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

Mesoscale and Nanoscale Physics;Atomic Physics;Quantum Physics