Coherent Control of Tunneling in Double-Well Potentials

For an asymmetric double-well potential system, it is shown that, if the potential is quadratic until it reaches several times of the zero-point energies from the bottoms in each well, the energy eigenvalues of the low lying excited states of the double-well system must be close to the eigenvalues of the quadratic potentials. These eigenvalue structures suggest a method for the coherent control of the tunneling as well as realizing almost complete localization of the wave packet in one of the wells, by handling the double-well asymmetry. Numerical examples are included to indicate that the method could be useful also in a more general potential, and to propose experimental confirmations.