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arXiv:2412.07898 · New Journal of Physics

Quantum backflow for two identical particles

Maximilien Barbier, Arseni Goussev

Published Feb 18, 2025• 3 citations
arXivHTMLPDF

Abstract

Abstract Quantum mechanics introduces the possibility for particles to move in a direction opposite to their momentum—a counter-intuitive and classically impossible phenomenon known as quantum backflow. The magnitude of this effect is relatively small, making its experimental observation, which has yet to be achieved, particularly challenging. Here, we investigate the influence of quantum statistics on the maximal backflow attainable for two identical particles confined to a ring. Notably, we demonstrate that the fermionic statistics significantly impedes quantum backflow compared to the bosonic statistics. Our findings suggest that any future experimental realization of quantum backflow should prioritize systems involving bosons rather than fermions.

DOI
10.1088/1367-2630/adb77e

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Abstract Quantum mechanics introduces the possibility for particles to move in a direction opposite to their momentum—a counter-intuitive and classically impossible phenomenon known as quantum backflow. The magnitude of this effect is relatively small, making its experimental observation, which has yet to be achieved, particularly challenging. Here, we investigate the influence of quantum statistics on the maximal backflow attainable for two identical particles confined to a ring. Notably, we demonstrate that the fermionic statistics significantly impedes quantum backflow compared to the bosonic statistics. Our findings suggest that any future experimental realization of quantum backflow should prioritize systems involving bosons rather than fermions.
Quantum backflow is the classically forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to many-particle systems. We give a general formulation of quantum backflow for systems formed of NNN free nonrelativistic structureless particles, either identical or distinguishable. Restricting our attention to bosonic systems where the NNN identical bosons are in the same one-particle state allows us in particular to analytically show that the maximum achievable amount of quantum backflow in this case becomes arbitrarily small for large values of NNN.
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.
In this work, dissipative quantum backflow is studied for a superposition of two stretched Gaussian wave packets and two identical spinless particles within the Caldirola-Kanai framework. Backflow is mainly an interference process and dissipation is not able to suppress it in the first case. For two identical spinless particles, apart from interference terms, the symmetry of the wave function seems to be crucial in this dynamics. The combined properties make bosons display this effect, even for the dissipative regime but, for fermions, backflow is not exhibited in any regime, dissipative and nodissipative. The anti-symmetric character of the corresponding wave function seems to be strong enough to prevent it. For bosons, backflow is also analyzed in terms of fidelity of one-particle states which is a well-known property of two quantum states. At very small values of fidelity, this effect is not seen even for bosons.
Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which the maximal amount of backflow has been found to be bounded. Quantum backflow exhibits dramatically different features in two-dimensional systems that, in contrast to the one-dimensional case, allow for degenerate energy eigenstates. Here we investigate the case of a charged particle that is confined to move on a finite disk punctured at the center and that is pierced through the center, and normally to the disk, by a magnetic flux line. We demonstrate that quantum backflow can be unbounded (in a certain sense), which makes this system a promising physical platform regarding the yet-to-be-performed experimental observation of this fundamental quantum phenomenon.
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.
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.