  We propose a method to measure the normal fraction of a two-dimensional Bose
gas, a quantity that generally differs from the non-condensed fraction. The
idea is based on applying a spatially oscillating artificial gauge field to the
atoms. The response of the atoms to the gauge field can be read out either
mechanically from the deposited energy into the cloud, or optically from the
macroscopic optical properties of the atomic gas. The local nature of the
proposed scheme allows one to reconstruct the spatial profile of the superfluid
component; furthermore, the proposed method does not require having established
thermal equilibrium in the gas in the presence of the gauge field. The
theoretical description of the system is based on a generalization of the
Dum-Olshanii theory of artificial gauge fields to the interacting many-body
context. The efficiency of the proposed measurement scheme is assessed by means
of classical field numerical simulations. An explicit atomic level scheme
minimizing disturbing effects such as spontaneous emission and light-shifts is
proposed for Rb 87 atoms.
