Mode-mashing and quantum interferometry with triphoton states

For a number of years, many proposals have observed that the resolution of interferometry could be vastly improved, reaching the ``Heisenberg limit'' of $\Delta \phi \quad \approx $ 1/N, if the particles in the interferometer could be in a maximally entangled state of all travelling one path or the other, $\vert $N,0$>+\vert $0,N$>$, or ``N00N.'' This is a quadratic improvement over the shot-noise limit in classical interferometers, and might lead to significant improvements in metrology, and possibly even lithography. Unfortunately, given the nearly non-interacting nature of photons, such states have proved elusive for N$>$2. Recently, a new theoretical approach based on post-selective nonlinearity has paved the way to scalable generation of such states, which we have generated for N=3. In this talk, I review this approach, our experiment based on what we term ``mode-mashing,'' and their future prospects and limitations. I also discuss the difficult issue of how to perform complete quantum characterisations of such multi-photon states, in which the particles are distinguished only by their polarisations, which are in a complicated entangled state. We have generalized the standard techniques of quantum tomography to take into account the potential presence of extra ``distinguishing'' information inaccessible to measurement, and discuss the resulting limitations on one's ability to fully describe a quantum state. In the limit of completely indistinguishable photons, we argue that the N-photon object should be thought of essentially as a single composite spin-N/2 particle, whose polarisation state may be described by a generalized Wigner quasiprobability distribution over the classical phase space which is the surface of the Poincar\'{e} sphere. We generate a variety of coherent, spin-squeezed, and maximally entangled states, and show the resulting Wigner functions and density matrices. \newline \textbf{References} \newline 1. M.W. Mitchell, J.S. Lundeen, and A.M. Steinberg, Nature \textbf{429}, 161 (2004) \newline 2. R.B.A. Adamson, L.K. Shalm, M.W. Mitchell, and A.M. Steinberg, Phys. Rev. Lett. \textbf{98}, 043601 (2007) \newline 3. R.B.A. Adamson, P.S. Turner, M.W. Mitchell, and A.M. Steinberg, quant-ph/0612081