Research data supporting "Observation of Weak Collapse in a Bose-Einstein Condensate"

Nonlocal energy functionals and long range interactions in collapsing condensates in a box

“…We can get an idea of what this energy looks like by plotting it in Figure 2 for the values q = 1.0783, d = 0.0240 (in units of R), N = 124021 (a value from set 2 of Ref. [7]), a = −1.018a 0 , ǫ = 1.018, α = 5.561 and…”

“…In order to determine the parameter d we shall examine the numbers of atoms in the condensate that were observed in set 2 of Ref. [7] (L = 30.2µm) when a took three consecutive values, since the variation of the other parameter q is going to be very slow in that case. All the corresponding observed values exhibit the texture of two plateaus for the remnant condensate (see for example Figure 1, which corresponds to one of the examined values).…”

“…[7], for the value a = −0.991963a 0 The value of c 0 found above can be used for all measured values of a, for all sets in Ref. [7], since it is just the proportionality constant between d and the magnetic length. Hence the dimensionless d is given by…”

“…Now that we have found d, we can use it for every value of a examined in Ref. [7] in order to find q as a function of ǫ/d. At the end, we shall compare all these values of q to see if they agree.…”

“…We use a nonlocal interatomic potential derived through general plausible arguments and we then calculate the energy using a very simple variational trial function for the condensate wavefunction. The result-ing energy is minimised and the minima are fitted to all six sets of data provided by the experimenters [7]. We find that the same values for the parameters of the interatomic potential can explain all six sets.…”