Experiments with Supersonic Beams as a Source of Cold Atoms

To put equations 3.3, and 3.4 into context, consider the following example.
The experiment uses Si(111) as the reflecting surface, for reasons described in section
3.2.1, and the following calculation is based on this surface. The average mass of a
single silicon atom in the crystal is 4.7 · 10 −26 kg and the crystal Debye temperature is
690K (at room temperature). For a supersonic beam of helium from a 77K nozzle, the
beam velocity is ≈ 900m/s and the mass of a helium atom is 6.7·10 −27 kg. From this,
the Debye-Waller factor indicates that 65% of the beam will be elastically scattered.
While this is a good approximation of the elastic scattering amplitude, it does not
indicate the fraction of the beam which will be specularly reflected, as the beam may
be distributed into many diffraction channels. Figure 3.1 shows what fraction of a
helium beam will be elastically scattered as a function of crystal temperature, for
several incident beam velocities.
3.2.1 Crystal Choice: Si(111)
The choice of crystal substrate is important when creating a good atomic mir-
ror. Ideally, an atomic mirror will be atomically flat, since diffuse scattering will
result from surfaces that are rough on a length scale above the wavelength of the
incident beam. Also, since a mirror requires high specular reflection, the crystal sub-
strate should have a high Debye temperature, as well as low surface corrugation to
minimize diffracted flux. Additionally, the surface must be stable against reconstruc-
tion and corrosion, and will ideally be passive, reducing the accumulation of dirt and
adsorbates on the surface that lower the specularly reflected intensity. Finally, the
surface needs to be simple and inexpensive to prepare.
Crystal surfaces for helium diffraction studies are typically prepared by cleav-
ing or annealing in-situ. Because the crystal must be mounted to the tip of a rotor,
these methods are not ideal for this experiment. However, some surfaces are so inert
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