Theory of filtered type-II parametric down-conversion in the continuous-variable domain: Quantifying the impacts of filtering

Parametric down-conversion (PDC) forms one of the basic building blocks for quantum optical experiments. However, the intrinsic multimode spectral-temporal structure of pulsed PDC often poses a severe hindrance for the direct implementation of the heralding of pure single-photon states or, for example, continuous-variable entanglement distillation experiments. To get rid of multimode effects narrowband frequency filtering is frequently applied to achieve a single-mode behavior. A rigorous theoretical description to accurately describe the effects of filtering on PDC, however, is still missing. To date, the theoretical models of filtered PDC are rooted in the discrete-variable domain and only account for filtering in the low-gain regime, where only a few photon pairs are emitted at any single point in time. In this paper we extend these theoretical descriptions and put forward a simple model, which is able to accurately describe the effects of filtering on PDC in the continuous-variable domain. This developed straightforward theoretical framework enables us to accurately quantify the tradeoff between suppression of higher-order modes, reduced purity, and lowered Einstein–Podolsky–Rosen entanglement, when narrowband filters are applied to multimode type-II PDC.