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Photon pairs with ultrabroad spectrum and a high degree of frequency entanglement can be obtained through parametric down-conversion (PDC) in aperiodically poled crystals. Similarly, one can generate ultra-broadband, up to ‘single-cycle’, squeezed light. Generally, reaching short correlation times requires not only spectral broadening achieved through aperiodic poling, but also the removal of the phase chirp by using, for instance, a dispersive material. However, for a specially designed nonlinear variation of the poling period along the crystal, it is possible to avoid additional phase compensation. This strategy was applied to poling a 5 mm long sample of lithium niobate crystal, the grating vector changing from 7000 cm-1 to 8600 cm-1 as a squared hyperbolic function. This provided a type-0 phase matching for pumping at 532 nm, the signal and idler wavelengths being around 790 nm and 1600 nm, respectively. The resulting spectral width was 35 THz, about two orders of magnitude larger than in a periodically poled sample. Frequency correlations were assessed by taking single-pulse spectra and measuring the covariance of signal and idler photon numbers at different frequencies. Despite the limited resolution and no spectral sensitivity above 1700 nm, the shape indicates 12 Schmidt modes as the lower bound; in reality, the number is about 10 times underestimated. The parametric gain exceeded 15 for pumping by 20 ps pulses with the energy per pulse 15 . To find the correlation time, we observed the sum-frequency generation of the signal and idler beams. On top of the ‘incoherent’ pedestal with the width determined by the pulse duration, we saw a 90 fs additional peak indicating ultrafast correlations of the twin beams. The correlation time can be further reduced by optimizing the grating design. Apart from applications in quantum information, such bright twin beams with ultrashort correlation times will be very useful for nonlinear optics and spectroscopy.