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Physical Review A

Discrete-time picture for multiphoton microwave spectroscopy

M. J. Cavagnero, S. T. Cornett

Published May 1, 1997• 1 citation
Publisher

Abstract

The time evolution of atomic and molecular systems driven by periodic external fields is reformulated to combine Floquet's theorem with time-dependent representations of the atomic degrees of freedom. This approach increases the flexibility of Floquet calculations of multiphoton processes in strong radiation fields, particularly at low frequencies, by incorporating adiabatic states into the basis. The depopulation of Rydberg states of He and Na in strong microwave fields illustrates the utility of the method. In particular, a study of the depopulation of the 11s state of Na in an oscillatory field reveals a strong correspondence between dc-field Stark maps and quasienergy spectra and predicts a resonance feature associated with Landau-Zener transitions between dc Stark levels.

DOI
10.1103/physreva.55.3746

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The time evolution of atomic and molecular systems driven by periodic external fields is reformulated to combine Floquet's theorem with time-dependent representations of the atomic degrees of freedom. This approach increases the flexibility of Floquet calculations of multiphoton processes in strong radiation fields, particularly at low frequencies, by incorporating adiabatic states into the basis. The depopulation of Rydberg states of He and Na in strong microwave fields illustrates the utility of the method. In particular, a study of the depopulation of the 11s state of Na in an oscillatory field reveals a strong correspondence between dc-field Stark maps and quasienergy spectra and predicts a resonance feature associated with Landau-Zener transitions between dc Stark levels.
In a phenomenological two-level model, by using Floquet method, we directly calculate the multiphoton transition probability between the Rydberg states of an alkali-metal atom in strong microwave fields. The convergence of the truncated Floquet matrix, and the influences of parameters upon the multiphoton resonant spectra are discussed. The results show that our method can give clearer physical picture and better results about the multiphoton transition than indirect methods. Moreover, our method can easily be generalized to treat multi-level models.
Rydberg atoms in a static electric field provide an experimental system with which many aspects of strong atom-field interactions can be tested. We report measurements of multiphoton transitions in Rydberg states of potassium driven by chirped pulses of rf radiation. Pulses of rf are produced with frequencies swept from 675 to 825 MHz at rates from 0.25 MHz/ns to 7.5 MHz/ns. We present measurements of population transfer in a two-level system as a function of rf field strength and sweep rate. The data is analyzed with a dynamical Floquet model using Landau-Zener transition probabilities; this model accurately describes these transitions.
The behavior of Rydberg atoms in a recent experiment involving selective excitation in combined ac and dc electric fields is shown to be consistent with the predictions of a one-dimensional model incorporating only the extreme level of each Stark manifold. For low microwave powers, the excitation is resonant and is described qualitatively by multiphoton perturbation theory. For higher powers, an alternative stochastic theory predicts rapid ionization at all frequencies, as observed experimentally.
A methodology to calculate generalized coherent states for a periodically driven system is presented. We study wave packets constructed as a linear combination of suitable Floquet states of the three-dimensional Rydberg atom in a microwave field. The driven coherent states show classical space localization, spreading, and revivals and remain localized along the classical trajectory. The microwave strength and frequency have a great effect in the localization of Floquet states, since quasienergy avoided crossings produce delocalization of the Floquet states, showing that tuning of the parameters is very important. Using wavelet-based time-frequency analysis, the classical phase-space structure is determined, which allows us to show that the driven coherent state is located in a large regular region in which the zzz coordinate is in resonance with the external field. The expectation values of the wave packet show that the driven coherent state evolves along the classical trajectory.