Selective phase-matched Bragg scattering for single-photon frequency conversion in a nonlinear waveguide

We describe a design for phase-matched Bragg scattering for single-photon conversion between two arbitrary frequencies. The bandwidth of the Bragg scattering process is calculated and immunity against competing processes is discussed. Bragg scattering is a four-wave mixing process where a signal beam is scattered into an idler beam via the refractive index grating generated by the interaction of two strong pump beams in a nonlinear medium. Recently, Bragg scattering has been explored for quantum frequency conversion because it avoids excess noise and preserves the quantum state of the frequency converted photonic state [1, 2]. Combined with time lens technique [3], Bragg scattering can be used to frequency convert the photonic wavepacket and impedance match it to a resonance simultaneously, enabling exchange of quantum information between different quantum platforms such as quantum dots and ions. In the Bragg scattering process, two pump beams (pump 1 and pump 2) are used to convert the signal photon (s) to the idler photon (i). Energy and momentum conservation requires that the frequency and wave vector differences between the signal beam and pump 1 matches the differences between the idler beam and pump 2, described by ωs − ωP1 = ωi − ωP2 (1