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 β is less than 1.9 ×107~for n=1 at
95\% confidence level, where n is an input parameter of the self--interaction
of the chameleon field φ inversely proportional to φn.Comment: 7 pages, 4 figure