Observing optical coherence across Fock layers with weak-field homodyne detectors

Abstract: Quantum properties of optical modes are typically assessed by observing their photon statistics or the distribution of their quadratures. Both particle- and wave-like behaviours deliver important information, and each may be used as a resource in quantum-enhanced technologies. Weak-field homodyne detection provides a scheme which combines the wave- and particle-like descriptions. Here we show that it is possible to observe a wave-like property such as the optical coherence across Fock basis states in the detection statistics derived from discrete photon counting. We experimentally demonstrate these correlations using two weak-field homodyne detectors on each mode of two classes of two-mode entangled states. Furthermore, we theoretically describe the response of weak-field homodyne detection on a two-mode squeezed state in the context of generalised Bell inequalities. Our work demonstrates the potential of this technique as a tool for hybrid continuous/discrete-variable protocols on a phenomenon that explicitly combines both approaches.