Field-Free Alignment of Molecules Observed with High-Order Harmonic Generation

High-order harmonic generation is demonstrated to provide a sensitive way for an extensive study of dynamic processes in the field-free alignment of strong-field-induced molecular rotational wave packets. The time-dependent harmonic signal observed from field-free-aligned ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{CO}}_2$ has been found to include two sets of beat frequency for pairs of coherently populated rotational states. One of them is the well-known frequency component characterizing the field-free alignment of molecules, and the other is ascribed to the beat that arises from coherence embedded in the wave packet. We discuss the effect of each frequency component on the revival signal observed with the harmonic generation.

Figure 1

(a) The 19th harmonic signal observed for ${\mathrm{N}}_2$ as a function of time delay between the pump and probe pulses at the intensities of 0.8 and $1.7\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, respectively, and (b) temporal evolution of $⟨{cos}^2\theta ⟩$ simulated under the same pump pulse conditions, where $T_{\mathrm{rot}}=300°\mathrm{K}$ is assumed so as to give the same $J$ value for the peak amplitude as in Fig. 2.

Figure 2

Frequency spectrum of the time-dependent 19th harmonic signal shown in Fig. 1a. The inset is the extended spectrum in the higher frequency region. The number on each peak denotes the frequency $4J+6$ (in black) at ${\omega }_1$ and $8J+20$ (in gray) at ${\omega }_2$.

Figure 3

(a) The 19th harmonic signal observed for ${\mathrm{O}}_2$ as a function of time delay and (b) its frequency spectrum, in which the number on each spectral peak denotes the frequency $4J+6$ (in black) at ${\omega }_1$ and $8J+20$ (in gray) at ${\omega }_2$. The pump and probe pulse intensities are 0.5 and $1.2\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$, respectively.

Figure 4

Time-dependent 19th harmonic signals (red solid lines) reproduced using (a) the frequency component at ${\omega }_1$, (b) at ${\omega }_2$, and (c) both at ${\omega }_1$ and ${\omega }_2$. For comparison, each trace includes the observed signal given by the gray solid line.