Polarizability measurements of a molecule via a near-field matter-wave interferometer

We present a method for measuring the scalar polarizability of molecules by means of near-field matter-wave interferometry. This technique is applicable to a wide range of complex neutral molecules. A key feature of our experiment is the combination of good transmission and high spatial resolution, gained by imprinting a submicrometer spatial modulation onto a wide molecular beam. Our method significantly improves the measurement sensitivity of the polarizability-dependent shifts. We have successfully performed measurements on fullerenes and report the polarizability to be $\alpha =88.9\pm 0.9\pm 5.1{\mathrm{\AA }}^3$ for ${\mathrm{C}}_{60}$ and $\alpha =108.5\pm 2.0\pm 6.2{\mathrm{\AA }}^3$ for ${\mathrm{C}}_{70}$.

Figure 1

(Color online) Experimental setup. The three gratings are used for coherence preparation, diffraction, and detection. Path-dependent matter-wave phase shifts in the external field lead to a deflection of the beam profile at the position of the mask grating. The lateral shift $\mathrm{\Delta }s$ of the interference fringes at the detector is directly proportional to the scalar molecular polarizability $\alpha$.

Figure 2

(Color online) Deflection of a ${\mathrm{C}}_{60}$ beam with $\overline{v}=117\mathrm{m}∕\mathrm{s}$ and ${\sigma }_v=8\%$. A phase shift of $\mathrm{\Delta }\varphi =\pi$ is obtained at a voltage of $6\mathrm{kV}$ (full circles). The open circles represent the reference at $U=0\mathrm{kV}$.

Figure 3

(Color online) Stark deflection of the ${\mathrm{C}}_{70}$ fringes. It follows precisely the quadratic voltage dependence $\mathrm{\Delta }s\propto U^2∕v^2$ of Eq. (1): full circles, $\overline{v}=199\mathrm{m}∕\mathrm{s}$, ${\sigma }_v=16\%$; open circles, $\overline{v}=173\mathrm{m}∕\mathrm{s}$, ${\sigma }_v=13\%$; full squares, $\overline{v}=109\mathrm{m}∕\mathrm{s}$, ${\sigma }_v=7\%$.

Figure 4

(Color online) Signal as a function of the deflection voltage for a fixed position of the mask grating. The open circles are data points for ${\mathrm{C}}_{70}$ at a velocity of $\overline{v}=103.2\mathrm{m}∕\mathrm{s}$, ${\sigma }_v=7\%$. The solid line is the theoretical expectation for $\alpha =108.5{\mathrm{\AA }}^3$. The dashed line is the envelope curve of the visibility function. The dash-dotted lines illustrate upper and lower bounds resulting from small variations of the velocity distribution, $\mathrm{\Delta }\overline{v}=\pm 1\%,$ $\mathrm{\Delta }{\sigma }_v=\pm 1\%$, and typical uncertainties of the visibility, $\mathrm{\Delta }V\left(v\right)=\pm 3\%$.