Controlling and measuring a superposition of position and momentum

TL;DR

This paper experimentally investigates the quantum limits of simultaneously controlling and measuring a particle’s position and momentum superposition using photons, demonstrating a quantum interference effect that surpasses classical bounds.

Contribution

It presents the first experimental demonstration of a superposition of position and momentum states with quantum interference, testing a theoretical lower bound on their joint measurement.

Findings

Observed quantum interference between position and momentum superpositions.

Achieved a measurement result 5.9% below the classical lower bound.

Validated theoretical predictions of quantum limits in position-momentum control.

Abstract

The dynamics of a particle propagating in free space is described by its position and momentum, where quantum mechanics prohibits the simultaneous identification of two non-commutative physical quantities. Recently, a lower bound on the probability of finding a particle after propagating for a given time has been derived for well-defined initial constraints on position and momentum under the assumption that particles travel in straight lines. Here, we investigate this lower limit experimentally with photons. We prepared a superposition of position and momentum states by using slits, lenses and an interferometer, and observed a quantum interference between position and momentum. The lower bound was then evaluated using the initial state and the result was 5.9\% below this classical bound.