Analogs of Spontaneous Emission and Lasing in Photonic Time Crystals

We report the first direct mapping of the frequency-resolved local density of states (LDOS) in a photonic time crystal (PTC) implemented as an array of time-periodically modulated LC resonators at microwave frequencies. Broadband white noise probes the system and yields an LDOS line shape near the momentum gap that can be decomposed into absorptive and dispersive Lorentzian components. The finite LDOS peak at the gap frequency, which grows with modulation strength, implies that the spontaneous emission rate of an emitter coupled to the PTC would be maximized at that frequency. The measured spectra are in good agreement with classical non-Hermitian Floquet theory. As the modulation-induced gain exceeds intrinsic losses, the system undergoes a transition to a narrow-band self-oscillation (lasing) regime. These results open a route to nonequilibrium photonics and bring time-periodic LDOS engineering closer to practical realization.