Neutron Interferometry constrains dark energy chameleon fields

We present phase shift measurements for neutron matter waves in vacuum and in low pressure Helium using a method originally developed for neutron scattering length measurements in neutron interferometry. We search for phase shifts associated with a coupling to scalar fields. We set stringent limits for a scalar chameleon field, a prominent quintessence dark energy candidate. We find that the coupling constant $\beta$ is less than 1.9 $\times {10}^7$~for $n=1$ at 95% confidence level, where $n$ is an input parameter of the self–interaction of the chameleon field $\phi$ inversely proportional to ${\phi }^n$.