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Physical Review Letters

Microwave multiphoton excitation of helium Rydberg atoms: The analogy with atomic collisions

Willem van de Water, K. A. H. van Leeuwen, Suzanne Yoakum, Enrique J. Galvez, Leo Moorman, T. H. Bergeman, B. E. Sauer, Patrick M. Koch

Published Aug 14, 1989• 14 citations
Publisher

Abstract

We study multiphoton transitions in helium Rydberg atoms subjected to a microwave electric field of fixed frequency but varying intensity. For each principal quantum number in the range n=25--32, the ${n}^{3}$S to ${n}^{3}$(L>2), n=25--32, transition probability exhibits very sharp structures as a function of the field amplitude. Their positions could be reproduced precisely using a Floquet Hamiltonian for the interaction between atom and field. Their shapes are determined by the transients of field turn-on and turn-off in a way that makes a close analogy with the theory of slow atomic collisions.

DOI
10.1103/physrevlett.63.762

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We observe and reproduce theoretically, Stueckelberg oscillations in the microwave excitation of helium (n=28) 3S^{3}\mathrm{S}3S Rydberg atoms. They are produced by the coherent evolution along two isolated Floquet potential curves as the microwave electric field amplitude varies along a half-sine-wave pulse shape. The measured visibility and separation of the oscillations depends sensitively on the Floquet structure, on the atomic beam velocity, and particularly on additive noise, which smears and broadens the pattern.
In a recent paper Stoneman, Thomson, and Gallagher [Phys. Rev. A 37, 1527 (1988)] studied the excitation of potassium Rydberg atoms in microwave fields for a few values of the initial S-state principal quantum number. In one case the measured excitation probability as a function of microwave amplitude showed a rather broad feature that was explained in terms of level crossings between quasienergy states. The details of a crucial ingredient of this explanation, namely, a broadening mechanism, were, however, left unexplained.
We report on an experimental study of the frequency dependence of the microwave ``ionization'' probability for laser-excited Rb(np)2{)}^{2})2P3/2{\mathit{P}}_{3/2}P3/2​(\ensuremath{\Vert}MJ{\mathit{M}}_{\mathit{J}}MJ​\ensuremath{\Vert}=1/2) Rydberg atoms. Most data are for n=84. The microwave field was produced by a low-noise frequency synthesizer, and the laser-excited atoms subsequently driven by microwaves were kept in an environment cooled to 77 K in order to minimize the perturbing effects of the thermal, blackbody-radiation field. The driving frequency covered 4--14-MHz intervals around three frequencies between 8.87 and 16.14 GHz. Data are shown for 1- and 5-\ensuremath{\mu}s interaction times, which correspond to the driving frequency being resolved by the atoms to about 1 and 0.2 MHz, respectively. The turnon and turnoff parts of the microwave pulse shape were slow, lasting about 6 ns (circa 70 field oscillations). For the narrow frequency intervals used, the microwave field amplitude was calibrated in situ with use of two-photon Rabi-nutation measurements, which also directly demonstrated the spatial uniformity of the driving field amplitude and its coherence over at least a 1-\ensuremath{\mu}s time scale. Within the frequency intervals studied experimentally, we have observed no sharp, frequency-dependent structure outside of that expected from experimental counting statistics. We give physical arguments based on experimental data and previous experimental and theoretical work on microwave ``ionization'' that show that the present experiments have been in the range of the scaled frequency above 1. Thus, these experimental data examine in a continuous fashion the frequency dependence of microwave ``ionization'' in the high-scaled-frequency regime. Finally, we discuss our results in the light of published theoretical discussions of what might be expected to be the frequency dependence of the microwave ``ionization'' probability for various quantal models for the one-dimensional hydrogen atom in this high-frequency regime.
We observe microwave multiphoton transitions in Rydberg states of Na using intense subnanosecond half-cycle electric field pulses in a microwave transmission line. Transition probabilities from ns and nd states, ranging in principal quantum number from 18 to 40, to nearby nl (l\ensuremath{\geqslant}2) states are measured both as a function of pulse amplitude and the delay between two identical temporally spaced pulses. The transition rate depends strongly on both the pulse amplitude and the temporal delay between the two pulses. Nearly 100% of the population can be transferred for certain amplitudes of the half-cycle pulse. Transition probabilities are successfully described both with a dynamic Stark model and direct numerical integration of the time-dependent Schr\"odinger equation. Ramsey interference between two delayed pulses is observed that shows strong-field behavior. The two-pulse experiment is a technique for high-order multiphoton spectroscopy without concern for ac Stark shifts.