Abstract We use previously obtained experimental results by neutron interferometry to effectively constrain the parameter space of several prominent dark energy models. This investigation encompasses the environment-dependent dilaton field, a compelling contender for dark energy that emerges naturally within the strong coupling limit of string theory, alongside symmetron and chameleon fields. Our study presents substantial improvements over previous constraints of the dilaton and symmetron fields, improving parameter constraints by several orders of magnitude. However, the analysis does not yield any new constraints on the chameleon field. Furthermore, we establish constraints for the projected neutron split interferometer, which has recently concluded a decisive proof-of-principle demonstration. Our symmetron simulations reveal that, depending on the parameter values, there are multiple static solutions with an increasing number of nodes and increasing energy inside a cylindrical vacuum chamber. This agrees with results obtained earlier in the literature for infinitely extended parallel plates. Interestingly, while these multiple solutions can correspond to domain walls forming inside the vacuum chamber, we also find solutions that do not reach their vacuum expectation value inside the vacuum chamber, but display multiple nodes nonetheless.