Schmidt modes and the time-dependent wavefunction of a broadband biphoton field

The wavefunction of a broadband biphoton field arising in parametric down-conversion in an aperiodically polarized nonlinear crystal with a linear chirp under the action of a short pump pulse has been studied theoretically. The form of Schmidt modes has been determined in both the spectral and temporal representations. The dependence of the number of Schmidt modes on the duration of the pump pulse has been found and it has been shown that it is minimal at a quite short duration of the pump pulse of about 100 fs. The form of the wavefunction of biphotons in the time representation has been determined and it has been examined how the region of maximum correlation between the detection times of the down-converted signal and idler photons changes under the variation of the duration of the pump pulse. It has been shown that the maximum of the time correlation function of the signal and idler radiation intensities is significantly asymmetric. Its sharper edge in the case of sufficiently long pump pulses has a small width shorter than 30 fs and can be used to synchronize events even without the compensation of the dispersion spreading of wave packets of the biphoton field.