Observation of the quantum Gouy phase

Controlling the evolution of a photonic quantum states is crucial for most quantum information processing and metrology tasks. Because of 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 not been studied in the context of elementary quantum states of light such as 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 related to the nature of the increased phase sensitivity of multi-photon quantum states.