Geometric mechanisms enabling spin- and enantio-sensitive observables in one photon ionization of chiral molecules

Abstract

We examine spin-resolved photoionization of randomly oriented chiral molecules via circularly polarized light, and revisit earlier predictions of Cherepkov (J. Phys. B: Atom. Mol. Phys. 16, 1543, 1983}). We will show that the dynamical origin of spin- and enantio-sensitive observables arise from two intrinsic mechanisms that are quantified by two pseudovectors stemming from the geometric properties of the photoionization dipoles in spin space and in real space, and an extrinsic mechanism which is a directional bias introduced by the well-defined direction of light polarization. These mechanisms arise solely from electric dipole interactions. Consequently, this means that the ten independent parameters that was earlier predicted by Cherepkov to fully describe spin-resolved photoionization of chiral molecules can be reduced as moments of these three pseudovectors. We also find that the molecular pseudoscalars describing the spin- and enantio-sensitive components of the yield can be described by the flux of these pseudovectors through the energy shell, which changes sign upon switching enantiomers. Our results provide compact expressions for these observables which provide an intuitive picture on what determines the strength of these spin- and enantio-sensitive observables. The approach can be readily generalized to photoexcitation, multiphoton processes, and arbitrary field polarizations. Regardless of the specific driving conditions, the resulting spin- and enantio-sensitive observables are still controlled by the same three pseudovectors, underscoring their universal role as the primary generators of chirality-induced spin asymmetries, emphasizing their fundamental geometric origin and the universality of the mechanism identified here.

Figures (9)

• Figure 1: Specification of coordinates in the laboratory frame. The light field propagates along $\boldsymbol{\hat{z}}$. The unit vector $\boldsymbol{\hat{\Xi}}=\xi\boldsymbol{\hat{z}}$ (solid red) is the direction of photon spin, where $\xi=\pm1$ is a dichroic parameter characterizing the direction of rotation of the light polarization vector. Upon ionization, the photoelectron is ejected in the direction of $\boldsymbol{\hat{k}}$ (solid green) with its spin measured parallel to $\boldsymbol{\hat{s}}$ (solid blue). The expansion $W^L(\boldsymbol{\hat{k}}^L,\boldsymbol{\hat{s}}^L)$, Eq. \ref{['eq:cherepkov-expansion']} is represented by the the solid green and dashed blue vectors.
• Figure 2: The momentum-resolved propensity field $\boldsymbol{\vec{\mathcal{B}}}_{\boldsymbol{\vec{k}}}$, Eq. \ref{['eq:D-flux']}, in k-space for the chiral state $|\psi_{1,-\frac{1}{2}}^\pm\rangle_p$. The spheres correspond to $\boldsymbol{\vec{\mathcal{B}}}_{\boldsymbol{\vec{k}}}$ with $|\boldsymbol{\vec{k}}|=0.525\,\text{Bohr}^{-1}$ where the vectors are colored as $|\boldsymbol{\vec{\mathcal{B}}}_{\boldsymbol{\vec{k}}}|$. The two-dimensional vector fields represent an equatorial cut in the $k_x-k_y$ plane and colored according to its radial component $(\boldsymbol{\hat{k}}\cdot\boldsymbol{\vec{\mathcal{B}}}_{\boldsymbol{\vec{k}}})$. It can be seen that the propensity field for opposite enantiomers $R$ and $S$ are related via inversion $\boldsymbol{\vec{\mathcal{B}}}_{\boldsymbol{\vec{k}}}^{(R)}=\boldsymbol{\vec{\mathcal{B}}}_{-\boldsymbol{\vec{k}}}^{(S)}$.
• Figure 3: The coefficient $D$ (solid line) as well as the contributions of the spin-up (dashed line) and spin-down (dotted-dashed line), Eq. \ref{['eq:D-flux']}, for the chiral states $|\psi_{1,-\frac{1}{2}}^\pm\rangle_p$ and $|\psi_{-1,\frac{1}{2}}^\pm\rangle_p$. The rapidly oscillating behavior of $D$ at higher values of $k$ are due to the Fano resonances, leading up to the ionization threshold for the 3s electrons Samson2002Carlstroem2024spinpolspectral.
• Figure 4: The momentum-resolved spin torque field $\boldsymbol{\vec{\tau}}_{\boldsymbol{\vec{k}}}$, Eq. \ref{['eq:C-flux']}, in k-space for the chiral state $|\psi_{1,-\frac{1}{2}}^\pm\rangle_p$. The spheres correspond to $\boldsymbol{\vec{\tau}}_{\boldsymbol{\vec{k}}}$ with $|\boldsymbol{\vec{k}}|=0.525\,\text{Bohr}^{-1}$ where the vectors are colored as $|\boldsymbol{\vec{\tau}}_{\boldsymbol{\vec{k}}}|$. The two-dimensional vector fields represent an equatorial cut in the $k_x-k_y$ plane and colored according to its radial component $(\boldsymbol{\hat{k}}\cdot\boldsymbol{\vec{\tau}}_{\boldsymbol{\vec{k}}})$. It can be seen that the spin torque field for opposite enantiomers $R$ and $S$ are related via inversion $\boldsymbol{\vec{\tau}}_{\boldsymbol{\vec{k}}}^{(R)}=\boldsymbol{\vec{\tau}}_{-\boldsymbol{\vec{k}}}^{(S)}$.
• Figure 5: The coefficient $C$ (solid line) as well as the contributions of the spin-up (dashed line) and spin-down (dotted-dashed line), Eq. \ref{['eq:D-flux']}, for the chiral states $|\psi_{1,-\frac{1}{2}}^\pm\rangle_p$ and $|\psi_{-1,\frac{1}{2}}^\pm\rangle_p$. The rapidly oscillating behavior of $D$ at higher values of $k$ are due to the Fano resonances, leading up to the ionization threshold for the 3s electrons Samson2002Carlstroem2024spinpolspectral.