Photon trapping in a time cavity flying at the speed of light

A strong optical pulse in a nonlinear medium can serve as a trap for photons. Photon confinement in such a trap moving at the speed of light is best described as time-trapping. Here we reveal unusual properties that fundamentally distinguish it from conventional trapping. Time-trapped states can exhibit zero leakage through the trap walls and possess extremely broad spectra while remaining genuine single modes with well-defined phase. Linear beatings between modes enable waveform reshaping in both the temporal and spectral domains. Time-trapped states support efficient coupling to external radiation, allowing fundamentally more efficient loading of energy than stationary cavities and surpassing the conventional Lorentz time-bandwidth limit linking lifetime and bandwidth in conventional resonant systems. Time-traps support exotic phenomena including halo states and anomalously large transmission delays. These properties apply equally to weak classical wavepackets and single-photon states, opening new opportunities for ultrafast classical and quantum photonics.