Measurement analysis of coherence in femtosecond laser-induced molecular alignment

Femtosecond laser-induced excitation of molecular rotational states can lead to phenomena such as alignment and orientation, which fundamentally stem from the coherence between the induced rotational states. In recent years, the quantitative study of coherence in the field of quantum information has received widespread attention. Different kinds of coherence measures have been proposed and investigated. In this work, the quantitative correlation is investigated in detail between the intrinsic coherence measurement and the degree of molecular alignment induced by femtosecond laser pulses at finite temperatures. By examining the molecular alignment induced by ultrafast non-resonant laser pulses, a quantitative relationship is established between the <inline-formula><tex-math id="M2">\begin{document}$l_1$\end{document}</tex-math></inline-formula> norm coherence measure <inline-formula><tex-math id="M3">\begin{document}$C_{l_1}(\rho)$\end{document}</tex-math></inline-formula> and the alignment amplitude <inline-formula><tex-math id="M4">\begin{document}${\cal{D}}\langle \cos^2 \theta \rangle$\end{document}</tex-math></inline-formula>. Here, <inline-formula><tex-math id="M5">\begin{document}$C_{l_1}(\rho)$\end{document}</tex-math></inline-formula> represents the sum of the absolute values of all off-diagonal elements of the density matrix <i>ρ</i>, <inline-formula><tex-math id="M6">\begin{document}${\cal{D}}\langle \cos^2 \theta \rangle$\end{document}</tex-math></inline-formula> represents the difference between the maximum alignment and the minimum alignment. A quadratic relationship <inline-formula><tex-math id="M7">\begin{document}$ C_{l_1} = (a + b{\cal{E}}^2_0)\times $\end{document}</tex-math></inline-formula><inline-formula><tex-math id="M7-1">\begin{document}$ {\cal{D}}\langle \cos^2 \theta \rangle$\end{document}</tex-math></inline-formula> between the the <inline-formula><tex-math id="M8">\begin{document}$l_1$\end{document}</tex-math></inline-formula> norm coherence measure and <inline-formula><tex-math id="M9">\begin{document}${\cal{D}}\langle \cos^2 \theta \rangle$\end{document}</tex-math></inline-formula> with respect to the electric field intensity <inline-formula><tex-math id="M10">\begin{document}${\cal{E}}_0$\end{document}</tex-math></inline-formula> is obtained. This relationship is validated through numerical simulations of the CO molecule, and the ratio coefficients <i>a</i> and <i>b</i> for different temperatures are obtained. Furthermore, a mapping relationship between this ratio and the pulse intensity area is established. The findings of this study provide an alternative method for experimentally detecting the coherence measure within femtosecond laser-excited rotational systems, thereby extending the potential applicability of molecular rotational states to the study of the coherence measure in the field of quantum resources. This will facilitate the interdisciplinary integration of ultrafast strong-field physics and quantum information.