title: 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 (WFH) detection provides a scheme that 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 WHF detectors on each mode of two classes of two-mode entangled states. Furthermore, we theoretically describe the response of WHF detection on a two-mode squeezed state in the context of generalized 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.
authors.affiliation: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
authors.forename: Gaia
authors.initials: G
authors.lastname: Donati
authors.affiliation: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
authors.forename: Tim J
authors.initials: TJ
authors.lastname: Bartley
authors.affiliation: 1] Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK [2] Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Xian-Min
authors.initials: XM
authors.lastname: Jin
authors.affiliation: 1] Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK [2] QOLS, Blackett Laboratory, Imperial College London, London SW7 2BW, UK.
authors.forename: Mihai-Dorian
authors.initials: MD
authors.lastname: Vidrighin
authors.affiliation: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
authors.forename: Animesh
authors.initials: A
authors.lastname: Datta
authors.affiliation: 1] Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK [2] Dipartimento di Scienze, Università degli Studi Roma Tre, Via della Vasca Navale 84, 00146 Rome, Italy.
authors.forename: Marco
authors.initials: M
authors.lastname: Barbieri
authors.affiliation: Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK.
authors.forename: Ian A
authors.initials: IA
authors.lastname: Walmsley