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Item Exceptional points of any order in a single, lossy waveguide beam splitter by photon-number-resolved detection(OSA, 2019-08) Quiroz-Juárez, Mario A.; Perez-Leija, Armando; Tschernig, Konrad; Rodriguez-Lara, Blas M.; Magaña-Loaiza, Omar S.; Busch, Kurt; Joglekar, Yogesh N.; León-Montiel, Roberto de J.; Physics, School of ScienceExceptional points (EPs) are degeneracies of non-Hermitian operators where, in addition to the eigenvalues, the corresponding eigenmodes become degenerate. Classical and quantum photonic systems with EPs have attracted tremendous attention due to their unusual properties, topological features, and an enhanced sensitivity that depends on the order of the EP, i.e., the number of degenerate eigenmodes. Yet, experimentally engineering higher-order EPs in classical or quantum domains remain an open challenge due to the stringent symmetry constraints that are required for the coalescence of multiple eigenmodes. Here, we analytically show that the number-resolved dynamics of a single, lossy waveguide beam splitter, excited by 𝑁 indistinguishable photons and post-selected to the 𝑁-photon subspace, will exhibit an EP of order 𝑁+1. By using the well-established mapping between a beam splitter Hamiltonian and the perfect state transfer model in the photon-number space, we analytically obtain the time evolution of a general 𝑁-photon state and numerically simulate the system’s evolution in the post-selected manifold. Our results pave the way toward realizing robust, arbitrary-order EPs on demand in a single device.Item Photonic quantum simulations of coupled PT -symmetric Hamiltonians(APS, 2022-01-26) Maraviglia, Nicola; Yard, Patrick; Wakefield, Ross; Carolan, Jacques; Sparrow, Chris; Chakhmakhchyan, Levon; Harrold, Chris; Hashimoto, Toshikazu; Matsuda, Nobuyuki; Harter, Andrew K.; Joglekar, Yogesh N.; Laing, Anthony; Physics, School of ScienceParity-time-symmetric (PT -symmetric) Hamiltonians are generally non-Hermitian and give rise to exotic behavior in quantum systems at exceptional points, where eigenvectors coalesce. The recent realization of PT -symmetric Hamiltonians in quantum systems has ignited efforts to simulate and investigate many-particle quantum systems across exceptional points. Here, we use a programmable integrated photonic chip to simulate a model composed of twin pairs of PT -symmetric Hamiltonians, with each the time reverse of its twin. We simulate quantum dynamics across exceptional points including two- and three-particle interference, and a particle-trembling behavior that arises due to interference between subsystems undergoing time-reversed evolutions. These results show how programmable quantum simulators can be used to investigate foundational questions in quantum mechanics.