Spatial Coherence of Tunneling in Double Wells

We argue that the tunneling between two 2D electron gases in a weak magnetic field is of resonance character, and involves a long lifetime excitonic state of an electron and hole {\it uniformly spread} over cyclotron orbits. We find that the tunneling gap is linear in the field, in agreement with the experiment, and is anomalously sensitive to the electron density mismatch in the wells. The spatial coherence of tunneling along the orbit can be probed by magnetic field parallel to the plane, which produces an Aharonov-Bohm phase of the tunneling amplitude, and leads to an oscillatory field dependence of the current.