  The quantum geometric potential is a gauge invariant carrying novel geometric
features between any two energy levels or bands in quantum systems. In generic
time-dependent systems it gives a vital physical modification for the
instantaneous energy gaps, laying down more appropriate quantum adiabatic
conditions for both non-degenerate and degenerate systems. Remarkably, for
generic parameterized quantum systems, the integration of the quantum geometric
potential on a closed loop leads to a novel type of quantized winding number,
which is a quantum counterpart of the Gauss-Bonnet theorem. The effects of the
quantum geometric potential had been indirectly supported by the experiments on
the quantum adiabatic evolution, however, a direct experimental observation so
far is lacking. In this paper we propose an interference measurement to
directly probe the quantum geometric potential, where the relevant parameters
are easily accessible by current experimental apparatus. A direct confirmation
of this new physical quantity could motive further theoretical and experimental
investigations as well as its potential real applications.
