Microfabricated magnetic waveguides for neutral atoms

Bose-Einstein beams: Coherent propagation through a guide

“…In this case, however, one does not remain in the low density regime where Eq. (14) holds (this regime is valid if n(0) a sc ≪ 1, which from (11) and (14) gives N max ≪ a ⊥ /a sc ∼ 10 3 ). Working in the high density regime instead, one obtains…”

“…On the other hand, the weakly interacting 1D Bose gas picture also breaks down at very low densities, in the Tonks gas regime (recent references relevant to this discussion are [13][14][15][16]). This occurs in the regime n a sc ≪ (a sc /a ⊥ ) 2 ∼ 10 −6 which we thus discard from the present study.…”

“…From this and from Eq. (14) it follows that for rubidium N max can be as large as 10 9 . In this case, however, one does not remain in the low density regime where Eq.…”

“…Thus the approximation of V by a δ-function' is well justified in that limit, and we expect Eq. (14) to be very accurate [23].…”

“…From (2) and (14) we get N max = a 2 ⊥ Θ/(8a sc R c ). For a guide with R c = 5a ⊥ , Θ = π/2 and a ⊥ ranging from 1 µm to 10 µm, N max ranges from 7 to 70 atoms for a condensate of 87 Rb atoms (a sc = 5.77 nm).…”