Theory of High Harmonic Generation for Probing Time-Resolved Large-Amplitude Molecular Vibrations with Ultrashort Intense Lasers

We present a theory that incorporates the vibrational degrees of freedom in a high-order harmonic generation (HHG) process with ultrashort intense laser pulses. In this model, laser-induced time-dependent transition dipoles for each fixed molecular geometry are added coherently, weighted by the laser-driven time-dependent nuclear wave packet distribution. We show that the nuclear distribution can be strongly modified by the HHG driving laser. The validity of this model is first checked against results from the numerical solution of the time-dependent Schrödinger equation for a simple model system. We show that in combination with the established quantitative rescattering theory this model is able to reproduce the time-resolved pump-probe HHG spectra of ${\mathrm{N}}_2{\mathrm{O}}_4$ reported by Li et al. [Science 322, 1207 (2008)].

Figure 1

(a) HHG spectrum from $v=0$ vibrational state of hydrogenlike ${\mathrm{H}}_2^{+}$ with the hydrogen atom mass of $4M_p$, calculated by the exact TDSE and the model. Spectrum calculated with a static nuclear distribution is also shown (thin blue line, only odd harmonics are shown). (b) Nuclear distributions at the beginning, the middle, and the end of the laser pulse calculated by the exact TDSE and by using Eq. (2).

Figure 2

HHG yields for a few different harmonics versus time delay from the TDSE (a) and the model using Eqs. (1, 2) (b) for a case of a nuclear wave packet. The hydrogen atom mass is $16M_p$.

Figure 3

(a) Photoionization cross section for a few different energies corresponding to H17, H21, and H25. (b),(c) HHG yields from ${\mathrm{N}}_2{\mathrm{O}}_4$ versus $R_{\mathrm{NN}}$ from the QRS and SFA, respectively.

Figure 4

Normalized HHG yields from ${\mathrm{N}}_2{\mathrm{O}}_4$ versus pump-probe time delay for a few different harmonics from the $\mathrm{\text{model}}+\mathrm{QRS}$ (a) and the $\mathrm{\text{model}}+\mathrm{SFA}$ (b). Probe laser intensity dependence of the modulation depth from the $\mathrm{\text{model}}+\mathrm{QRS}$ (c) and the JILA experiment [10] (d). Molecules are assumed to be perfectly aligned along the pump laser polarization direction.