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

TL;DR

This paper critiques a previous claim that a superselection principle prevents superpositions of Bloch states in periodic systems, demonstrating that such superpositions are experimentally feasible and observable.

Contribution

It refutes the claimed superselection principle for Bloch states and shows how localized measurements can detect superpositions, challenging prior theoretical assertions.

Findings

Superpositions of Bloch states can be experimentally observed.

Localized measurements can determine relative phases of superposed states.

The superselection principle for Bloch states is not valid in practice.

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.