Scattering of cold-atom coherences by hot atoms: Frequency shifts from background-gas collisions

Frequency shifts from background-gas collisions currently contribute significantly to the inaccuracy of atomic clocks. Because nearly all collisions with room-temperature background gases that transfer momentum eject the cold atoms from the clock, the interference between the scattered and unscattered waves in the forward direction dominates these frequency shifts. We show they are ≈10 times smaller than in room-temperature clocks and that van der Waals interactions produce the cold-atom background-gas shift. General considerations allow the loss of the Ramsey fringe amplitude to bound this frequency shift.