  The realization of deterministic photon-photon gates is a central goal in
optical quantum computation and engineering. A longstanding challenge is that
optical nonlinearities in scalable, room-temperature material platforms are too
weak to achieve the required strong coupling, due to the critical
loss-confinement tradeoff in existing photonic structures. In this work, we
introduce a novel confinement method, dispersion-engineered temporal trapping,
to circumvent the tradeoff, paving a route to all-optical strong coupling.
Temporal confinement is imposed by an auxiliary trap pulse via cross-phase
modulation, which, combined with the spatial confinement of a waveguide,
creates a "flying cavity" that enhances the nonlinear interaction strength by
at least an order of magnitude. Numerical simulations confirm that temporal
trapping confines the multimode nonlinear dynamics to a single-mode subspace,
enabling high-fidelity deterministic quantum gate operations. With realistic
dispersion engineering and loss figures, we show that temporally trapped
ultrashort pulses could achieve strong coupling on near-term nonlinear
nanophotonic platforms. Our results highlight the potential of ultrafast
nonlinear optics to become the first scalable, high-bandwidth, and
room-temperature platform that achieves a strong coupling, opening a new path
to quantum computing, simulation, and light sources.
