10.7 Microwave-Driven Hydrogen
371
atoms leave the region F 3 is altered into a statistical mixture of parabolic substates
of the same n-value by stray fields before the atoms entered the microwave cavity.
Classically, this corresponds to a microcanonical ensemble of trajectories filling all
spatial dimensions. Thus, three-dimensional theory is needed to completely model
the experiments. However, the theory of one-dimensional hydrogen does explain
some qualitative features of the experimental data quite well.
Two different methods, called ionization and quenching, are used to study
hydrogen atoms with principal quantum numbers in the range n = 27 to n = 90. In
most experiments, the microwave field has frequency f =
ω
2π = 9.9233(4) GHz.
This corresponds to an angular frequency in atomic units of ω = 1.51 × 10 −6 a.u.
The binding energy for a hydrogen atom with principal quantum number n = 66,
for example, is E = −1/2n 2 = −1.15 × 10 −4 a.u. Therefore it requires about 76
photons from the microwave field to ionize the atom. It is interesting to note also
that hydrogen atoms that are excited to level n = 66 are huge objects on the atomic
scale. They have a radius of about a B n 2 = 2.3 × 10 −5 cm as compared to hydrogen
in the ground state, which has the Bohr radius a B = 5.3 × 10 −9 cm.
As the hydrogen atoms enter the microwave cavity, in their own reference frame
they see the microwave field turn on as they enter the cavity and turn off as they leave
the cavity. The precise shape of the turnon-turnoff envelope of the microwave field
varies from experiment to experiment. For example, in Koch’s experiments, turn-on
and turn-off times of the field each last for about 60 oscillations of the microwave
field, and in between the hydrogen atoms move in a constant-amplitude microwave
field that lasts for about 300 oscillations. In Bayfield’s experiments, the envelope of
the microwave field, as viewed by the atom, looks like half a sine wave. The strength
of the microwave field can be determined to about ±5%. In all the experiments,
the hydrogen beam is in the microwave field for only a few hundred periods of
the microwave field, and any theory of microwave-driven hydrogen should take
this fact into account. The ionization experiments detect one or another of the
ionization products (the electron or proton) as a function of the microwave electric
field amplitude. The quenching experiments detect hydrogen atoms that survive the
interaction with the microwave field.
Experimental data from the ionization experiments are shown in Fig. 10.15 for
principal quantum numbers in the range n = 32 to n = 90 and for microwave
frequency f = 9.923 GHz. One notices a number of flat regions in the data for
n < 82 and a qualitative change in the data for n > 82. The isolated flat regions for
n < 82 are due to isolated higher-order nonlinear resonance zones. As we shall see
below, n = 82 is the lower edge of the region of overlap of the primary nonlinear
resonance zones (the lower edge of the classically chaotic region).
It is interesting to look more closely at the experimental data giving rise to the flat
regions in Fig. 10.15. In Fig. 10.16 we show the ionization data for hydrogen atoms
with principal quantum numbers in the range n = 65 to n = 74. The microwave
frequency is 9.92 GHz. Notice that, in Fig. 10.15, the ionization curves for atoms
with principal quantum numbers n = 66 to n = 72 appear to require the same field
strength for 90% ionization. This indicates that they lie in a resonance zone.
371
atoms leave the region F 3 is altered into a statistical mixture of parabolic substates
of the same n-value by stray fields before the atoms entered the microwave cavity.
Classically, this corresponds to a microcanonical ensemble of trajectories filling all
spatial dimensions. Thus, three-dimensional theory is needed to completely model
the experiments. However, the theory of one-dimensional hydrogen does explain
some qualitative features of the experimental data quite well.
Two different methods, called ionization and quenching, are used to study
hydrogen atoms with principal quantum numbers in the range n = 27 to n = 90. In
most experiments, the microwave field has frequency f =
ω
2π = 9.9233(4) GHz.
This corresponds to an angular frequency in atomic units of ω = 1.51 × 10 −6 a.u.
The binding energy for a hydrogen atom with principal quantum number n = 66,
for example, is E = −1/2n 2 = −1.15 × 10 −4 a.u. Therefore it requires about 76
photons from the microwave field to ionize the atom. It is interesting to note also
that hydrogen atoms that are excited to level n = 66 are huge objects on the atomic
scale. They have a radius of about a B n 2 = 2.3 × 10 −5 cm as compared to hydrogen
in the ground state, which has the Bohr radius a B = 5.3 × 10 −9 cm.
As the hydrogen atoms enter the microwave cavity, in their own reference frame
they see the microwave field turn on as they enter the cavity and turn off as they leave
the cavity. The precise shape of the turnon-turnoff envelope of the microwave field
varies from experiment to experiment. For example, in Koch’s experiments, turn-on
and turn-off times of the field each last for about 60 oscillations of the microwave
field, and in between the hydrogen atoms move in a constant-amplitude microwave
field that lasts for about 300 oscillations. In Bayfield’s experiments, the envelope of
the microwave field, as viewed by the atom, looks like half a sine wave. The strength
of the microwave field can be determined to about ±5%. In all the experiments,
the hydrogen beam is in the microwave field for only a few hundred periods of
the microwave field, and any theory of microwave-driven hydrogen should take
this fact into account. The ionization experiments detect one or another of the
ionization products (the electron or proton) as a function of the microwave electric
field amplitude. The quenching experiments detect hydrogen atoms that survive the
interaction with the microwave field.
Experimental data from the ionization experiments are shown in Fig. 10.15 for
principal quantum numbers in the range n = 32 to n = 90 and for microwave
frequency f = 9.923 GHz. One notices a number of flat regions in the data for
n < 82 and a qualitative change in the data for n > 82. The isolated flat regions for
n < 82 are due to isolated higher-order nonlinear resonance zones. As we shall see
below, n = 82 is the lower edge of the region of overlap of the primary nonlinear
resonance zones (the lower edge of the classically chaotic region).
It is interesting to look more closely at the experimental data giving rise to the flat
regions in Fig. 10.15. In Fig. 10.16 we show the ionization data for hydrogen atoms
with principal quantum numbers in the range n = 65 to n = 74. The microwave
frequency is 9.92 GHz. Notice that, in Fig. 10.15, the ionization curves for atoms
with principal quantum numbers n = 66 to n = 72 appear to require the same field
strength for 90% ionization. This indicates that they lie in a resonance zone.