Strongly coupled chameleons and the neutronic quantum bouncer

We consider the potential detection of chameleons using bouncing ultracold neutrons. We show that the presence of a chameleon field over a planar plate would alter the energy levels of ultracold neutrons in the terrestrial gravitational field. When chameleons are strongly coupled to nuclear matter, β≳10(8), we find that the shift in energy levels would be detectable with the forthcoming GRANIT experiment, where a sensitivity of the order of 1% of a peV is expected. We also find that an extremely large coupling β≳10(11) would lead to new bound states at a distance of order 2  μm, which is already ruled out by previous Grenoble experiments. The resulting bound, β≲10(11), is already 3 orders of magnitude better than the upper bound, β≲10(14), from precision tests of atomic spectra.