Cold collision frequency shift

Implementing rf evaporation required an apparatus redesign, but the method opened the way to rapid progress. The atomic density grew to the point that the cold-collision frequency shift of the 1S-2S transition became visible [8], providing an in situ measurement of the density. With this tool, the BEC transition was soon achieved [9]. We shall describe our BEC studies below. 

Fig. 4. Cold collision frequency shift observed in the spectra of a single 120 /rK sample with initial maximum density of 6.6xlO13 cm3. The farthest red shifted spectrum corresponds to the largest density...

Interactions between neighboring atoms shift and broaden the line. This can be described from a many-body picture as a result of the mean field energy shift, AEe = (Anh2aeyg/ m) rig, where ae,g is the s-wave scattering length of atoms in state e and g, m is the atomic mass, and ng is the density of g-state atoms. From the an atomic standpoint it is equal to a cold collision frequency shift which we... 

The cold collision frequency shift is important in precision frequency measurements and has been observed in hydrogen maser [31] and fountain clock [32,33] experiments. From the point of view of precision measurements, the cold collision shift is an obstacle. However, in BEC experiments, the shift provides a helpful diagnostic for the density. 

When the transition temperature is achieved, a finite fraction of the atoms fall into the lowest energy quantum state of the trap. The spatial extent of the condensate is much smaller than the thermal radius of the cloud. Only a small fraction of the atoms are required to create a narrow region of very high density at the bottom of the trap. This high density region is readily observed because of its large cold collision frequency shift. The spectrum arising from the condensate can be seen in (Fig. 5), red-shifted up to 0.5 MHz from the Doppler free line. 

The Doppler-sensitive line gives a second clear signature for Bose-Einstein condensation. Because the lowest energy state is the lowest momentum state, the condensate appears as a relatively narrow peak at the center of the Gaussian spectrum. Its width is given by the cold collision frequency shift and is the same as in the case of Doppler free spectrum. 

It is now recognized that cold collision frequency shifts [32] is a crucial issue for every high precision atomic frequency standard, microwave or optical. For hydrogen at a density of 109 cm-3 the shift of the 1S-2S transition is about 0.4 Hz, [8], or a fractional shift of 1.7 x 10-16. For a rubidium hyperfine standard operating at the same density, the shift is about 6 xlO-14 [45,46]. 

The cold collision frequency shifts of 2S-nS transitions are a potential source of uncertainty. There are no theoretical predictions, and so they will have to be measured. However, if the scattering lengths are comparable to the 1S-2S scattering length the cold collision shift will not be a limiting factor. 

Because of the large density contrast between the condensed and noncondensed fraction, we are able to study the density of the noncondensed fraction even in the presence of the condensate. We determine the peak density from the cold collision shift of the Doppler free line. Reducing the trap depth by lowering the rf-frequency reduces the temperature while increasing the density. However, when the critical density is achieved, as observed by the onset of the far red-shifted signal, the peak density in the noncondensed cloud decreases with... 

Verhaar BJ, Gibble K, Chu S. (1993) Cold-collision properties derived from frequency shifts in a Cs fountain. Phys. Rev. A 48 R3429-R3432. 

---