Observation of the quantum Gouy phase

Abstract

Controlling the evolution of photonic quantum states is crucial for most quantum information processing and metrology tasks. Due to its importance, many mechanisms of quantum state evolution have been tested in detail and are well understood; however, the fundamental phase anomaly of evolving waves, called the Gouy phase, has had a limited number of studies in the context of elementary quantum states of light, especially in the case of photon number states. Here we outline a simple method for calculating the quantum state evolution upon propagation and demonstrate experimentally how this quantum Gouy phase affects two-photon quantum states. Our results show that the increased phase sensitivity of multi-photon states also extends to this fundamental phase anomaly and has to be taken into account to fully understand the state evolution. We further demonstrate how the Gouy phase can be used as a tool for manipulating quantum states of any bosonic system in future quantum technologies, outline a possible application in quantum-enhanced sensing, and dispel a common misconception attributing the increased phase sensitivity of multi-photon quantum states solely to an effective de Broglie wavelength.