  A microscopic theory of superfluid drag in a two-component Bose gas is
developed. The drag factor is shown to be proportional to the square root of
the gas parameter. Basing on the similarity between the drag force and vector
potential of magnetic field we propose how the superfluid drag can be used to
detect a Berry phase in a Bose counterpart of the Josephson charge qubit. We
consider a system in which the drag component, situated inside the drive
component, is confined in two half-ring traps separated by two Josephson
barriers. Under cyclic adiabatic change of Josephson coupling parameters and an
asymmetry of two traps a Berry phase is generated. This phase can be observed
though measurements of relative number of atoms in two traps. The Berry phase
depends on the drag factor and its detection can be used for determining the
value of the drag.
