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arXiv:2211.06539 · Physical Review A

Unbounded quantum backflow in two dimensions

Maximilien Barbier, Arseni Goussev, Shashi C. L. Srivastava

Published Mar 7, 2023• 13 citations
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Abstract

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.

DOI
10.1103/physreva.107.032204

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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.
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.
We study the phenomenon of quantum backflow in tight-binding systems with complex couplings, considering different boundary conditions and lattice sizes. Backflow is an intrinsically non-classical effect where the density flux associated with a particle described by the superposition of wave functions with, say, positive momentum, acquires negative values. We calculate the superposition of positive momentum states that gives rise to the strongest backflow in the system. We also evaluate the bounds on the total amount of probability that flows in the opposite direction of the particle's momentum.
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.
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.
Abstract Quantum particles moving in one dimension with rightwards momentum can exhibit the surprising phenomenon of quantum backflow (QB): a net probability transfer to the left-hand half-line over a finite time interval. We generalize this phenomenon by considering the sum of probability differences for M disjoint time intervals. In classical mechanics, the total backflow lies in the interval [−1,0] for all M, indicating rightwards probability transfer. By contrast, we show that the maximum M-fold QB is positive and unbounded from above as M increases, demonstrating the existence of repeated backflow. For M≥2, a new phenomenon of ‘quantum overflow’ is discovered: there are states whose total backflow is below −1, which is impossible for classical particles. The extent of the backflow and overflow effects is described by a hierarchy of backflow and overflow functions and constants, of which the M=1 backflow constant was first studied by Bracken and Melloy. Limiting cases of the backflow and overflow functions are studied, including cases in which two disjoint intervals merge. The analytical results are supported by detailed numerical investigations. Using numerical acceleration methods, we obtain a new estimate of the Bracken–Melloy constant of 0.0384506, slightly lower than the previously accepted value of 0.038452.
Backflow is the phenomenon that the probability current of a quantum particle on the line can flow in the direction opposite to its momentum. In this paper, previous investigations of backflow, pertaining to interaction-free dynamics or purely kinematical aspects, are extended to scattering situations in short-range potentials. It is shown that backflow is a universal quantum effect which exists in any such potential, and is always of bounded spatial extent in a specific sense. The effects of reflection and transmission processes on backflow are investigated, both analytically for general potentials and numerically in various concrete examples.