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Radiative emission experienced by a subwavelength particle near a resonant cavity is typically characterized by the well-known Purcell factor figure of merit. In recent work, we presented a generalization of Purcell enhancement that applies to situations involving exceptional points (EP)---spectral singularities in non-Hermitian systems where two or more eigenvectors and their corresponding complex eigenvalues coalesce, leading to a non-diagonalizable, defective Hamiltonian. EPs are attended by many intriguing physical effects and have been studied in various contexts, including lasers, atomic and molecular systems, photonic crystals, parity-time symmetric lattices, and optomechanical
resonators. Thus far, the main focus of these works has been on analyzing the impact of second-order exceptional points on scattering from eternally incident light, e.g. for unidirectional transmission.
An important but little explored property of EPs related to light-matter interactions is their ability to modify and enhance the local density of states (LDOS). Recently, we showed that EPs can modify the spontaneous emission rate or Purcell factor of narrow-band emitters embedded in resonant cavities. In this talk, we show that EPs can have an even greater impact on nonlinear optical processes like frequency conversion. In particular, we derive a general formula quantifying radiative emission from a subwavelength emitter in the vicinity of a triply resonant χ(2) cavity that supports an EP near the emission frequency and a bright mode at the second harmonic. We show that the resulting frequency up-conversion process can be enhanced by up to two orders of magnitude compared to nondegenerate scenarios and that, in contrast to the recently predicted spontaneous-emission enhancements, nonlinear EP enhancements can persist even when considering spatial distributions of broadband emitters, provided that the cavity satisfies special nonlinear selection rules. This is demonstrated via a two-dimensional proof-of-concept PhC designed to partially fulfill the various criteria needed to approach the derived bounds on the maximum achievable up-conversion efficiencies. Along these lines, we show that similar enhancements can arise in quantum systems consisting of single and multi-level atoms embedded in photonic cavities. Our predictions suggest an indirect but practically relevant route to experimentally observe the impact of EPs on spontaneous emission and related light–matter interactions, with implications to quantum information science.
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