Quantum Interference between a Single- Photon Fock State and a Coherent State A. Windhager, M. Suda, C. Pacher, M. Peev, A. Poppe Contact: martin.suda@ait.ac.at Motivation Optical quantum computing [1] became feasible using linear optical elements, single-photon sources, and detectors. It requires an integrated optics architecture for improved performance, miniaturization, and scalability [2]. Abstract We present a simple analytical expression for the single mode quantum field state at the individual output ports of a beam splitter when a coherent state and a single-photon Fock state are incident on the input ports. This output state turns out to be a statistical mixture between a coherent state and a displaced Fock state. Consequently we are able to find an analytical expression for the corresponding Wigner function. We further extend our calculations to the case of a Mach Zehnder interferometer with the same input fields, obtaining analytical results formally analogous to those of the beam splitter output ports. We also make some remarks about the general case for which the single-photon Fock state is replaced with an arbitrary input state. 2) Beam splitter: BS Single Photon Fock State (FS): 1) Introduction Optical quantum computing employs linear optical elements like beam splitters (BS) and Mach – Zehnder interferometers (MZ) as basic building blocks. Displaced Fock states (DFS) [3] emerge which are non-classical states of the harmonic oscillators generated by acting upon Fock states with displacement operators using coherent states (CS). Wigner functions of various states and mean photon numbers are presented. The calculations can be generalized with a CS at one input port and an arbitrary state at the other. Coherent State (CS): TQC 2010 / Page 1 TQC 2010 / Page 2 BS (99:1) TQC 2010 / Page 3 TQC 2010 / Page 4 3) Mach – Zehnder (MZ): phase shift Θ MZ TQC 2010 / Page 5 TQC 2010 / Page 6 [1] J.L.O’Brian: “Optical quantum computing”, Science, 318:1566 (2007) [2] A. Politi, M.J. Cryan, J.R. Rarity, S. Yu, and J.L. O’Brian: “Silica-on-silicon waveguide quantum circuits”, Science: 320:646 (2008) [3] A.I. Lvovsky and S.A. Babichev: “Synthesis and tomographic characterization of the displaced Fock state of light”, Phys. Rev. A, 66:011801 (2002) REFERENCES