Experiments with Supersonic Beams as a Source of Cold Atoms

n=∞
n=3
n=2
243 nm
243 nm
n=1
L=0 L=1 L=2
121 nm
-13.6 eV
-3.4 eV
0 eV
-1.5 eV
Figure 5.22: A simplified energy level diagram of atomic hydrogen, with the transition
wavelengths illustrating the dipole forbidden two-photon 1S − 2S transition, as well
as the dipole allowed 1S − 2P transition.
both practically (only one laser is needed) and physically (elimination of the Doppler
shift) to use a single wavelength. Energy and momentum must be conserved in the
process, and so for a resonant transition from a single beam the laser frequency must
be
2ωlaser = E2Spf − E1Spi = ω1S−2S + 2k · pi
m + 22k2 ,
m
(5.1)
where pi and pf are the initial and final momentum states of the atom, k is the wave
vector of the beam, and m is the mass of the hydrogen atom. The term 2 k·pi
m
referred to as the Doppler shift of the transition, and the 22k2 term is the recoil shift.
m
The Doppler shift due to the momentum distribution in the trap leads to a broad
excitation spectrum and thus a low transition rate, decreasing the number of atoms
which will be excited and detected.
Instead of a single beam, it is relatively simple to use two counterpropagating
beams from the same laser. Here an atom can absorb one photon from each beam,
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is