Nonlocal photonic time crystals: Infinite momentum bandgaps with minimal modulation speed and strength

Abstract

For over a decade, photonic time crystals have promised access to novel and exotic optical phenomena, offering fundamentally new ways to manipulate classical and quantum light. Central to these capabilities is the emergence of momentum bandgaps -- the counterpart of the more familiar frequency bandgaps in spatial crystals -- which have proven difficult to observe experimentally due to the combined need for high modulation speed and strength. To date, these requirements have all but hindered the development of time crystals at optical frequencies. Here, we show that the stringent modulation-speed requirement is a direct consequence of the Manley-Rowe relations governing conventional modulation schemes. We further demonstrate that modulating the plasma frequency of a Lorentz-dispersive material overcomes this limitation. Incorporating a specific form of spatial nonlocality (spatial dispersion) into this already temporally nonlocal (frequency dispersive) framework removes all remaining constraints, enabling momentum bandgaps of infinite extent -- in both frequency and momentum -- with arbitrarily small modulation speeds and strengths.