Physical Origin of the Interference Signal

The best way to extract physics from the present experiment quantitatively is applying the Feynman s path integral method [14,15] fully to the dynamics of the nuclei and the electron. The action that determines HHG in a molecule i reads 

Here S j ree +. S n = S is the action of the active electron used in the Lewenstein s model, which indicates that a few trajectories are responsible for HHG. Among them, the so-called short trajectory, which starts at time t s and ends at time ts = t s+ rs, can be selected by using propagation effects.5 S tl JqS dr/p(f (r)) determines the interaction between molecular ion and the electron, where Ip(R) is the ionization potential of the molecules as a function of internuclear distance R1 and was assumed to be constant in [32]. S = JJ dr / 2/(2/IP) — V(I 1(t)) is the action of the nuclei with the reduced mass M , the canonical momentum P, and the potential energy 

5 For complex time, integrand is extended to complex function using analytic continuation. 

Finally, 5rad and SGt are the actions of radiation oscillator and that of the interaction between matter and radiation field, respectively [14,15]. 

we treat the nuclear dynamics classically to clarify the quantum effects. For the /th harmonic generation, by using the steepest descent method, the induced dipole moment in a linear molecule whose axis is oriented at an angle of 0 with respect to the x axis of the laboratory system is given by 

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