Penetration of Arbitrary Double Potential Barriers with Probability Unity: Implications for Testing the Existence of a Minimum Length

Quantum tunneling across double potential barriers is studied. With theassumption that the real space is a continuum, it is rigorously proved thatlarge barriers of arbitrary shapes can be penetrated by low-energy particleswith a probability of unity, i.e., realization of resonant tunneling (RT), bysimply tuning the inter-barrier spacing. The results are demonstrated bytunneling of electrons and protons, in which resonant and sequential tunnelingare distinguished. The critical dependence of tunneling probabilities on thebarrier positions not only demonstrates the crucial role of phase factors, butalso points to the possibility of ultrahigh accuracy measurements nearresonance. By contrast, the existence of a nonzero minimum length puts upperbounds on the barrier size and particle mass, beyond which effective RT ceases.A scheme is suggested for dealing with the practical difficulties arising fromthe delocalization of particle position due to the uncertainty principle. Thiswork opens a possible avenue for experimental tests of the existence of aminimum length based on atomic systems.