Abstract:
Time of flight images reflect the momentum distribution of the atoms in
the trap, but the spatial noise in the image holds information on more
subtle correlations. Using Bosonization, we study such noise correlations
in several generic one dimensional systems of ultra cold fermions and
bosons. Specifically, we show how pairing as well as spin and charge
density correlations may be identified and extracted from the time of
flight images for fermionic systems, and what the signature of a
bosonic superfluid and Mott insulator state in one dimension in the noise
correlations is. The incipient orders in these systems manifest themselves
as power law singularities in the noise correlations, that depend on the Luttinger
parameters, which might suggest a general experimental technique to obtain
them.