Rydberg microwave ionization

In alkali atom experiments no explicit resonances have been observed in microwave ionization. However, there are indirect confirmations of the multiphoton resonance picture. First, according to the multiphoton picture the sidebands of the extreme n and n + 1 Stark levels should overlap if E = 1/3n5. In the laser excitation spectrum of Na Rydberg states from the 3p3/2 state in the presence of a 15 GHz microwave field van Linden van den Heuvell et al. observed sidebands spaced by 15.4 GHz, as shown in Fig. 10.15.18 The extent of the sidebands increases linearly with the microwave field, as shown in Fig. 10.15, and the n = 25 and n = 26 sidebands overlap at microwave fields of 150 V/cm or higher, matching the observation that the 25d state has an ionization threshold of 150 V/cm in a 15 GHz field. 

While ionization by linearly polarized fields has been well studied, there is only one report of ionization by a circularly polarized field, the ionization of Na by an 8.5 GHz field.36 In the experiment Na atoms in an atomic beam pass through a Fabry-Perot microwave cavity, where they are excited to a Rydberg state using two pulsed tunable dye lasers tuned to the 3s — 3p and 3p —> Rydberg transitions at 5890 A and —4140 A respectively. The atoms are excited to the Rydberg states in the presence of the circularly polarized microwave field which is turned off 1 fis after the laser pulses. Immediately afterwards a pulsed field is applied to the atoms to drive any ions produced by microwave ionization to a microchannel plate detector. To measure the ionization threshold field the ion current is measured as the microwave power is varied. 

A much higher circularly polarized field is required to ionize the atoms than a linearly polarized field, as shown by Fig. 10.21, a plot of the threshold fields, where 50% ionization occurs, for linearly and circularly polarized 8.5 GHz fields. As shown by Fig. 10.21, the circularly polarized microwave ionization threshold field is very nearly E = l/16n4, the same as the the static field required to ionize a Rydberg Na atom and much higher than the field required for ionization by... 

The three switches defined above rest on the mechanism of interspersed resonances, which was first suggested theoretically by Howard (1991). In the following we demonstrate the action of such a switch in the case of bichromatically driven hydrogen Rydberg atoms. It results in the prediction of a new kind of ionization peak in the microwave ionization of hydrogen Rydberg atoms. Recently performed experiments indicate that the effect actually exists. 

There are also important advances concerning the theoretical description of Rydberg atoms in strong radiation fields. Buchleitner et d. (1995) report on fully fiedged three-dimensional computations of the microwave ionization problem. They use the method of complex rotation discussed in Section 10.4.1, adapted to the computation of the resonances of the Floquet operator. The computed ionization probabilities are in good overall agreement with existing experimental data. 

Bliimel, R. (1994b). Microwave ionization of hydrogen Rydberg atoms Resonance analysis and critical fields, Phys. Rev. A49, 4787-4793. 

Lai, Y.-C., Grebogi, C., Bliimel, R. and Ding, M. (1992 ). Algebraic decay and phase-space metamorphoses in microwave ionization of hydrogen Rydberg atoms, Phys. Rev. A45, 8284-8287. 

Leopold, J.G. and Percival, I.C (1978). Microwave ionization and excitation of Rydberg atoms, Phys. Rev. Lett. 41, 944-947. 

Moorman, L. and Koch, P.M. (1992). Microwave ionization of Rydberg atoms, in Quantum Non-Integrability, eds. D. H. Feng and J. M. Yuan (World Scientific, Singapore). 

Using Rydberg atoms and microwave fields it has been possible to observe virtually all one electron strong field phenomena. The attraction of these experiments is that they can be more controlled than most laser experiments, with the result that more quantitative information can be extracted. The insights gained from these experiments can be profitably transferred to optical experiments. To demonstrate the latter point we demonstrate that apparently non-resonant microwave ionization, in fact, occurs by resonant transitions through intermediate states. These experiments demonstrated clearly the power of Floquet analysis of such processes, and the ideas were subsequently applied to the analogous problem of laser multiphoton ionization. 

Rydberg atoms and microwave fields constitute an ideal system for the study of atom-strong field effects, and they have been used to explore the entire range of one electron phenomena [5]. Here we focus on an illustrative example, which has a clear parallel in laser experiments, a series of experiments which show that apparently non-resonant microwave ionization of nonhydronic atoms proceeds via a sequence of resonant microwave multiphoton transitions and that this process can be understood quantitatively using a Floquet, or dressed state approach. 

The second approach is to use thermal beams of alkali atoms as shown in Fig. 10.2.4 A beam of alkali atoms passes into a microwave cavity where the atoms are excited by pulsed dye lasers to a Rydberg state. A1 /zs pulse of microwave power is then injected into the cavity. After the microwave pulse a high voltage pulse is applied to the septum, or plate, inside the cavity to analyze the final states after interaction with the microwaves. By adjusting the voltage pulse it is possible to detect separately atoms which have and have not been ionized or to analyze by selective field ionization the final states of atoms which have made transitions to other bound states. 

When a) l/n3, the field required for ionization is E = 1/9n4, and as a> approaches l/n3 it falls to E=0.04n. These observations can be explained qualitatively in the following way. At low n, so that a> 1/n3, the microwave field induces transitions between the Stark states of the same n and m by means of the second order Stark effect. With only a first order Stark shift a state always has the same dipole moment and wavefunction, as indicated by the constant slope dW/d of the energy level curve. Thus when the field reverses, — — , the Rydberg electron s orbit does not change. With a second order Stark shift as well, the slope dW/d is not the same at E and —E, and as a result the dipole moment and wavefunction are not the same. If the field is reversed suddenly a single Stark state in the field E is projected onto several Stark states of the same n and m when E — - E. Since all the Stark states of the same n make transitions among themselves they ionize once the field is adequate to ionize one of them, the red one, at E = 1/9n4 for m n. 

A way of doing microwave spectroscopy peculiar to the study of Rydberg atoms is to use selective field ionization to discriminate between the initial and final states of the microwave transition. An example of the application of this technique is the measurement of millimeter wave intervals between Na Rydberg states by Fabre et a/.13 using the arrangement shown in Fig. 16.5. 

Three different methods have been used to make microwave resonance measurements of intervals between alkaline earth Rydberg states. In all of these measurements state selective laser excitation of alkaline earth atoms in a beam was combined with one of three forms of state selective ionization of the final states. 

Both definitions are natural since wq turns out to be the ratio of the microwave frequency w and the Kepler firequency H of the Rydberg electron, and Sq is the ratio of the microwave field strength and the field strength experienced by an electron in the noth Bohr orbit of the hydrogen atom. Motivated by the above discussion we have redrawn the results obtained by Bayfield and Koch (1974) and present them in Fig. 7.2 as an ionization signal (in arbitrary units) versus the scaled field strength defined in (7.1.3). For no in (7.1.3) we chose no = 66, the centroid of the band of Rydberg states present in the atomic beam. 

Bliimel, R. and Smilansky, U. (1990b). Ionization of hydrogen Rydberg atoms in strong monochromatic and bichromatic microwave fields, J. Opt. Soc. Am. B7, 664-679. 

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