Controlling and measuring a superposition of position and momentum

We present an observation of quantum interference between position and momentum with photons. We prepared a superposition of position and momentum states by using slits, lenses, and an interferometer. The precise control and measuring of propagation time of the photon results in a clear quantum interference of 85% visibility. The generated quantum state is then used to verify the violation of particle propagation inequality proposed by Hofmann [Phys. Rev. A 96, 020101(R) (2017)], resulting in 5.9% below the statistically predicted lower bound. We believe that this result is a major step towards further developments in quantum theory, such as fundamental modifications to the interpretation of quantum mechanics.