  Many theories that attempt to formulate a quantum description of gravity
suggest the existence of a fundamental minimum length scale. A popular method
for incorporating this minimum length is through a modification of the
Heisenberg uncertainty principle known as the generalised uncertainty principle
(GUP). Experimental tests of the GUP applied to composite systems can be
performed by searching for the induced frequency perturbations of the modes of
mechanical resonators, thus constraining the degree of minimum length in
certain scenarios. In this work previous constraints made with mechanical
resonators are improved upon by three orders of magnitude, via the utilisation
of a cryogenic quartz bulk acoustic wave resonator. As well as purely
mechanical resonant modes; hybrid electromechanical anti-resonant modes are
investigated, and shown to be sensitive to the same GUP induced effects.
