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Physical Review A

Microwave multiphoton transitions between Rydberg states of potassium

R. C. Stoneman, D. S. Thomson, Thomas F. Gallagher

Published Mar 1, 1988• 56 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.37.1527

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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.
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.
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 have used the interaction of hydrogen Rydberg atoms with microwave fields to study multiphoton ionization. The minimum number of photons absorbed in the experiments ranges from about 300 to only 15. A brief overview is given of the extensive theoretical work that is under development to explain experimental data, including various observed structures. Similarly we report on ionization of helium Rydberg atoms, qualitatively explained in terms of a static picture. Finally we show selective excitation of He triplet s‐state to higher angular momentum states, via absorption of several photons from the field. Using the Floquet method a close analogy between the microwave problem and slow atomic collisions can be made. Sharp resonant structures in the spectra can be linked to individual avoided crossings of calculated Floquet quasi‐energy curves. Our theory that exploits a separation of timescales explains very well the positions, depths, and shapes of the observed structures, but a discrepancy still remains concerning their widths.
We study experimentally and theoretically the detailed field-amplitude dependence of the multiphoton ionization and excitation probability of highly excited n0{\mathit{n}}_{0}n0​ 3^{3}3S helium atoms in a 9.924-GHz linearly polarized microwave electric field. For ionization, with principal quantum numbers in the range n0{\mathit{n}}_{0}n0​=25--32, we use a quasistatic analysis that employs integration of the time-dependent Schr\"odinger equation using basis states of the static field Hamiltonian. The calculated results are used to interpret the observed ionization threshold structure. For excitation, the results of n0{\mathit{n}}_{0}n0​ 3^{3}3S\ensuremath{\rightarrow}n0{\mathit{n}}_{0}n0​ 3^{3}3L, L>2 excitation experiments are explained quantitatively and precisely using a theory of multiphoton resonances. We present maps of quasienergy levels that allow the study of the dynamics of the field-switching transients. These transient effects are analyzed along the lines of standard atomic collision theory and are shown to determine the shape of the observed resonances.