Broadband parametric downconversion: an analogy with Fano's theory of atomic autoionization

We develop a unified theoretical framework based on Fano’s theory for discrete-continuum interactions to analyze the dynamics of broadband parametric downconversion (PDC) in the few-pump-photon regime. Strong coupling of a discrete pump state to a continuum of signal states gives rise to several exotic dynamical features such as unit-efficiency PDC (i.e., complete pump depletion) and Rabi-like oscillations with subexponential decay. Our framework not only leads to fully analytic expressions for the PDC dynamics but also allows us to derive intuition via a direct analogy to Fano physics; e.g., unit-efficiency PDC is identified as analogous to atomic autoionization. As a demonstration of the utility of our framework, we investigate a pair of coupled nonlinear waveguides on which two discrete pump states are coupled to a common signal continuum, and destructive and constructive interferences between these two coupling paths critically control the PDC rate. In particular, perfect destructive interference leads to complete suppression of PDC, a quantum manifestation of a bound pump state in the continuum. Experimental numbers suggest these highly quantum dynamics may be relevant to dispersion-engineered nanophotonic platforms in the future.