Fig. 3: Dynamic modulation between interband and intraband regimes.

a Fermi energy as a function of time t using a sinusoidal function of frequency \({f}_{{\rm{mod}}}\) (schematic). The slow topgate is used to tune to E_F ~ 0.45 eV, whereas the fast backgate provides the modulation between 0.3 and 0.6 eV. b–f Time-resolved photon emission while the Fermi energy is modulated at different frequencies between 20 Hz and 300 kHz (green dots). Every time-modulated emission measurement is normalized to its mean value, so that the modulation does not depend on the excitation laser power or the photon collection efficiency. The black solid curves show the dynamic simulations of N ions located at the distribution of distances from graphene P(z), obtained from the emission contrast measurements and decay curves (see “Methods”). Note that f shows modulation on a time scale of microseconds, whereas the radiative lifetime of erbium ions in Y₂O₃ is  ~10 ms, a difference of 4 orders of magnitude.