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 ultra cold neutrons in the terrestrial
gravitational field. When chameleons are strongly coupled to nuclear matter,
$\beta\gtrsim 10^8$, we find that the shift in energy levels would be
detectable with the forthcoming GRANIT experiment, where a sensitivity of order
one percent of a peV is expected. We also find that an extremely large coupling
$\beta\gtrsim 10^{11}$ would lead to new bound states at a distance of order 2
microns, which is already ruled out by previous Grenoble experiments. The
resulting bound, $\beta\lesssim 10^{11}$, is already three orders of magnitude
better than the upper bound, $\beta\lesssim 10^{14}$, from precision tests of
atomic spectra.
