Controlling and measuring a superposition of position and momentum

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.