Chiral Discrimination through Bielliptical High-Harmonic Spectroscopy

Molecular chirality plays an essential role in most biochemical processes. The observation and quantification of chirality-sensitive signals, however, remains extremely challenging, especially on ultrafast timescales and in dilute media. Here, we describe the experimental realization of an all-optical and ultrafast scheme for detecting chiral dynamics in molecules. This technique is based on high-harmonic generation by a combination of two-color counterrotating femtosecond laser pulses with polarization states tunable from linear to circular. We demonstrate two different implementations of chiral-sensitive high-harmonic spectroscopy on an ensemble of randomly oriented methyloxirane molecules in the gas phase. Using two elliptically polarized fields, we observe that the ellipticities maximizing the harmonic signal reach up to $4.4\pm 0.2\%$ (at 17.6 eV). Using two circularly polarized fields, we observe circular dichroisms ranging up to $13\pm 6\%$ (28.3–33.1 eV). Our theoretical analysis confirms that the observed chiral response originates from subfemtosecond electron dynamics driven by the magnetic component of the driving laser field. This assignment is supported by the experimental observation of a strong intensity dependence of the chiral effects and its agreement with theory. We moreover report and explain a pronounced variation of the signal strength and dichroism with the driving-field ellipticities and harmonic orders. Finally, we demonstrate the sensitivity of the experimental observables to the shape of the electron hole. This technique for chiral discrimination will yield femtosecond temporal resolution when integrated in a pump-probe scheme and subfemtosecond resolution on chiral charge migration in a self-probing scheme.

Popular Summary

One’s hands can be thought of as chiral objects—they are mirror images of one another, yet they cannot be superimposed. Some molecules are constructed in the same way: They come in two chiral versions known as isomers. This plays a huge role in certain biochemical processes, which often rely on just one isomer of a molecule. However, it is often difficult for researchers to distinguish between chiral isomers in the lab. We introduce a new all-optical technique for detecting chiral dynamics in molecules.

Current techniques for discrimination rely on circularly polarized light, which is itself chiral. Chiral isomers will absorb or scatter left- and right-polarized light by different amounts, however, the effect is typically very small—on the order of 0.01%.

Our technique depends on high-harmonic generation by a combination of two-color counterrotating femtosecond laser pulses with polarization states tunable from linear to circular. We demonstrate two different implementations of chiral-sensitive spectroscopy on an ensemble of randomly oriented methyloxirane molecules in the gas phase. We observe that the intensity of the emitted high-harmonic radiation is 3% to 13% more intense for one isomer than the other. Comparison of the results and their dependence on the intensity of the laser pulses establishes chiral electron dynamics on subfemtosecond timescales as the origin of the chiral effects.

This research will evolve to measure the time evolution of molecular chirality during chemical reactions on the femtosecond timescale and to reconstruct electronic dynamics in chiral molecules on attosecond timescales.

Figure 1

Circular dichroism measurement using the bicircular scheme. (a) HHG yields for harmonic 20 of $R$- and $S$-MOX as a function of the QWP rotation angle. A moving average with a span of 5 data points was applied on the measured signal. The insets show Lissajous representations of the electric component of the driving laser fields. (b) Ellipticity-dependent differential circular dichroism signal $\mathrm{CD}(20\omega ,\alpha )$. (c) Top: Spectrum of $R$-MOX recorded for the setting $\alpha =-45°$; bottom: spectrogram showing the CD as a function of the QWP angle and the photon energy. The colors encode the sign of the CD. The intensities are $I_{\omega }\sim 3\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and $I_{2\omega }\sim 1.1\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The error bars in (a) represent 2 standard deviations of the measured signal.

Figure 2

Ellipticity dependence of the spectral intensity and the CD. (a)–(c) Comparison of the HHG intensity modulations for harmonic orders 18, 19, and 20 of 1800 nm (full lines) with the calculation results (dashed lines) obtained with the theoretical model discussed in the text. The data sets shown correspond to the measurement presented in Fig. 1 for $R$-MOX. Panels (d)–(f) show the corresponding ellipticity-dependent chiral response $\mathrm{CD}(n\omega ,\alpha )$. The strong-field (SFA) calculations have been performed assuming a single-cycle continuous-wave bicircular pulse centered at $1800+900\mathrm{nm}$, with intensity of the fundamental driving field set at $I_{\omega }=5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and a field strength ratio of $\eta =F_{2\omega }/F_{\omega }=0.75$.

Figure 3

Intensity dependence of CD. (a),(b) Angle-integrated [$\alpha \in \pm (20°-55°)$] ${\overline{\mathrm{CD}}}^{\pm }(n\omega )$ for bielliptical fields of opposite handedness ($+$ or $-$, encoded as blue or red) as a function of the photon energy for two different intensities [cf. text insets in (c) and (d)]. (c),(d) Energy dependence of the ratio of two neighboring allowed harmonics [$I(3q+2)/I(3q+1)$] at $\alpha =45°$ for the measurements in (a) and (b). (e),(f) HHG spectra of $R$-MOX at the bicircular configuration (QWP angle $\alpha =45°$) recorded under the experimental conditions reported in (c) and (d), respectively. The error bars in (c)–(f) represent 2 standard deviations of the measured signal.

Figure 4

Bielliptical high-harmonic spectroscopy. (a) HHG yield (data points) as a function of the driving ellipticity and Gaussian fits (full lines). The displacement of the maxima from $\alpha =0$ is a signature of the chiral response. The Lissajous figures indicate the polarization ellipses of the two drivers. The black points and curve have been shifted vertically for better visibility. The displayed data correspond to $H28$ of 1900 nm recorded at $I_{\omega }=1.2\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and $I_{2\omega }=1.8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. (b),(c) Maximizing ellipticity ${\epsilon }_{\max }$ as a function of the photon energy for two different intensities. (b) $I_{\omega }=1.2\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, $I_{2\omega }=1.8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$ and (c) $I_{\omega }=1.5\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, $I_{2\omega }=2.1\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The error bars in (b) and (c) represent the 95% confidence interval obtained from the fitting procedure.

Figure 5

Comparison of predicted and observed CD in BHHS. (a) Schematic illustration of the four ionization-recombination paths considered in the model. (b) Comparison (experiment versus theory) of the intensity ratios between two neighboring allowed harmonics at two different experimental conditions (cf. legends). (c) Energy dependence of the calculated CD: theory (markers) versus experiment (solid lines). (d) and (e) Calculated result for the intensity ratios (d) and the CD degree (e) using three different values of the initial phase $\varphi$ between the two cationic states.

Figure 6

Electron-hole dynamics underlying the chiral response. These simulations were done for laser parameters matching the experimental results in Fig. 1 (1800 and 900 nm, $I_{\omega }=3.0\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$, $I_{2\omega }=1.1\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$) and $\varphi =-\pi /8$, as estimated by comparison with the experimental results. Top row: Absolute magnitude of the hole density at the time of recombination for 5 harmonic orders ($H17$, 24, 32, 40, and 48). The corresponding transit times of the continuum electron $\tau$ are indicated. Bottom row: Difference between the hole densities calculated with and without the contribution of the magnetic-dipole interaction. The contour levels are coded in the colors of the isocontour surfaces (color bar on the right). Top right: Spatial profiles of the electric (blue) and the magnetic (red) fields. The ionization times of the five trajectories are indicated as black circles (electric field) or black squares (magnetic field), respectively. Bottom right: Real part of the spatial quantum trajectories.