Polarization Shaping for Unidirectional Rotational Motion of Molecules

Control of the orientation of the angular momentum of linear molecules is demonstrated by means of laser polarization shaping. For this purpose, we combine two orthogonally polarized and partially time-overlapped femtosecond laser pulses so as to produce a spinning linear polarization which in turn induces unidirectional rotation of ${\mathrm{N}}_2$ molecules. The evolution of the rotational response is probed by a third laser beam that can be either linearly or circularly polarized. The physical observable is the frequency shift imparted to the probe beam as a manifestation of the angular Doppler effect. Our experimental results are confirmed by theoretical computations, which allow one to gain a deep physical insight into the laser-molecule interaction.

Figure 1

(a) Experimental setup (see text). (b) Polarization shaping setup (see text). (c) and (d) Illustration of the electric field for phase ${\phi }_p=0$ and $\pi$ [$2\pi$], producing a linear “twisted” polarization in the clockwise and counterclockwise direction, respectively. (e) The same for intermediate phase ${\phi }_p$ leading to an elliptical polarization in the overlapping region of the two pulses.

Figure 2

(Top panels) Angular distributions of the rotational axis of ${\mathrm{N}}_2$ calculated at different times within the revival at the half rotational period. (Bottom panels) Traces of the angular distribution projected to the $(x,y)$ plane characterizing the counterclockwise direction of the UDR.

Figure 3

Normalized spectra of the circularly polarized probe beam recorded at a pump-probe time delay $\tau =4.2\mathrm{ps}$ for a shaped pulse with phase (a) ${\phi }_p=0$ (red-filled area), (b) ${\phi }_p=\pi$ (blue-filled area), and (c) ${\phi }_p=\pi /2$ (orange-filled area). The respective theoretical spectra are represented with solid circles. The input probe spectrum is shown in (a) with a black dashed line.

Figure 4

Normalized spectrum of the linearly polarized probe beam recorded at a pump-probe time delay $\tau =4.2\mathrm{ps}$ for ${\phi }_p=0$ (red circles) and ${\phi }_p=\pi /2$ (black triangles).