Comment on "Do Bloch waves interfere with one another?"

Abstract: We point out that argumentation presented in [Phys. Lett. A 417, 127699 (2021)], leading to the conclusion that in periodic systems there is a superselection principle forbidding two different Bloch states to form a coherent superposition of a fixed phase, is unjustified and false. As an example, we show that the operator projecting to the selected Wannier state can be experimentally utilized to determine relative phase between superposed Bloch states. In this way we argue that, in fact, the non-existence of the aforementioned superselection principle is manifested always when localized measurements are performed, for example in state-of-the-art experiments with ultracold atoms confined in optical lattices.