Microwave ionization

Fig. 10.2 Major components of a thermal atomic beam apparatus for microwave ionization experiments,the atomic source, the microwave cavity, and the electron multiplier. The microwave cavity is shown sliced in half. The Cu septum bisects the height of the cavity. Two holes of diameter 1.3 mm are drilled in the side walls to admit the collinear laser and Na atomic beams, and a 1 mm hole in the top of the cavity allows Na+ resulting from a field ionization of Na to be extracted. Note the slots for pumping (from ref. 4).

As we shall see, microwave ionization can be thought of as a multiphoton absorption or as a process driven by a time varying field. We first discuss microwave ionization of alkali atoms, which can be described by the notions used to describe pulsed field ionization. To show the connection between the time varying field point of view and the photon absorption point of view we then discuss... 

Fig. 10.4 Field ionization signal ( ) and 15 GHz microwave ionization signal ( ) for the Na 20s state showing the ionization threshold as both the disappearance of the field ionization signal and the appearance of the microwave ionization signal with increasing microwave power (decreasing attenuation). For convenience the microwave-field amplitude is also...

The similarity of the K (n + 2)s — (n,k) transitions to the n—>n + 1 transitions of microwave ionization is verified by measuring the number of atoms making the former transition as a function of the microwave field amplitude.10 As the... 

First, we shall approach the problem as a transition driven by the time variation of a quasi-static field, in other words, in the Landau-Zener terms we used to describe microwave ionization. We can write the Schroedinger equation for this problem as... 

Having considered the connection between the multiphoton resonances and the microwave threshold field for the K (n + 2)s —> (n,k) transitions, it is now interesting to return to the analogous n — n + 1 transitions which are responsible for microwave ionization and consider them from this point of view. We start with a two level description based on the extreme n and n + 1 m = 0 Stark states, a description which is the multiphoton resonance counterpart to the single cycle Landau-Zener model presented earlier. The problem is identical to the problem... 

Due to the n(n + 1) possible n— n + 1 transitions it is in general difficult to observe resonance effects in microwave ionization as obvious as those shown in Fig. 10.9. Nonetheless several experiments show clearly the importance of multiphoton resonance in microwave ionization. In Ba and in He the observed microwave ionization thresholds are structured by resonances3,6. An excellent example is the microwave ionization probability of the He 28 3S state shown in Fig. 10.14. In He the 3S states intersect the Stark manifold at fields approaching l/3n5, and as a result making transitions from the energetically isolated 3S state requires a field comparable to the field required to drive n — n + 1 transition. The structure in Fig. 10.14 is quite similar to the structure in Fig. 10.8, which is not... 

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. 

The first measurements of microwave ionization in any atom were carried out with a fast beam of H by Bayfield and Koch1, who investigated the ionization of a band of approximately five n states centered at n = 65. Using microwave and rf fields with frequencies of 9.9 GHz, 1.5 GHz, and 30 MHz, to ionize the atoms they found that the same field was required at 30 MHz and 1.5 GHz to ionize the atoms, but that a smaller field was required at 9.9 GHz. The measurements showed that at n = 65 frequencies up to 1.5 GHz are identical to a static field. Later, more systematic measurements have confirmed the initial measurements and have allowed significant refinements of our understanding. In Fig. 10.16 we show the ionization threshold fields (in this case the field at which there is 10% ionization) of H in a 9.9 GHz field.21 The ionization fields are plotted as n4E vs n3a>, and they bring out two factors. First, at low frequencies the field required is l/9n4, the static field required to ionize the red n Stark state of m n. Second, as shown by the scaling of the horizontal axis, the required field drops below l/9n4 as the microwave frequency approaches the interval between adjacent n states, 1 In3. 

Fig. 10.16 Scaled microwave ionization field, nAE, for H plotted against the scaled microwave frequency n3co experimental ( ) one dimensional theory (x) two dimensional theory (O). n3co = 0.05 corresponds to n = 32 and n3aj = 0.6 corresponds to n = 73. Note the decline from n4E = 1/9 at n = 30 to progressively lower values as n approaches 60 (from...

If the microwave ionization can be described by a resonance multiphoton picture, it should be possible to observe other manifestations of resonance... 

Fig. 10.20 H 36 GHz microwave ionization fields (10% ionization) experimental ionization mode results (o) three dimensional classical calculations (x, ( ) (from ref. 30).

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... 

We now use the method defined in (6.2.58) to compute microwave ionization probabiUties for the same field strength and frequencies as were used above in connection with the Sturmian method. Using the exact decay rates A = 7re g /2 according to (6.2.48) and (6.2.49), and retaining only the first five SSE states in (6.2.58), we obtain the ionization probabilities shown in Fig. 6.10. They compare favourably with the probabiUties... 

The data shown in Fig. 6.9 and Fig. 6.10 confirm our suspicion that for weak microwave fields no chaos mechanisms have to be invoked for an adequate physical understanding of microwave ionization data. The situation, however, is quite different in the case of strong microwave fields. In this case the ionization routes are very comphcated, and the multiphoton pictmre loses its attractiveness. It has to be replaced by a picture based on chaos. Chaos provides a simpler description of the ionization process and consequently a better physical insight. The discussion of the chaotic strong-field regime is the topic of the following section. 

Fig. 7.1. Schematic sketch of a typical microwave ionization experiment.

---