Stochastic field effects and transform-limited laser pulses

In many ultrashort-laser-pulse experiments the field is transform limited, and under these conditions it is usually assumed that the stochastic nature of the field can be ignored in the interpretation of experimental data. We theoretically consider the 3 + 2 photoionization of xenon, using a pulsed stochastic field. Our results show that the field's stochastic nature always has an effect on the ac Stark shift modification factor Re(M), no matter what the pulse width, and that a short-pulse approximation to Re(M) can require a Fourier-transform bandwidth 1000 times larger than the laser's intrinsic (cw) spectral width.