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Physical Review Research

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

Yaakov Y. Fein, Philipp Geyer, Filip Kiałka, Stefan Gerlich, Markus Arndt

Published Dec 9, 2019• 13 citations
Publisher

Abstract

In this work the polarizability of fullerenes is measured by sending them through a tailored electric field inside a long-baseline matter-wave interferometer. The molecule interference fringes are shifted in proportion to the molecule's polarizability and the universality of the device allows us to reference the molecular data to those of atomic cesium. This way the accuracy is improved over previous fullerene polarizability measurements.

DOI
10.1103/physrevresearch.1.033158

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In this work the polarizability of fullerenes is measured by sending them through a tailored electric field inside a long-baseline matter-wave interferometer. The molecule interference fringes are shifted in proportion to the molecule's polarizability and the universality of the device allows us to reference the molecular data to those of atomic cesium. This way the accuracy is improved over previous fullerene polarizability measurements.
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 $\ensuremath{\alpha}=88.9\ifmmode\pm\else\textpm\fi{}0.9\ifmmode\pm\else\textpm\fi{}5.1\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{3}$ for C60{\mathrm{C}}_{60}C60​ and $\ensuremath{\alpha}=108.5\ifmmode\pm\else\textpm\fi{}2.0\ifmmode\pm\else\textpm\fi{}6.2\phantom{\rule{0.3em}{0ex}}{\mathrm{\AA{}}}^{3}$ for C70{\mathrm{C}}_{70}C70​.
We review the concept of matter-wave assisted molecule metrology and present the most recent experiments which exploit the capability of universal matter-wave interferometers to measure forces as small as 10-26 N via shifts of the interference fringes in the presence of well-controlled fields. This technique allows us to compare, in the same instrument, a variety of electronic and magnetic properties for a large range of atoms and molecules. We exemplify this here with precision measurements of the static polarizability of cesium atoms and the fullerenes C60 and C70 as well as dynamically-induced susceptibilities of tailored tripeptides. We also present measurements of magnetic properties such as the diamagnetic susceptibility of ground-state atoms and aromatic and non-aromatic hydrocarbons.
We discuss new de Broglie coherence experiments in a near-field molecule interferometer with a variety of large organic molecules. While de Broglie coherence is to first order only associated with the center-of-mass motion of the diffracted particle, we here investigate the question as to which extent the internal molecular property is relevant for, compatible with or detrimental for maintaining coherence in the translational degree of freedom. External perturbations, such as inhomogeneous external electric fields, may influence the delocalized molecules inside the matter wave interferometer and they allow us to access the molecular polarizabilities, permanent or even fluctuating electric dipole moments. We extract information about the molecular states from the interference phase shifts as well as from the observed dephasing in a Kapitza-Dirac Talbot-Lau-Stark-deflectometer. We discuss the relevance of our experiments with regard to both molecule metrology and the foundations of quantum mechanics, i.e. the preservation of coherence for highly complex particles in external fields.
We investigate the influence of different electric moments on the shift and dephasing of molecules in a matter wave interferometer. Firstly, we provide a quantitative comparison of two molecules that are non-polar yet polarizable in their thermal ground state and that differ in their stiffness and response to thermal excitations . While C 25 H 20 is rather rigid, its larger derivative C 49 H 16 F 52 is additionally equipped with floppy side chains and vibrationally activated dipole moment variations. Secondly, we elucidate the role of a permanent electric dipole moment by contrasting the quantum interference pattern of a (nearly) non-polar and a polar porphyrin derivative. We find that a high molecular polarizability and even sizeable dipole moment fluctuations are still well compatible with high-contrast quantum interference fringes. The presence of permanent electric dipole moments, however, can lead to a dephasing and rapid degradation of the quantum fringe pattern already at moderate electric fields. This finding is of high relevance for coherence experiments with large organic molecules, which are generally equipped with strong electric moments.
We demonstrate a near-field Talbot-Lau interferometer for C70 fullerene molecules. Such interferometers are particularly suitable for larger masses. Using three free-standing gold gratings of 1 microm period and a transversally incoherent but velocity-selected molecular beam, we achieve an interference fringe visibility of 40% with high count rate. Both the high visibility and its velocity dependence are in good agreement with a quantum simulation that takes into account the van der Waals interaction of the molecules with the gratings and are in striking contrast to a classical moiré model.
We have constructed an atom interferometer with interfering beams that are physically isolated by a metal foil. By applying an interaction to one of the two interfering beams, we can measure ground-state energy shifts with a spectroscopic precision of 6.6\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}14}$ eV/\ensuremath{\surd}min , or 16 Hz/\ensuremath{\surd}min . Applying an electric field to one beam of the interferometer, we have measured the phase shift induced from the quadratic Stark effect. By analyzing these phase shifts, we have determined the ground-state polarizability of sodium, with much improved accuracy, to be 24.11(6)statistical{)}_{\mathrm{statistical}})statistical​(6)systematic{)}_{\mathrm{systematic}})systematic​\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}24}$ cm3{\mathrm{cm}}^{3}cm3.