Control of molecular rotation in helium nanodroplets with an optical centrifuge

Abstract

We experimentally demonstrate that the rotation of molecules embedded in helium nanodroplets can be controlled with an optical centrifuge, allowing for the study of molecular dynamics inside the strongly interacting many-body environment of superfluid helium at variable levels of rotational excitation. By doping the droplets with dimers of nitric oxide, (NO)$_2$, and measuring the degree of their centrifuge-induced alignment as a function of time, we show both the forced in-field rotation of molecules in a continuous range of frequencies, as well as the field-free resonant rotation with a long nanosecond-scale decay. The ability to control and monitor the rotational dynamics of molecular rotors inside the superfluid medium may shed new light on superfluidity and the interaction of superfluids with defects at the atomic level.

Figures (4)

• Figure 1: Geometry of the experiment. The brown corkscrews represent the electric field of the centrifuge, $\mathbf{\vec{E}}_{\mathrm{CFG}}$, propagating along the $Y$ axis and rotating in the $XZ$ plane. The TOFVMI setup is oriented along the $Z$ axis, projecting a 2D velocity map image of ion fragments onto the $XY$ plane. $\theta_{\text{2D}}$ in panel (a) is the angle of the detected ion hits with respect to the $X$ axis. Two red "dumbbells" and a "donut" illustrate the distributions of the N-N axis of the NO dimer (inset in the upper right corner) in three representative situations: alignment to the centrifuge field during the excitation process, when $\mathbf{\vec{E}}_{\mathrm{CFG}}$ is either parallel (a) or perpendicular (b) to the detector plane, and confinement to the plane of rotation after the excitation by the centrifuge (c). Numerically simulated VMI images are shown below the corresponding distributions.
• Figure 2: Centrifuge-induced rotation of $\mathrm{(NO)_2}$ molecules in helium nanodroplets. $\langle \cos^2 \theta_{\text{2D}} \rangle(t)$ (blue markers with red error bars) was recorded during the centrifuge pulse, whose constant rotation frequency $f_{\text{CFG}}$ was tuned to (a) ≈8.5GHz, (b) ≈13GHz, and (c) ≈17GHz. Values of $\langle \cos^2 \theta_{\text{2D}} \rangle$ at the peaks of the oscillations indicate molecular alignment along the laboratory $X$ axis, while values at the troughs represent molecular alignment along the $Z$ axis (see Fig. \ref{['fig:Geometry']}). A probe delay of $t=0$ corresponds to the peak of the cfCFG intensity profile. Grey dashed lines are fits to decaying sinusoids with frequencies of (a) 18.1(3)GHz, (b) 27.2(3)GHz, and (c) 36.2(5)GHz, respectively, closely matching the anticipated values of $2\times f_{\text{CFG}}$.
• Figure 3: $\langle \cos^2 \theta_{\text{2D}} \rangle$ of $\mathrm{(NO)_2}$ in helium droplets, at a probe delay of 550ps, measured as a function of the rotational frequency of the optical centrifuge (black curve with red error bars). The latter exhibits a small degree of rotational acceleration (due to the third-order dispersion), amounting to the frequency difference of about 4GHz over its full duration An-ultra-slow-optical-centrifuge.2025. We consider this the primary factor contributing to the observed lineshape and its finite linewidth.
• Figure 4: $\langle \cos^2 \theta_{\text{2D}} \rangle (t)$ of $\mathrm{(NO)_2}$ in helium droplets (blue diamonds with error bars), with cfCFG tuned to the resonant frequency of $f_{\text{CFG}} = 8.5$ GHz. The cyan curve represents an exponential fit (Eq. \ref{['eq:fit']}) of the field-free decay in $\langle \cos^2 \theta_{\text{2D}} \rangle(t)$ after the centrifuge, with a fixed asymptote of $\langle \cos^2 \theta_{\text{2D}} \rangle(t\rightarrow \infty) = 0.5$. The extracted decay constant is $\tau=3200$ ps $\pm~300$ ps. Also plotted (grey squares with error bars) is the adiabatic alignment Alignment-and-Trapping-of-Molecules1995 of $\mathrm{(NO)_2}$ by a pulse of the same duration as cfCFG, linearly polarized parallel to the plane of the TOFVMI detector.