Improved accuracy fullerene polarizability measurements in a long-baseline matter-wave interferometer

We present electric deflection results for the fullerenes ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ obtained with a long-baseline matter-wave interferometer. The second grating of the interferometer is interchangeable between a material grating for fast atom beams and an optical phase grating for polarizable molecules. This allows us to use cesium as a calibration particle and thus measure molecular susceptibilities with improved systematic uncertainty. The static polarizabilities of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ are measured as $4\pi {\varepsilon }_0\times 87.4\pm 0.4\pm 2.5{\AA }^3$ and $4\pi {\varepsilon }_0\times 106.4\pm 0.2\pm 1.1{\AA }^3$, respectively, in excellent agreement with previous deflection experiments, but with improved uncertainties.

Figure 1

Experimental setup, from left to right: the thermal source, beam collimators, chopper, and the three gratings $\left({\mathrm{G}}_1–{\mathrm{G}}_3\right)$. ${\mathrm{G}}_2$ is interchangeable between a mechanical and an optical phase grating, and the electrode is between ${\mathrm{G}}_2$ and ${\mathrm{G}}_3$. The fullerenes are detected by thermal ionization in an optical cavity (OC) while the cesium atoms are counted after Langmuir-Taylor surface ionization (LT) and quadrupole mass selection (not shown).

Figure 2

(a) Time-resolved interference scan taken at the reference electrode voltage of 250 V. (b) As (a) but for 2500 V. (c) Cesium deflection curves for velocities ranging from 380 to 640 m/s, extracted from time-resolved data as shown in (a) and (b). (d) A selection of the curves in (c) is used to determine the mean calibration factor. Every fourth point is shown for clarity. Error bars are 68% confidence intervals of the fitted phase values.

Figure 3

(a)–(f) Deflection data for ${\mathrm{C}}_{60}$ with sine fits for increasing deflection voltages from 500 to 3000 V in steps of 500 V. Red curves are with the deflection voltage applied, blue with a fixed 250 V reference voltage. The mean velocity for these measurements was 221 m/s. The fringe deflection and visibility loss due to velocity averaging are clearly visible.

Figure 4

(a) ${\mathrm{C}}_{60}$ deflection curves for a range of mean velocities. (b) ${\mathrm{C}}_{70}$ deflection curves. (c) ${\mathrm{C}}_{60}$ extracted polarizability values for the various velocities with error bars corresponding to 68% confidence intervals of the fitted phases and the mean velocity. (d) As (c), but for ${\mathrm{C}}_{70}$. The smaller horizontal error bars are because more data were taken for the velocity calibration during the ${\mathrm{C}}_{70}$ data run.