Imprinting Chirality on Atoms Using Synthetic Chiral Light Fields

Atoms are usually thought of as achiral objects. However, one can construct superpositions of atomic states that are chiral [1]. Here, we show how to excite such superpositions with tailored light fields both in the weak-field and strong-field regimes, using realistic laser parameters. First, we use time-dependent Schrödinger equation simulations to demonstrate the creation of a time-dependent bound chiral wave packet in sodium atoms. Second, we show how the time-dependent handedness of this wave packet can be probed by photoelectron circular dichroism, in spite of the central symmetry of the core potential. Third, we use time-dependent Schrödinger equation simulations to show how chirality can be directly imprinted on a photoelectron wave packet created by strong-field ionization and introduce an unambiguous chiral measure that allows us to characterize its handedness.

Figure 1

(a) Isosurface plot of the chiral superposition $|{\chi }_{p_{+}}⟩$, colored according to the phase. (b) Photon pathways leading to the excitation of a chiral superposition $|{\chi }_{p_{\pm }}⟩$. (c) Generation of synthetic chiral light by crossing two corotating elliptically polarized beams at $\omega$ and $2\omega$ frequencies at an angle $\alpha$. The figure shows the Lissajous curve of the resulting chiral light for ${\varphi }_{\omega ,2\omega }=0$, colored according to the value of the $E_z$ component, together with its two-dimensional projections.

Figure 2

Imprinting chirality on a sodium atom in the weak-field regime. Panels (a),(b) show the photoelectron angular distributions for the right (${\varphi }_{\omega ,2\omega }=0$) and left (${\varphi }_{\omega ,2\omega }=\pi$) field enantiomers of the pump pulse, respectively. The probe is a RCP pulse carried at $\lambda =400\mathrm{nm}$, with pump-probe delay of 30 fs. Panel (c) shows the pump-probe delay-resolved photoionization current along the $z$ axis in sodium for the right $I_R$ (blue line) and left $I_L$ (red line) enantiomers, while the black line shows the PECD signal, defined as $I_R-I_L$.

Figure 3

Imprinting chirality on a hydrogen atom in the strong-field regime. (a) Chiral setup formed by three sets of detectors placed along orthogonal directions, with handedness characterized by the pseudoscalar $h={\mathbf{e}}_x·({\mathbf{e}}_y\times {\mathbf{e}}_z)$. The Lissajous curve shows the chiral bicircular field, colored according to time. (b),(c) Slices through the 3D photoelectron spectrum at $k_y=0$ obtained by TDSE simulations in hydrogen for the left and right enantiomers of the field, on logarithmic scale. The left enantiomer is found by shifting the phase in each beam by $\pi$, corresponding to an inversion. For long pulses, the same result is achieved by changing the relative phase between the two colors by $\pi$.