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