Wave Function Renormalization Effects in Resonantly Enhanced Tunneling

Resonantly enhanced tunneling is a quantum effect in which the probability for the tunneling of a particle between two potential wells is increased when the quantized energies of the initial and final states of the process coincide. A Bose-Einstein condensate in an accelerated optical lattice potential can be used to study the phenomenon of resonantly enhanced tunneling. In a tilted periodic potential, atoms can escape by tunneling to the continuum via higher-lying levels. The tunneling process of atoms out of the tilted lattice is resonantly enhanced when the energy difference between lattice wells matches the distance between the energy levels in the wells. We study here the time evolution of a Bose-Einstein condensate with a narrow quasi-momentum distribution in a shallow (accelerated) optical lattice. The decay of the survival probability in the ground band has a step-like structure. In this regime we establish a connection between the wave function renormalization parameter Z, characterizing non-exponential decay, and the phenomenon of resonantly enhanced tunneling.