  We present a quantum theory of parametric down-conversion of light in chirped
quasi-phase-matched second-order nonlinear crystals with undepleted
quasi-monochromatic pump. This theory allows us to consider generation of
ultrabroadband squeezed states of light and is valid for arbitrary,
sufficiently slowly-varying nonlinear poling profiles. Using a first-order
approximate quantum solution for the down-converted light field, we calculate
the squeezing spectra and the characteristic squeezing angles. We compare the
approximate solutions with the exact and numerical ones and find a very good
agreement. This comparison validates our approximate solution in the regime of
moderate gain, where the existing approaches are not applicable. Our results
demonstrate that aperiodically poled crystals are very good candidates for
generating ultrabroadband squeezed light with the squeezing bandwidth covering
almost all the optical spectrum and the correlation time approaching a single
optical cycle.
