Strong nonlinearity-induced correlations for counterpropagating photons scattering on a two-level emitter

Abstract

We analytically treat the scattering of two counterpropagating photons on a two-level emitter embedded in an optical waveguide. We find that the nonlinearity 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 coincidence 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.

Quantum scattering theory of a single-photon Fock state in three-dimensional spaces

“…(1) without any approximation. The theoretical framework is built upon methods developed for electrons scattered by magnetic impurities in condensed matter physics [2,3] as well as recent progress in one-dimensional waveguide quantum electrodynamics [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Although we illustrate the theory based on single photons, the framework is fundamentally compatible with and can be extended to multi-photons.…”

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

“…(4) and (8), we see that a good gate performance requires |k| ˜ , which corresponds to pulses with a spectrum that is much narrower than the emitter linewidth. For spectrally broader photons for which ξ (k) extends beyond k ∼˜ , terms of higher order in k will have an influence and introduce chirping effects [19,20].…”

“…Most notably, we find that Lorentzian spectral profiles result in a worse gate fidelity of F ≈ 62%. Although a Lorentzian-shaped single-photon is expected to most efficiently populate a two-level emitter, two such coincident pulses give rise to a smaller induced nonlinearity [19], which is an essential requirement for the gate to operate. We find that sech 2 pulses achieve a fidelity marginally better than Gaussian pulses, raising the gate fidelity by only 0.5%.…”

“…Generating photon-photon interactions can be achieved by "off-line nonlinearities" consisting of measurements and feed-forward [1][2][3][4]7], or deterministically by using "in-line" nonlinearities based on a nonlinear material through which two or more photons interact [14][15][16][17]. These in-line nonlinearities can in principle also be generated by few-level emitters [18][19][20], suggesting a quantum photonic architecture in which few-level systems act as both photon sources and photon couplers.…”

“…The idealized gate we consider uses the in-line nonlinearities of two two-level-emitters embedded in lossless waveguides. The fundamental operating principle of the gate relies on the saturability of a two-level emitter, which means that the phase imparted onto a photon or photons scattering on such an emitter depends on how many photons are present [19,20,37,38]. Although it has been shown that such a gate can never perform with perfect fidelity [38,39], the purpose of this work is to understand the limits and origins of its imperfections with a view towards improved future implementations.…”