Generalized protocol for the preparation of bright Schrödinger cat states via degenerate spontaneous parametric down-conversion with photon-number measurement
Abstract We analyze the performance of quantum repeaters where the protocols of entanglement generation and swapping are based on multimode optical Schrödinger cat states produced using electro-optic modulation of single-mode optical cats. We employ both the mean-only approximation and exact results to calculate the distance dependencies of the mean waiting time and the repeater rate depending on the number of elementary links. The results are compared with the rates of quantum repeater schemes based on photon pairs generated via spontaneous parametric down-conversion.
Optimizing the brightness of a spontaneous parametric down-conversion (SPDC) source is an important task for many quantum information applications. We investigate the optimal focusing conditions to maximize the number of photons produced in an SPDC process and coupled with single-mode fibers. We provide a general expression for the two-photon wave function, generalizing previous known results, by considering collinear and noncollinear emission. We present analytical expressions for our results in the thin-crystal limit and clarify the relation between different focusing conditions already existing in the literature. Differently from what was previously reported, we show that the optimal ratio between the pump waist and the generated photons waist depends on the emission angle: It is 1/2 for collinear degenerate emission and approaches 1/2 for larger collection angles. The role of spectral filters is also analyzed. We support and enrich our discussion with numerical simulations, performed for type-I SPDC in a $\ensuremath{\beta}$ barium borate crystal. For this type of emission, we also investigate the role of the transverse walk-off outside the thin-crystal regime.