  Simultaneous localization of light to extreme spatial and spectral scales is
of high importance for testing fundamental physics and various applications.
However, there is a long-standing trade-off between localizing light field in
space and in frequency. Here we discover a new class of twisted lattice
nanocavities based on mode locking in momentum space. The twisted lattice
nanocavity hosts a strongly localized light field in a 0.048 lambda^3 mode
volume with a quality factor exceeding 2.9*10^11 (~250 us photon lifetime),
which presents a record high figure of merit of light localization among all
reported optical cavities. Based on the discovery, we have demonstrated silicon
based twisted lattice nanocavities with quality factor over 1 million. Our
result provides a powerful platform to study light-matter interaction in
extreme condition for tests of fundamental physics and applications in
nanolasing, ultrasensing, nonlinear optics, optomechanics and quantum-optical
devices.
