Experiment-friendly formulation of quantum backflow

Abstract

Quantum backflow is usually understood as a quantum interference phenomenon where probability current of a quantum particle points in the opposite direction to particle's momentum. Here, we quantify the amount of quantum backflow for arbitrary momentum distributions, paving the way towards its experimental verification. We give examples of backflow in gravitational and harmonic potential, and discuss experimental procedures required for the demonstration using atomic gravimeters. Such an experiment would show that the probability of finding a free falling particle above initial level could grow for suitably prepared quantum state with most momentum downwards.

On the experiment-friendly formulation of quantum backflow

“…We show that, for some parameter values, the EF criterion of Ref. [33] can be violated for this particular state. Then, in Section 4, we address the question of the maximal backflow, computed in accordance with the EF formulation, that can be obtained for an arbitrary positive-momentum state.…”

“…However, as we show in this brief paper, unless used with care the EF criterion of Ref. [33] may fail to identify QB in the standard case of a free particle with a positive momentum.…”

“…In Ref. [33], the authors consider a particular class of phase-space distributions f t (x, p) that are everywhere positive. This property, along with the normalization condition…”

“…Of particular significance to the present study is Ref. [33] that addresses QB for a particle, moving in a potential V (x), whose state ψ t (x) contains a priori both positive and negative momenta. In order to treat this scenario, the authors propose an alternative, "experimentfriendly" (EF) definition of QB, which is based on replacing the right-hand side of Eq.…”

“…In Section 2, we provide a concise summary of the EF formulation of QB put forward in Ref. [33]. In Section 3, we analyze a concrete example of a positivemomentum state that is known to exhibit QB according to the standard criterion, Eq.…”