Enabling Single-Photon Nonlinear Optics with XPM Temporal Trapping

Cavity nonlinear optics (NLO) is an exciting platform for room-temperature quantum computing, buoyed by recent advances in low-loss dispersion-engineered LiNbO₃ fabrication.  Quantum (single-photon) NLO generally requires operation in the pulsed regime in order to simultaneously leverage the high Q factors of ring resonators and the small effective mode volumes of femtosecond pulses.  However, achieving quantum gates in the pulsed regime is complicated by the multimode nature the system, where cavity dispersion and nonlinearity lead to pulse shape distortion and effective qubit decoherence.  We propose a temporal-trapping technique based on cross-phase modulation (XPM) that projects this complex multimode dynamics down to a single mode set, eliminating the effects of mode distortion.  Motivated by optical solitons, XPM trapping works by injecting a classical "trapping" pulse to the cavity and using the XPM phase to induce a time-dependent cavity phase shift, leading to temporal confinement to a discrete mode set even in the presence of cavity dispersion.  We analyze XPM trapping using matrix-product state and full quantum simulations, highlight the limitations of the approach, and discuss the prospects for near-term implementation in a thin-film LiNbO₃ platform.