Detecting Chirality in Molecules by Linearly Polarized Laser Fields

A new scheme for enantiomer differentiation of chiral molecules using a pair of linearly polarized intense ultrashort laser pulses with skewed mutual polarization is presented. The technique relies on the fact that the off-diagonal anisotropic contributions to the electric polarizability tensor for two enantiomers have different signs. Exploiting this property, we are able to excite a coherent unidirectional rotation of two enantiomers with a $\pi$ phase difference in the molecular electric dipole moment. The approach is robust and suitable for relatively high temperatures of molecular samples, making it applicable for selective chiral analysis of mixtures, and to chiral molecules with low barriers between enantiomers. As an illustration, we present nanosecond laser-driven dynamics of a tetratomic nonrigid chiral molecule with short-lived chirality. The ultrafast time scale of the proposed technique is well suited to study parity violation in molecular systems in short-lived chiral states.

Figure 1

One-dimensional cut through the PES of HSOH calculated along the torsional coordinate ${\tau }_{\mathrm{HSOH}}$ together with the definition of the $abc$ molecule fixed axes system for two enantiomeric molecular configurations.

Figure 2

Calculated time evolution of the electric dipole expectation value (${\mu }_Z$) in the laboratory fixed frame, induced by the double-pulse excitation of the enantiomeric states ${\psi }_L$ and ${\psi }_R$ (blue and red colors) initially in the ground rotational state. The time delay between two pulses is set to 6 ps and the pulse mutual polarization angle $\gamma$ is 45°. For comparison, the results of the microwave three-wave mixing (3-WAVE) simulation for ${\mu }_Z$ are shown on the bottom panel. The chosen three-level transition system: $|Jkm⟩=|000⟩\stackrel{{\mu }_X}{\to }|10\pm 1⟩\stackrel{{\mu }_Y}{\to }|110⟩$, where $⟨000|i{\mu }_X|10\pm 1⟩=\mp 0.003\mathrm{D}$, $⟨10\pm 1|{\mu }_Y|110⟩=\pm 0.237\mathrm{D}$, and $⟨110|i{\mu }_Z|000⟩=-0.732\mathrm{D}$ with the corresponding pulse lengths ${\tau }_X=\pi /2$ and ${\tau }_Y=\pi$, respectively, and microwave fields of $10\mathrm{kV}/\mathrm{cm}$.

Figure 3

Calculated amplitudes of the electric dipole oscillations (as Fourier transform of the dipole time evolution) of the rotational wave packet created by a double-pulse excitation of one of the enantiomers in the ground rotational state ($T=0\mathrm{K}$), display (a) and the $T=100\mathrm{K}$ (display (b)) thermal equilibrium distribution of rovibrational states, plotted against delay time for selected frequency regions.

Figure 4

Probability density functions $P(\theta ,\chi )$, averaged over the $0.99{\mathrm{cm}}^{-1}$ rotational period, for the delay times (a) $\tau =4\mathrm{ps}$ and (b) $\tau =6\mathrm{ps}$. For a simpler visual representation, the densities have been obtained in a simulation with polarization vectors of two excitation pulses set in the $XZ$ plane, which induced an electric dipole polarized along the $Y$ axis.