Quantum Backflow Study Demonstrates 4% Probability Flow Against Momentum in Realistic Wave Packets

The seemingly straightforward notion of a particle’s movement encounters a surprising twist in the quantum world, where probability can flow against the direction of momentum in a phenomenon known as backflow. Tomasz Paterek from Xiamen University Malaysia and Arseni Goussev from the University of Geneva, along with their colleagues, now demonstrate a significantly enhanced understanding of this counterintuitive effect, formulating a general theory applicable to a wider range of quantum states. This new framework overcomes long-standing challenges in observing backflow, which is typically a small effect and difficult to verify in realistic conditions, and predicts that probability flow exceeding the standard limit can reach nearly thirteen percent, more than tripling previous theoretical bounds. By extending the concept to include related phenomena like reentry, the team reveals states exhibiting these nonclassical effects and establishes a pathway toward finally observing backflow in practical experiments, potentially reshaping our understanding of quantum particle behaviour.

This work investigates quantum backflow in more realistic scenarios than typically considered, moving beyond idealized wave packets to explore conditions closer to those found in experiments. The research focuses on wave packets constructed from superpositions of Gaussian wave functions, allowing for detailed analysis of the probability flux and calculation of the conditions under which backflow occurs. Specifically, the team examines wave packets composed of two Gaussian functions with differing widths and centres, systematically investigating how these parameters influence the resulting backflow.

The calculations demonstrate that backflow is a robust feature of quantum mechanics that can occur with significant magnitude even for relatively broad wave packets. A key achievement is the derivation of an analytical expression for the backflow probability as a function of the wave packet parameters, revealing that the magnitude of backflow is sensitive to the separation between the Gaussian components and their respective widths, providing a means to control and enhance the effect. The backflow probability can reach values as high as 0. 1 for certain parameter combinations, representing a substantial fraction of the total probability flux, with implications for the interpretation of quantum measurements and the design of experiments probing the foundations of quantum mechanics.

As a counterintuitive phenomenon, quantum backflow describes the propagation of a quantum particle’s probability density opposite to its momentum. Experimental observation has remained elusive due to its intrinsically small magnitude and the difficulty of preparing and verifying wave packets with a well-defined momentum direction. To address these challenges, researchers introduce a general formulation of quantum backflow applicable to arbitrary momentum distributions, recovering the standard backflow limit for unidirectional states and identifying conditions under which backflow occurs even for complex momentum profiles, facilitating a more comprehensive understanding and potential observation in a wider range of experimental scenarios.

Largest Eigenvalue Scales with Inverse System Size

This study investigates the largest eigenvalue of a specific operator as a function of a parameter L through numerical calculations. The team performed calculations for L = 10 and 40, determining the largest eigenvalue and its standard deviation for each value. The data was then fitted to a linear function of 1/L to extrapolate the behavior as L approaches infinity, demonstrating that the largest eigenvalue appears to approach a finite limit as L becomes very large.

The fitted linear function took the form sup{λL} = a + b/L, yielding fitted parameters of a = 0. 1280997589328653 and b = -0. 09050752023369246. The extrapolated limit of the largest eigenvalue as L approaches infinity is estimated as sup{λ} = 0. 128100 ±0. 000002, representing a 68% confidence level. This provides a numerical estimate for the supremum of the eigenvalue spectrum of the operator in the limit of large L.

Large Backflow and Reentry in Quantum Systems

This research presents a generalized formulation of quantum backflow, a counterintuitive phenomenon where probability density propagates opposite to a particle’s momentum. Scientists have demonstrated that this effect, previously limited by its small magnitude and the difficulty of preparing appropriate quantum states, can be significantly larger than previously thought, exceeding established bounds by a factor of three. The team achieved this by developing a framework applicable to arbitrary momentum distributions, identifying general backflow as probability flow exceeding that predicted by the particle’s momentum alone.

Furthermore, the work extends to the related phenomenon of reentry, providing explicit examples of states exhibiting both large backflow and reentry. These findings open a pathway towards the experimental observation of backflow in realistic settings, which has proven challenging due to the subtlety of the effect.