Exceptional points of any order in a single, lossy, waveguide beamsplitter by photon-number-resolved detection

Abstract

Exceptional points (EPs) are degeneracies of non-Hermitian operators where, in addition to the eigenvalues, 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 remains 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 beamsplitter, 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 beamsplitter 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 towards realizing robust, arbitrary-order EPs on demand in a single device.

arXiv comment5 pages, 2 figures

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• Higher-order exceptional point in a pseudo-Hermitian cavity optomechanical system
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• Quantum statistical signature of $\mathcal{P}\mathcal{T}$ symmetry breaking
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• Reconfigurable Network for Quantum Transport Simulation
• Essential role of quantum speed limit in violation of Leggett-Garg inequality across a PT-transition
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Temporal array with superconducting nanowire single-photon detectors for photon-number-resolution
• Classification of multiple arbitrary-order non-Hermitian singularities
• Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Fast-response silicon photonic microheater induced by parity-time symmetry breaking
• Quantum correlations in dissipative gain-loss systems across exceptional points
• Generating high-order exceptional points in coupled electronic oscillators using complex synthetic gauge fields
• Liouvillian exceptional points in continuous variable system
• Multiphoton processes via conditional measurements in the two-field interaction
• Stability of time-periodic $\mathcal{P}\mathcal{T}$ and anti-$\mathcal{P}\mathcal{T}$-symmetric Hamiltonians with different periodicities
• A Passive $\mathcal{P}\mathcal{T}$-Symmetric Floquet-Coupler
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