Controlling the degree of rotational directionality in laser-induced molecular dynamics

We demonstrate experimentally a method of varying the degree of directionality in laser-induced molecular rotation. To control the ratio between the number of clockwise and counterclockwise rotating molecules (with respect to a fixed laboratory axis), we change the polarization ellipticity of the laser field of an optical centrifuge. The experimental data, supported by numerical simulations, show that the degree of rotational directionality can be varied in a continuous fashion between unidirectional and bidirectional rotation. The control can be executed with no significant loss in the total number of rotating molecules. The technique could be used for studying the effects of orientation of the molecular angular momentum on molecular collisions and chemical reactions. It could also be utilized for controlling magnetic and optical properties of gases, as well as for the enantioselective detection of chiral molecules.

Figure 1

(a) Illustration of the main principle of making an optical centrifuge (see text for details). PBC: Polarizing beam combiner; $\lambda /4$: quarter-wave plate. (b) Depending on the orientation of the wave plate with respect to the polarization vectors of the input pulses, expressed via angle $\alpha$ [inset in (a)], the centrifuge polarization undergoes different evolution in time. The three representative examples show, from top to bottom, the behavior of the field polarization over half a period of a “linear” (conventional), “elliptical,” and “circular” centrifuge, respectively. The three-dimensional shapes on the left show the surfaces traced by the polarization vector in the course of a few periods of the field evolution. The two horizontal bars at the bottom correspond to 1.2 ps and relate the two types of plots to one another.

Figure 2

Examples of Raman spectra from a gas of oxygen molecules under ambient conditions, rotationally excited by a conventional linear centrifuge produced by orienting the quarter-wave plate at $\alpha ={45}^{\circ }$ (solid blue), and a circular centrifuge created by setting $\alpha$ to zero degrees (dashed red). For reference, two Raman peaks are labeled with their corresponding mean rotation quantum numbers $\overline{J}$ (note the use of mean values due to the unresolved splitting of each line into three spin-rotation components [25]). The three-dimensional inset shows a full continuous evolution of the Raman spectrum from purely Stokes at $\alpha ={45}^{\circ }$ to purely anti-Stokes at $\alpha =-{45}^{\circ }$. Dashed lines at 398 nm mark the central probe wavelength.

Figure 3

(a) Experimentally determined relative amount of “positive” super-rotors ${\mathrm{SR}}_{+}$ (solid lines) and “negative” super-rotors ${\mathrm{SR}}_{-}$ (dashed lines) as a function of the orientation angle of the quarter-wave plate. Peak intensities of the centrifuge pulses are indicated under the right-hand side of each solid curve. ${\mathrm{SR}}_{+}$ lines connect to the corresponding ${\mathrm{SR}}_{-}$ lines at $\alpha =0$, where, by the symmetry of the “circular” centrifuge, the numbers of CW and CCW rotors are equal to one another. (b) Comparison of the experimental data for the peak intensity of $5.1\times {10}^{12}$ W/${\mathrm{cm}}^2$ (blue solid lines) with the result of numerical simulations (blue dashed lines). The curves representing the total number of super-rotors are labeled with ${\mathrm{SR}}_{\text{total}}(\equiv {\mathrm{SR}}_{+}+{\mathrm{SR}}_{-})$. The dotted green line at the top shows the calculated value of ${\mathrm{SR}}_{\text{total}}$ for the centrifuge intensity of $2.0\times {10}^{13}$ W/${\mathrm{cm}}^2$.

Figure 4

Experimentally measured (solid, filled markers) and numerically calculated (dashed, empty markers) degree of rotational directionality $\mathrm{\Theta }$ as a function of the quarter-wave plate angle $\alpha$. Best fits to the experimental observations were obtained by using the centrifuge intensity as a single fitting parameter, and are plotted with the markers of the same shape as the corresponding experimental curve. In the experimental study, the intensity was limited by $\approx 5\times {10}^{12}$ W/${\mathrm{cm}}^2$.