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

Abstract

Abstract:In this paper, we consider the effects of nonlinear phase modulation on frequency conversion by four-wave mixing (Bragg scattering) in the low-conversion regime. We derive the Green functions for this process using the time-domain collision method, for partial collisions, in which the four fields interact at the beginning or the end of the fiber, and complete collisions, in which the four fields interact at the midpoint of the fiber. If the Green function is separable, there is only one output Schmidt mode, which is free from temporal entanglement. We find that nonlinear phase modulation always chirps the input and output Schmidt modes and renders the Green function formally nonseparable. However, by pre-chirping the pumps, one can reduce the chirps of the Schmidt modes and enable approximate separability. Thus, even in the presence of nonlinear phase modulation, frequency conversion with arbitrary pulse reshaping is possible, as predicted previously [Opt. Express 20, 8367-8396 (2012)].

Temporal mode sorting using dual-stage quantum frequency conversion by asymmetric Bragg scattering

“…The GF kernels found here are similar in form to those earlier presented for FWM BS [15,16], and to those for three-wave mixing [6], apart from the exponential phase terms which are seen to be linear in both the input and output times. We adopt the notation that β r and β s are to be measured relative to the average group slowness β av = (β r + β s ) /2, such that they obey β r = −β s > 0.…”

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).…”

Efficient sorting of quantum-optical wave packets by temporal-mode interferometry

“…Nonlinear phase-modulation in FWM severely affects the Schmidt-mode phase-profiles, and restricts FWM-TMI to the RC configuration. The pumps must be prechirped with specific phase-profiles [18] for each stage to enhance inter-stage mode-matching. Figure 3(f)-3(o) shows the numerically computed CE, Schmidt-mode amplitudes, and phases corresponding to FWM-TMI with selectivity 0.9873 (|ρ 1 | 2 = 0.9973, |ρ 2 | 2 = 0.0082).…”