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arXiv:2504.12489 · Physical Review A

Searching for Bloch wave packets with almost definite momentum direction

Arseni Goussev, G. V. Morozov

Published Sep 4, 2025• 2 citations
arXivHTMLPDF

Abstract

The motion of a quantum particle in a one-dimensional periodic potential can be described in terms of Bloch wave packets. Like free-particle wave packets, they can propagate without attenuation. Here, we examine this similarity more closely by investigating whether Bloch wave packets can maintain a definite -- or nearly definite -- momentum direction, a property inherent to free-particle wave packets. This question is particularly relevant to the feasibility of using solid-state-based systems in the search for the first experimental realization of quantum backflow, a quantum interference effect in which a particle's probability density flows in a direction opposite to its momentum.

DOI
10.1103/k9km-k3dm

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The motion of a quantum particle in a one-dimensional periodic potential can be described in terms of Bloch wave packets. Like free-particle wave packets, they can propagate without attenuation. Here, we examine this similarity more closely by investigating whether Bloch wave packets can maintain a definite -- or nearly definite -- momentum direction, a property inherent to free-particle wave packets. This question is particularly relevant to the feasibility of using solid-state-based systems in the search for the first experimental realization of quantum backflow, a quantum interference effect in which a particle's probability density flows in a direction opposite to its momentum.
Quantum backflow is a counterintuitive phenomenon in which the probability density of a quantum particle propagates opposite to its momentum. Experimental observation of backflow has remained elusive due to two main challenges: (i) the effect is intrinsically small, with less than 4% of the probability able to flow backward, and (ii) it requires wave packets with a well-defined momentum direction, which are difficult both to prepare and to verify under realistic, noisy conditions. Here, we overcome these challenges by introducing a general formulation of quantum backflow applicable to arbitrary momentum distributions. The framework recovers the standard backflow limit for unidirectional states and identifies general backflow as probability flow exceeding that predicted by the particle's momentum distribution alone. We show that this excess can reach nearly 13%, surpassing the standard backflow bound by more than a factor of three. Furthermore, we extend the framework to the closely related phenomenon of quantum reentry, provide explicit examples of quantum states exhibiting large general backflow and reentry, and discuss the foundational implications of these nonclassical effects. Our results open a pathway toward the experimental observation of quantum backflow in realistic settings.
Abstract In his study of the ‘time of arrival’ problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.
Quantum backflow is usually understood as a quantum interference phenomenon where the probability current and momentum point in the opposite direction. 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. The former is especially appealing as the probability of finding a free falling particle above initial level grows for suitably prepared quantum state with most momentum downwards.
In his study of the ‘time of arrival’ problem in the nonrelativistic quantum mechanics of a single particle, Allcock [1] noted that the direction of the probability flux vector is not necessarily the same as that of the mean momentum of a wave packet, even when the packet is composed entirely of plane waves with a common direction of momentum. Packets can be constructed, for example for a particle moving under a constant force, in which probability flows for a finite time in the opposite direction to the momentum. A similar phenomenon occurs for the Dirac electron. The maximum amount of probabilitiy backflow which can occur over a given time interval can be calculated in each case.
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.
Abstract Quantum backflow is a counterintuitive effect in which the probability density of a free particle moves in the direction opposite to the particle’s momentum. If the particle is electrically charged, then the effect can be viewed as the contrast between the direction of electric current and that of the momentum. To date, there has been no direct experimental observation of quantum backflow. However, the effect has been simulated numerically (using classical computers) and optically (using classical light). In this study, we present the first simulation of quantum backflow using a real quantum computer.