The name is absent

21

3.3.1 N=200 at zero temperature

We already finished a systematic canonical calculation for N = 200 particles at zero tem-
perature. Several representative density profiles are illustrated in Fig. 3.2 for various polar-
izations defined as

P = (N↑-N_i)∕(N_x+N_l),

and for two different trap geometry: a moderately cigar-shaped trap with λ = 5 and a very
elongated trap with λ = 50. For each set of parameters, we show the column densities
n_σ{z, x) = ʃ dy n_σ(x, y, z) for both spin components as well as their difference, and also
the double-integrated axial spin density s(z) = f dxdy [n↑(x,y,z) - n_i(x,y,z)]. Note that
the column densities are the ones that are directly measured in the experiment with the
imaging laser beam propagating along one radial axis, while the axial densities can be
easily obtained from column densities by integrating over the remaining radial axis.

As a verification of the code correctness, we first performed the calculation for the
spherical trap case (Λ = 1) which has been studied in Ref [22]. Our calculation shows that,
in this case, the density profiles always obey the spherical symmetry. When comparing
to the results in Ref. [22], we found that, other than an overall scaling, our results are al-
most identical to theirs at the same polarization P, despite the fact that the total number of
atoms used in Ref. [22] is two orders of magnitude larger than ours. We refer the readers to
Ref. [22] for details. Here we just give a brief description of the key features. Note that the
authors of Ref. [22] solved the one-dimensional radial equation, hence the spherical sym-
metry of the cloud is automatically imposed. Whereas in our calculation, we only impose

<<   27   28   29   30   31   32   33   >>

More intriguing information