Passive and Deterministic Controlled-phase Gate for Single-photon Wavepackets Based on Time-reversal Symmetric Photon Transport

We report the construction of a passive, deterministic and near-unity-fidelity controlled-$\pi$-phase gate for single-photon wavepackets with a node comprising a two-level emitter and a small number of cavities. The proposed gate is rooted in the concept of time-reversal symmetric photon transport, which makes the entire photon transport process into a perfect absorption and re-emission process. Consequently, it can circumvent the longstanding issue of wavepacket distortion inherent in photonic phase gates employing nonlinear media. Moreover, such time-reversal symmetric transport ensures the nonlinear $\pi$ phase shift by a single two-level emitter for the two-photon case. We develop analytical solutions to reveal the temporal dynamics of the nonlinear photon transport and to optimize the gate structure. Notably, the gate fidelity can exceed 99\% for a node with only four cavities for both single-photon and two-photon operations. Moreover, the proposed gate architecture is compatible with the platforms of integrated photonics.