Current drag in two leg quantum ladders

• Study of coupled superconducting wires or bosonic tubes.
• Determination of the induced in one wire by the other.
• Connection of this problem to the commensurate–incommensurate transition.

A two-leg ladder of either interacting bosons or tightly bound cooper pairs is investigated when a supercurrent is forced in one of the legs of the ladder. The two legs of the ladder are connected by a tunneling term. Using a bosonization representation of such an interacting ladder we show that up to a certain critical current the current in the first wire induces an identical supercurrent in the second wire. When this threshold is exceeded vortices are formed in the system and the current in the second wire reduces even if the driving current increases. Potential applications to condensed matter or cold atomic systems are discussed.