 68, 120, 152 and 193 V cm(-1)) as the static field strength is varied from 200 to 550 V cm(-1). More resonances have been found in the higher microwave field-strength theoretical spectra than previously found experimentally. An understanding of butterfly like structures in the plot of quasi-energy against static electric field strength has allowed an improved understanding of these novel features.

DOI
10.1088/0953-4075/32/19/315

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We refine an earlier method for calculating the spectra of atoms and molecules in a strong microwave or laser field plus a static electric field. Results are reported for microwave resonance transition spectra of potassium for transitions from the 19s state at five choices of fixed microwave field strength (38, 68, 120, 152 and 193 V cm(-1)) as the static field strength is varied from 200 to 550 V cm(-1). More resonances have been found in the higher microwave field-strength theoretical spectra than previously found experimentally. An understanding of butterfly like structures in the plot of quasi-energy against static electric field strength has allowed an improved understanding of these novel features.
Observations are reported of complete sequences of N-photon resonant microwave transitions, in potassium, from the (n+2)s state to the lowest energy state of the linear Stark manifold of principal quantum number n. The number N of photons absorbed ranges from 1 to as high as 30, and n is in the range from 16 to 19. A sequence is observed by scanning the static electric field, starting at the field at which the levels undergo an avoided crossing, until zero field is reached. The maximum number of photons absorbed is observed to be proportional to the microwave field amplitude, with an offset of two photons at zero field. Dynamic Stark shifts of the levels are observed to be proportional to the microwave power. The n dependence and absolute size of the shift are in agreement with Floquet calculations. The relation between the N-photon resonances and microwave ionization is discussed. In particular, resonances in microwave ionization spectra are seen to be due to dynamic-Stark-shifted multiphoton transitions.
By a direct approach that is based on the Floquet method plus a kind of atomic potential model, we obtain the theoretical microwave threshold spectra with threshold fields and resonance fields that are in good agreement with the experimental ones. Our results confirm that the threshold fields do not exhibit smooth n dependence and show that, in general, the structure does not appear before the threshold field is achieved in the microwave threshold spectrum except for a few special cases. The explanation why the threshold fields do not exhibit a smooth n dependence and why the structure does not always appear before the threshold field is provided by our detailed theoretical calculations for the microwave threshold spectra.
We have applied a nonperturbative resonant theory to study the Rabi frequency of microwave multiphoton transitions between two Rydberg states of potassium in a static electric field. The Stark electric dipole moments used to calculate the Rabi frequency are determined by the Stark states' wave functions, which are obtained by the diagonalization method. The frequencies of the Rabi oscillations are in good agreement with either experimental ones or ones calculated by the time-dependent close-coupling method and the Floquet theory. Furthermore, we are able to show that the size of avoided crossings between the (n+2)s(n+2)s(n+2)s and (n,3)(n,3)(n,3) states can be predicted from the Stark electric dipole moment and the difference of the two Stark states' energy at a given resonance.
We report the observation of sequences of from 1- to as many as 28-photon transitions between potassium (n+2)s(n+2)s(n+2)s states and the lowest-energy Stark states of the nnn manifolds for $n=15\ensuremath{-}18$. The sequences are observed by the scanning of a static electric field from the field at which these pairs of levels nearly cross, to zero field where they are well separated. The maximum number of photons absorbed is observed to be proportional to the microwave field.