  We evaluate the coupling of a Bose-Einstein condensate of ultracold,
paramagnetic atoms to the magnetic field of the current in a mechanically
vibrating carbon nanotube within the frame of a full quantum theory. We find
that the interaction is strong enough to sense quantum features of the nanowire
current noise spectrum by means of hyperfine-state-selective atom counting.
Such a non-destructive measurement of the electric current via its magnetic
field corresponds to the classical galvanometer scheme, extended to the quantum
regime of charge transport. The calculated high sensitivity of the interaction
in the nanowire-BEC hybrid systems opens up the possibility of quantum control,
which may be further extended to include other relevant degrees of freedom.
