Quantum trajectories of electrons in arbitrary laser fields

We present a method to trace quantum trajectories of electrons in a high-order harmonic generation process. The method relies on the saddle-point technique and, unlike previously developed analytical techniques, it enables an arbitrary variation in time of the driving fields. The trajectory phases yield information about phase-matching conditions at the optical cycle level, especially useful in investigating attosecond pulse generation. Specially prepared laser pulses, as well as propagation effects can be included in these phase-matching calculations. The method can handle both one- and two-dimensional electron trajectories produced by corresponding driving fields. We show the potentials of the method by calculating trajectories and phase-matching conditions for a polarization gate configuration proposed recently [Altucci, C.; Esposito, R.; Tosa, V.; Velotta, R. Opt. Lett. 2008, 33, 2943-2945.] to obtain isolated attosecond pulse from multi-cycle laser pulses.