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.

Gouy phase and quantum interference with cross-Wigner functions for matter-waves

“…Experiments were performed with acoustic and water waves 13 – 15 , surface plasmon-polaritons with non-Gaussian spatial properties 16 , focused cylindrical phonon-polariton wave packets in LiTaO 3 crystals, and for Bose-Einstein condensates and electron waves 17 – 20 . Interestingly, the effects of the quantum Gouy phase was also verified with the evolution of two-photon states 21 .…”

Supporting quantum technologies with an ultralow-loss silicon photonics platform

“…2.1) to support spatial shaping of their qubits 34 – 36 We have also identified turbulence mitigation 158 for satellite QKD as a promising application of our low-loss PICs with efficient phase shifters and integrated responsive detectors. We additionally have an ongoing collaboration with the Max Planck Institute for Quantum Optics to implant erbium in our silicon waveguides to achieve quantum emitters with narrow linewidth 159 …”

“…6(c). In other words, the bends preserve the mode power distribution, which is useful when designing PICs for mode multiplexing 32 and when using spatial modes as a quantum degree of freedom 33 – 36 (see also Sec. 5).…”

Riccati equations of opposite torsions from the Lie-Darboux method for spatial curves and possible applications

“…The physical origin of this phase shift is still debatable despite its centenary history. There are proposals to interpret it as a Berry phase, e.g., in [9] it is discussed for paraxial Gaussian beam optics whose propagation is described in terms of the complex beam width parameter evolving under a bilinear Möbius transform as in (10). Very recently, the Gouy phase shift has been discussed in a pure quantum optical approach [10], i.e.…”