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arXiv:1703.04597 · Physical Review A

Quantum backflow and scattering

Henning Bostelmann, Daniela Cadamuro, Gandalf Lechner

Published Jul 13, 2017• 24 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.96.012112

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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.
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.
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 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.
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.
We present an introduction to the backflow effect in quantum mechanics – the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We show that the effect is present even for simple states consisting of superpositions of gaussian wave packets, although the size of the effect is small. Inspired by the numerical results of Penz et al, we present a wave function whose current at any time may be computed analytically and which has periods of significant backflow, with a backwards flux equal to about 70 percent of the maximum possible backflow, a dimensionless number c bm ≈ 0.04, discovered by Bracken and Melloy. This number has the unusual property of being independent of ℏ (and also of all other parameters of the model), despite corresponding to a quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We conclude by discussing a specific measurement model in which backflow may be identified in certain measurable probabilities.
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.