We study spectral properties of quantum radiation of ultimately short duration. In particular, we introduce a continuous multimode squeezing operator for the description of subcycle pulses of entangled photons generated by coherent-field driving in a thin nonlinear crystal with second-order susceptibility. We find the ultrabroadband spectra of the emitted quantum radiation perturbatively in the strength of the driving field. They can be related to the spectra expected in an Unruh-Davies experiment with a finite time of acceleration. In the time domain, we describe the corresponding behavior of the normally ordered electric field variance.