Strong non-linearity-induced correlations for counter-propagating photons scattering on a two-level emitter

We analytically treat the scattering of two counter-propagating photons on a two-level emitter embedded in an optical waveguide. We find that the non-linearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could be quantified via a reduction in coincident clicks in a Hong-Ou-Mandel measurement setup, analogous to a linear beam splitter. Changes to the spectra and phase of the scattered photons, however, would lead to reduced interference with other photons when implemented in a larger optical circuit. We introduce suitable fidelity measures which account for these changes, and find that high values can still be achieved even when accounting for all properties of the scattered photonic state.Comment: 10 pages, 7 figure

Limitations of two-level emitters as nonlinearities in two-photon controlled-phase gates

We investigate the origin of imperfections in the fidelity of a two-photon controlled-phase gate based on two-level-emitter non-linearities. We focus on a passive system that operates without external modulations to enhance its performance. We demonstrate that the fidelity of the gate is limited by opposing requirements on the input pulse width for one- and two-photon scattering events. For one-photon scattering, the spectral pulse width must be narrow compared to the emitter linewidth, while two-photon scattering processes require the pulse width and emitter linewidth to be comparable. We find that these opposing requirements limit the maximum fidelity of the two-photon controlled-phase gate for Gaussian photon pulses to 84%.Comment: 7 pages, 6 figure