An ultraslow optical centrifuge with arbitrarily low rotational acceleration

TL;DR

The paper addresses the challenge of adiabatically controlling molecular rotation in viscous or strongly interacting environments by reducing the rotational acceleration of optical centrifuges. It introduces the ultraslow optical centrifuge (usCFG), implemented with a grating-based pulse compressor in one arm of a two-arm interferometer to produce a tunable, arbitrarily small angular acceleration $epsilon_{us}$ while independently setting the central rotation frequency $f_0$ and bandwidth $Delta f_{us}$. Calibration via cross-correlation with a reference pulse and velocity-map imaging on CS2 confirms time-resolved control of rotation and accelerations up to about $100$ GHz, validating the approach. This ultraslow centrifuge enables spin-up in viscous media and opens routes to study rotational dynamics in quantum many-body environments such as helium nanodroplets, with broad implications for molecular spectroscopy and nanotechnology.

Abstract

We outline the design and characterization of a laser pulse shaper, which creates an ``ultraslow optical centrifuge'' - a linearly polarized field whose polarization vector rotates with arbitrarily low angular acceleration. By directly recording this rotation in time with nonlinear cross-correlation, we demonstrate the tunability of such centrifuge (both in terms of its initial and its final rotational frequencies) in the range of accelerations which are three orders of magnitude lower than those available with a conventional centrifuge design. We showcase the functionality of the ultraslow centrifuge by spinning CS$_2$ molecules in a molecular jet. Utilizing the extremely low angular acceleration to control molecular rotation inside viscous media is a promising application for this unique optical tool.

Figures (7)

• Figure 1: Time-frequency spectrograms of the two "centrifuge arms" for (a) a constant-frequency centrifuge, (b) an ultraslow centrifuge with zero central frequency, and (c) an ultraslow centrifuge with zero initial frequency. Both $\Delta t$ and $\Delta\beta$ have been exaggerated for illustrative purposes. The diamonds mark the central frequencies of the two chirped pulses, used to define $\Delta t$. See text for the definition of $\Omega$, $\beta _{0}$, and $\Delta \beta$.
• Figure 2: Ultraslow centrifuge pulse shaper. The input pulse (purple) is split into two arms with a half-wave plate ($\lambda/2$) and a polarizing beam splitter (PBS). The transmitted portion (green) is sent through the double-grating pulse compressor with a variable distance $L$ between the gratings ($\mathrm{GR}_1$ and $\mathrm{GR}_2$). After being vertically displaced with a retro-reflector (RR), this "compressor arm" is overlapped with the "delay arm" (cyan) on the output PBS. IM/OM mark the input/output mirrors of the compressor, respectively. A quarter-wave plate ($\lambda/4$) converts the two orthogonal linear polarizations into the circular polarizations of opposite handedness, to form the field of the centrifuge (corkscrew shape). The inset shows our definition of the grating orientation angle $\theta_0$, used in the main text.
• Figure 3: Experimental layout for the cross-correlation characterization of the centrifuge field. The centrifuge pulse is passed through a linear polarizer (PBS), to project the centrifuge field vector onto the axis of a nonlinear barium borate (BBO) crystal, where it is overlapped with the linearly polarized short reference pulse. The pulses intersect at a slight angle, allowing the collection of the sum frequency generation signal with a photodiode (PD), after blocking the second harmonic generation signals from each individual pulse with an aperture. The delay time between the centrifuge and reference pulses is controlled with a variable delay stage.
• Figure 4: (a) Sample cross-correlation trace of usCFG (red diamonds), and its reconstruction from the numerically extracted instantaneous frequency (solid black). The dashed black line outlines the pulse envelope. (b) Extracted instantaneous frequency (red), where positive and negative values represent opposite directions of rotation. The dashed black curve shows $f_{\mathrm{us}}(t)$, modeled to minimize the reconstruction error of the cross-correlation trace from the solid black line (a), with quadratic time dependence to account for third-order dispersion (see text for details).
• Figure 5: Tunable behaviour of usCFG, characterized by means of optical cross-correlation. (a) Central frequency of usCFG, $f_0$, at different delays between the centrifuge arms, $\Delta t$. The grating separation in the compressor was recorded with a fixed $L \approx 39mm$. (b) The frequency bandwidth of usCFG, $\Delta f_{\mathrm{us}}$, at different grating separations $L$, recorded with a fixed value of $\Delta t \approx 3ps$. (c) Measurements of $f_{\mathrm{us}}(t)$ for three different centrifuges, tuned to have terminal frequencies of approximately 20G Hz (solid blue), 30G Hz (dashed orange), and 40G Hz (dotted green). By adjusting both $\Delta t$ and $L$ (and, thus, $f_0$ and $\Delta f_{\mathrm{us}}{}$) in a coordinated fashion, all centrifuges were tuned to pass zero frequency around -150ps, but reach different terminal frequencies by the end of the pulse at 150p s.