10.7 Microwave-Driven Hydrogen
369
Resonance zones occur at n k =
2πk
ξ for k ≤ N. Thus the resonances cut off at some
value n = n N + n ≡ n L . The Floquet matrix has elements U n,n ≈ |J 0 (2)| 2 for
n < n L , U n,n ≈ 1 for n > n L , U n,n+1 ≈ |J 1 (2)| 2 for n < n L , and U n,n+k → 0 for
n > n L . For this truncated delta-kicked rotor, they found that the Floquet eigenstates
are exponentially localized for irrational kicks and extended for rational kicks.
10.7 Microwave-Driven Hydrogen
It requires only one photon to ionize hydrogen as long as we choose its energy to be
equal to or greater than the ionization energy. Therefore, even a very low amplitude
field can ionize hydrogen if the proper frequency is used. Ionization occurs as a
function of frequency and not amplitude. This is the photoelectric effect.
In 1974, Bayfield and Koch (1974) published a somewhat surprising result. They
found that in highly excited microwave-driven hydrogen there is a multiphoton
process for which the critical parameter for ionization of hydrogen is the amplitude
and not the frequency. For fixed frequency in the microwave region (such that
the photon energy is well below the ionization energy), ionization starts to occur
suddenly as the amplitude of the field is raised. Although they did not realize it at
the time, they had observed a new multiphoton ionization mechanism due to the
overlap of microwave-induced nonlinear resonances.
10.7.1 Experimental Apparatus
The experimental results that we will show in this section are due to several different
groups, but there are great similarities in the experimental techniques they use. We
will paraphrase descriptions of the experimental procedure found in Bayfield and
Pinnaduwage (1985); Koch (1988); Koch et al. (1989) (see also Koch (1983)).
In the microwave experiments, hydrogen atoms are excited to high Stark states
while moving in a fast beam, and the interaction of the hydrogen atoms with the
microwave field takes place when the atoms pass through a microwave cavity.
A schematic picture of the apparatus is shown in Fig. 10.13. Before entering the
microwave cavity, the hydrogen atoms are raised to high excited states using a
double-resonance excitation scheme involving two CO 2 lasers. As a first step in this
excitation process, electron transfer collisions of a 14 keV proton beam with Xe or
Ar produce neutral hydrogen atoms in excited states, including those with principal
quantum number n = 7. Then, as the atoms pass through the region with static field,
F 1 in Fig. 10.13 (typically F 1 ≈ 10 4 V/cm), atoms with parabolic quantum numbers
(n; n 1 , n 2 , m) = (8; 0, 7, 0), where n = n 1 + n 2 + |m| + 1 (see Appendix K), are
laser-excited to the state (n; n 1 , n 2 , m) = (10; 0, 9, 0). The atoms in the “tagged”
369
Resonance zones occur at n k =
2πk
ξ for k ≤ N. Thus the resonances cut off at some
value n = n N + n ≡ n L . The Floquet matrix has elements U n,n ≈ |J 0 (2)| 2 for
n < n L , U n,n ≈ 1 for n > n L , U n,n+1 ≈ |J 1 (2)| 2 for n < n L , and U n,n+k → 0 for
n > n L . For this truncated delta-kicked rotor, they found that the Floquet eigenstates
are exponentially localized for irrational kicks and extended for rational kicks.
10.7 Microwave-Driven Hydrogen
It requires only one photon to ionize hydrogen as long as we choose its energy to be
equal to or greater than the ionization energy. Therefore, even a very low amplitude
field can ionize hydrogen if the proper frequency is used. Ionization occurs as a
function of frequency and not amplitude. This is the photoelectric effect.
In 1974, Bayfield and Koch (1974) published a somewhat surprising result. They
found that in highly excited microwave-driven hydrogen there is a multiphoton
process for which the critical parameter for ionization of hydrogen is the amplitude
and not the frequency. For fixed frequency in the microwave region (such that
the photon energy is well below the ionization energy), ionization starts to occur
suddenly as the amplitude of the field is raised. Although they did not realize it at
the time, they had observed a new multiphoton ionization mechanism due to the
overlap of microwave-induced nonlinear resonances.
10.7.1 Experimental Apparatus
The experimental results that we will show in this section are due to several different
groups, but there are great similarities in the experimental techniques they use. We
will paraphrase descriptions of the experimental procedure found in Bayfield and
Pinnaduwage (1985); Koch (1988); Koch et al. (1989) (see also Koch (1983)).
In the microwave experiments, hydrogen atoms are excited to high Stark states
while moving in a fast beam, and the interaction of the hydrogen atoms with the
microwave field takes place when the atoms pass through a microwave cavity.
A schematic picture of the apparatus is shown in Fig. 10.13. Before entering the
microwave cavity, the hydrogen atoms are raised to high excited states using a
double-resonance excitation scheme involving two CO 2 lasers. As a first step in this
excitation process, electron transfer collisions of a 14 keV proton beam with Xe or
Ar produce neutral hydrogen atoms in excited states, including those with principal
quantum number n = 7. Then, as the atoms pass through the region with static field,
F 1 in Fig. 10.13 (typically F 1 ≈ 10 4 V/cm), atoms with parabolic quantum numbers
(n; n 1 , n 2 , m) = (8; 0, 7, 0), where n = n 1 + n 2 + |m| + 1 (see Appendix K), are
laser-excited to the state (n; n 1 , n 2 , m) = (10; 0, 9, 0). The atoms in the “tagged”