Quantum frequency translation by four-wave mixing in a fiber: low-conversion regime

Abstract

Abstract:In this paper we consider frequency translation enabled by Bragg scattering, a four-wave mixing process. First we introduce the theoretical background of the Green function formalism and the Schmidt decomposition. Next the Green functions for the low-conversion regime are derived perturbatively in the frequency domain, using the methods developed for three-wave mixing, then transformed to the time domain. These results are also derived and verified using an alternative time-domain method, the results of which are more general. For the first time we include the effects of convecting pumps, a more realistic assumption, and show that separability and arbitrary reshaping is possible. This is confirmed numerically for Gaussian pumps as well as higher-order Hermite-Gaussian pumps.

Temporally uncorrelated photon-pair generation by dual-pump four-wave mixing

“…Proceeding with G rs , we use the time-domain collision method formulated in Refs. [26,35]. Consider an input signalray moving along the line from (0,t ) to (l,t + β s l).…”

“…(B3) has an analytical Schmidt decomposition (for a thorough derivation, see Appendix A of Ref. [26]), for which the two sets of Schmidt modes take the form of the normalized Hermite-Gaussian functions and the Schmidt coefficients satisfy…”

“…To this end, instead of neglecting the Heaviside functions as in Eq. (B1), we approximate their product by an effective Gaussian [10,17,26]. For the shifted time variables defined below Eq.…”

“…This deficiency is due to unavoidable spectral-temporal correlations, which arise from the abrupt change of nonlinear interaction at the endpoints of the waveguide. On the other hand, SFWM enables dualpump configurations [24,25], which despite their increased complexity do not necessarily suffer from the same limitation [19,26,27]. By demanding a full pump-pump walk-off inside the waveguide, a gradual variation in the nonlinear interaction can be achieved.…”

Effects of nonlinear phase modulation on Bragg scattering in the low-conversion regime

“…It was recently shown theoretically that in the low-conversion efficiency regime, BS enables QFC without temporal entanglement for fibers that are long enough for a complete pumpsideband interaction [33]. The lack of temporal entanglement is important for many quantum optical experiments, since temporal entanglement might compromise the interference procedures for entanglement in other degrees of freedom [34].…”