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Focus: Golfing with a Single Photon

Rebecca M Slayton

Published Aug 1, 2001• 0 citations
OpenAlex

Abstract

The probability of finding a photon in a narrow range of both position and momentum simultaneously appears to be negative, thanks to the uncertainty principle.

Related papers

Golfing with a Single Photon

Rebecca M Slayton

The probability of finding a photon in a narrow range of both position and momentum simultaneously appears to be negative, thanks to the uncertainty principle.

Focus•Aug 1, 2001•0 citations

Single Photon Position and Momentum Uncertainty Relations

Giacomo Guarnieri, Mário Motta, L. Lanz

•Mar 25, 2014•0 citations

Characterization of non-classical particle propagation using superpositions of position and momentum

Yuki Senoo, Holger F. Hofmann, Hiroki Yamakami +1 more

The uncertainty principle suggests a quantitative trade-off between the control of position and the control of momentum in particle propagation. However, a superposition of two states with very different uncertainty trade-offs introduces an interference term that seems to combine precise statements about position and about momentum, allowing us to study how quantum mechanics describes the propagation of individual particles in free space. Here, we present a detailed experimental study of photons prepared in a superposition of position and momentum generated in a Sagnac interferometer. The transverse distribution of photons was obtained with three different measurement settings at the output port of the interferometer, corresponding to the initial position distribution, the initial momentum distribution, and an intermediate propagation time at which the contributions of initial position and momentum uncertainties are approximately equal to each other. We show that the interference effect localizes the photons in narrow intervals of position and momentum, resulting in a quantitative violation of Newton's first law as the interference pattern spreads out at the intermediate position. The data obtained can be used to demonstrate the negativity of the Wigner function in regions outside the position and momentum intervals in which the position and momentum contributions are confined.

quant-pharXiv:2604.00417•Journal of Physics Photonics•Apr 2, 2026•0 citations

Radar Ambiguity Functions of Positive Type

Walter Schempp

In radar analysis there exists an analogue of the Heisenberg uncertainty principle of quantum mechanics. These uncertainty principles say that it is impossible to determine simultaneously the range (resp. position) and range rate (resp. momentum) of a moving target (resp. non-relativistic quantum-mechanical particle) with an arbitrarily high accuracy at a given instant of time. This analogy suggests that there should be a common mathematical structure behind that explains both of them. The concept of real Heisenberg nilpotent group lies at the foundations of signal theory as well as of quantum mechanics. Adopting the view point of nilpotent harmonic analysis it becomes obvious that the radar auto-ambiguity functions are of pure positive type on the symplectic time-frequency plane which will be identified with the tangent space to the Schrödinger coad-joint orbit of the Heisenberg group. Combining the classical Bochner theorem with Hudson’s characterization of the state vectors that give rise to non-negative Wigner quasi-probability densities we identify the Gabor functions as pulse envelopes of those radar auto-ambiguity functions on the time-frequency plane that are of positive type simultaneously with respect to its usual vector group structure as well as to its symplectic structure.

International series of numerical mathematics•Jan 1, 1984•5 citations

Testing Heisenberg's Uncertainty Principle with Polarized Single Photons

Sofia Fahlvik Svensson, Mohamed Bourennane

•Jan 1, 2013•0 citations

Negative probability

Andreas R. Blass, Yuri G. Gurevich

This article was written for the Logic in Computer Science column in the February 2015 issue of the Bulletin of the European Association for Theoretical Computer Science. The intended audience is general computer science audience. The uncertainty principle asserts a limit to the precision with which position x and momentum p of a particle can be known simultaneously. You may know the probability distributions of x and p individually but the joint distribution makes no physical sense. Yet Wigner exhibited such a joint distribution f(x,p). There was, however, a little trouble with it: some of its values were negative. Nevertheless Wigner's discovery attracted attention and found applications. There are other joint distribution, all with negative values, which produce the correct marginal distributions of x and p. But only Wigner's distribution produces the correct marginal distributions for all linear combinations of position and momentum. We offer a simple proof of the uniqueness and discuss related issues.

arXiv:1502.00666•Feb 2, 2015•4 citations
The uncertainty principle suggests a quantitative trade-off between the control of position and the control of momentum in particle propagation. However, a superposition of two states with very different uncertainty trade-offs introduces an interference term that seems to combine precise statements about position and about momentum, allowing us to study how quantum mechanics describes the propagation of individual particles in free space. Here, we present a detailed experimental study of photons prepared in a superposition of position and momentum generated in a Sagnac interferometer. The transverse distribution of photons was obtained with three different measurement settings at the output port of the interferometer, corresponding to the initial position distribution, the initial momentum distribution, and an intermediate propagation time at which the contributions of initial position and momentum uncertainties are approximately equal to each other. We show that the interference effect localizes the photons in narrow intervals of position and momentum, resulting in a quantitative violation of Newton's first law as the interference pattern spreads out at the intermediate position. The data obtained can be used to demonstrate the negativity of the Wigner function in regions outside the position and momentum intervals in which the position and momentum contributions are confined.
In radar analysis there exists an analogue of the Heisenberg uncertainty principle of quantum mechanics. These uncertainty principles say that it is impossible to determine simultaneously the range (resp. position) and range rate (resp. momentum) of a moving target (resp. non-relativistic quantum-mechanical particle) with an arbitrarily high accuracy at a given instant of time. This analogy suggests that there should be a common mathematical structure behind that explains both of them. The concept of real Heisenberg nilpotent group lies at the foundations of signal theory as well as of quantum mechanics. Adopting the view point of nilpotent harmonic analysis it becomes obvious that the radar auto-ambiguity functions are of pure positive type on the symplectic time-frequency plane which will be identified with the tangent space to the Schrödinger coad-joint orbit of the Heisenberg group. Combining the classical Bochner theorem with Hudson’s characterization of the state vectors that give rise to non-negative Wigner quasi-probability densities we identify the Gabor functions as pulse envelopes of those radar auto-ambiguity functions on the time-frequency plane that are of positive type simultaneously with respect to its usual vector group structure as well as to its symplectic structure.
This article was written for the Logic in Computer Science column in the February 2015 issue of the Bulletin of the European Association for Theoretical Computer Science. The intended audience is general computer science audience. The uncertainty principle asserts a limit to the precision with which position x and momentum p of a particle can be known simultaneously. You may know the probability distributions of x and p individually but the joint distribution makes no physical sense. Yet Wigner exhibited such a joint distribution f(x,p). There was, however, a little trouble with it: some of its values were negative. Nevertheless Wigner's discovery attracted attention and found applications. There are other joint distribution, all with negative values, which produce the correct marginal distributions of x and p. But only Wigner's distribution produces the correct marginal distributions for all linear combinations of position and momentum. We offer a simple proof of the uniqueness and discuss related issues.