I'm not quite sure about your background so I'll try to give you a gentle introduction: The article you were reading was probably about Bose-Einstein-Condensation. This is a phenomenon where all the atoms (with bosonic statistics) sit in the ground state of some external confining potential (e.g. a magneto optical trap) at finite temperature. The important part is the one about finite temperature. This is non trivial since we would expect that at finite temperature some fraction of the atoms were excited by thermal fluctuations. This state of matter was predicted by <PERSON> and <PERSON> in 1924 and realized in 1995 by several groups at JILA and MIT.
ad 1) What the people do in order to measure the momentum distribution of an ensemble of atoms (not just one) is the following: They trap their ensemble in an external potential which is suddenly switched off. Particles with higher momenta will fly further than particles with lower momenta. By shining light on the expanding cloud and checking how much was absorbed they find the velocity distribution of the cloud. 795
(see your pictures http://jila.colorado.edu/bec/) This is also called TOF imaging (time-of-flight imaging). Thus one has measured the momentum distribution via the spatial density distribution.
ad 2) The BEC is a remarkable phenomenon occuring in ideal quantum gases relying only on the bosonic statistics of the atoms. Yet if the atoms interact weakly, the gas still exhibits a condensation into its ground state. The temperatures when this occurs are about $T_c\approx10^{-7}K$. If we look at TOF images at increasingly colder temperatures we observe a Gaussian distribution of the particle density (with width proportional to the temperature). Ones we cool the ensemble below the critical temperature (BEC) we observe a so called Thomas-Fermi-profile (an upside down parabola growing out of the thermal Gaussian distribution http://phys.strath.ac.uk/laser/BEC.jpg) given that the trapping potential was harmonic. The width of the density distribution of a BEC is merely due to the interactions between the gas atoms. At $T=0$ the distribution would look the same.
ad 3) The Bose-Einstein distribution for "hot" gases almost looks like the <PERSON> and thus in momentum space like a Gaussian distribution. (You can see this by doing a high temperature expansion) Differences arise, roughly speaking, at low temperatures and give rise to the condensation phenomenon. 795