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, $\beta \gtrsim {10}^8$, 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 $\beta \gtrsim {10}^{11}$ would lead to new bound states at a distance of order $2\mu \mathrm{m}$, which is already ruled out by previous Grenoble experiments. The resulting bound, $\beta \lesssim {10}^{11}$, is already 3 orders of magnitude better than the upper bound, $\beta \lesssim {10}^{14}$, from precision tests of atomic spectra.

Figure 1

The chameleon exclusion plot. We find that above the bottom green line the chameleon field is independent of the coupling, above the top blue line chameleons produce a quantum state with a size of $2\mu \mathrm{m}$, and finally above the red dashed line the chameleons shift the $3\to 1$ resonance by more than 0.01 peV. We have also drawn the ultimate sensitivity limit at the ${10}^{-7}\mathrm{peV}$ level.