Ultrafast All-Optical Switching via a Supersolid Phase Transition of Light

We propose ultrafast all-optical switching exploiting the bistability between a spatially uniform photon superfluid and a spontaneously ordered supersolid in a driven-dissipative microcavity. The key ingredient is a tunable nonlocal photon--photon interaction engineered by embedding a high-mobility two-dimensional electron gas (2DEG) inside the cavity. A drift current displaces the Fermi disk, imparting a negative region to the Lindhard interaction kernel at finite wavevectors and triggering a roton instability. The resulting bistable $S$-curve supports a write--hold--erase protocol in which short optical pulses toggle the system between branches with a switching contrast of order 120~dB. The hysteretic ON state persists under a constant sub-threshold drive after the write pulse is removed, realizing an all-optical bistable memory. Since the photon field couples additively to each embedded quantum well, stacking layers with distinct drift angles allows the roton profile to be engineered with higher-order symmetries, imprinting richer spatial order on the supersolid and enabling nonbinary generalizations of the switch. Operating in the ultrafast, sub-fJ regime, this platform outperforms most existing all-optical switches in contrast and reconfigurability.