Long-range quantum tunneling via matter waves

Quantum tunneling is a quantum phenomenon in which a microscopic object crosses through a potential barrier even if its energy cannot overcome the barrier. A general belief is that tunneling occurs only when the barrier width is comparable to, or smaller than the de Broglie's wavelength of the object. Here, we study the tunneling of an ultracold atom among N far-separated trapping potentials in a state-selective optical lattice and present a mechanism to realize long-range tunneling. We find that, mediated by the propagating matter wave emitted from the atom, coherent tunneling of the atom to the remote lattices occurs as long as bound states are present in the energy spectrum of the system formed by the atom and its matter-wave. Going beyond the Markovian approximation, and breaking through the conventional distance constraint, our result opens another avenue to realizing tunneling and gives a guideline for developing tunneling devices.