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arXiv:1506.06026 · Physical Review A

Molecular rotations in matter-wave interferometry

Benjamin A. Stickler, Klaus Hornberger

Published Aug 13, 2015• 23 citations
arXivHTMLPDF

Abstract

We extend the theory of matter-wave interferometry of pointlike particles to nonspherical objects by taking the orientational degrees of freedom into account. In particular, we derive the grating transformation operator, which maps the impinging state onto the outgoing state, for a general, orientation-dependent interaction potential between the grating and the molecule. The grating operator is then worked out for the diffraction of symmetric top molecules from standing light waves, and the resulting interference pattern is calculated in the near field. This allows us to identify a signature of the orientational degrees of freedom in near-field matter-wave experiments.

DOI
10.1103/physreva.92.023619

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We extend the theory of matter-wave interferometry of pointlike particles to nonspherical objects by taking the orientational degrees of freedom into account. In particular, we derive the grating transformation operator, which maps the impinging state onto the outgoing state, for a general, orientation-dependent interaction potential between the grating and the molecule. The grating operator is then worked out for the diffraction of symmetric top molecules from standing light waves, and the resulting interference pattern is calculated in the near field. This allows us to identify a signature of the orientational degrees of freedom in near-field matter-wave experiments.
The present thesis deals with two main topics. First, I study in detail the interaction of a delocalized molecular matter-wave with a standing-wave laser grating. Due to absorption of photons in an optical grating, molecules can get excited and numerous internal photophysical processes are induced. For the theoretical description of the molecule-light interaction I take three relevant internal molecular processes into account: intersystem crossing, fluorescence and internal conversion. Furthermore, the fact that molecules can change their optical properties because of the photoexcitation is shown to have a measurable effect on matter-wave interferometry. The second topic of this thesis is about collisions between a polar molecule and non-polar environmental gas atoms, and their effects on the coherence of the center-of-mass state. Because the scattering potential depends on the molecular orientation the molecular rotational state must also be considered. Assuming a slow rotation of the molecule compared to the scattering time and that the molecular mass fairly exceeds the mass of a gas atom, I present a master equation of collisional decoherence, which depends on the molecular orientation. Its predictions for matter-wave interferometry are discussed both in the near and far field.
For various experiments to investigate quantum effects, matter-wave diffraction is an apparent example. Particle diffractions have been measured even at the large molecular level, such as the C 60 molecules. In order to describe the matter-wave diffraction of C 60 beam, we assume the initial wave functions behind a grating in form of the Fourier series with a Gaussian distribution function. By applying the Feynman path integral, the exact wave functions of the molecule diffraction in the near-field regime can be derived analytically. The obtained probability density distributions are corresponding to interference fringes as found in the Fresnel diffraction. The probability of finding C 60 molecules, behind the grating at the Talbot length, consistency with the mentioned experimental data of C 60 diffractions.
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 thermally activated internal molecular dynamics on the phase shifts of matter waves inside a molecule interferometer. While de Broglie physics generally describes only the center-of-mass motion of a quantum object, our experiment demonstrates that the translational quantum phase is sensitive to dynamic conformational state changes inside the diffracted molecules. The structural flexibility of tailor-made organic particles is sufficient to admit a mixture of strongly fluctuating dipole moments. These modify the electric susceptibility and through this the quantum interference pattern in the presence of an external electric field. Detailed molecular dynamics simulations combined with density-functional theory allow us to quantify the time-dependent structural reconfigurations and to predict the ensemble-averaged square of the dipole moment which is found to be in good agreement with the interferometric result. The experiment thus opens a different perspective on matter wave interferometry, as we demonstrate here that it is possible to collect structural information about molecules even if they are delocalized over more than 100 times their own diameter.
We study the theory behind a Talbot–Lau interferometer. This consists of three gratings in each other's Fresnel near field and accepts spatially incoherent illumination. Our formalism gives a clear physical picture and permits efficient numerical simulations. We concentrate on the case of matter waves and provide an adequate description of recent fullerene experiments taking into account the Casimir–Polder interaction between a molecular beam and mechanical gratings. For more massive molecules, the influence of this interaction is more drastic and leads to a forbiddingly narrow velocity distribution requirement for future experiments with very massive molecules. This problem can be avoided by configurations where at least one mechanical grating is replaced with an optical grating, i.e. a standing light wave. Such interferometers show improved scaling behaviour. Magnifying or demagnifying interferometer variants are also discussed.
Abstract When Otto Stern embarked on molecular-beam experiments in his new lab at Hamburg University a century ago, one of his interests was to demonstrate the wave-nature of atoms and molecules that had been predicted shortly before by Louis de Broglie. As the effects of diffraction and interference provide conclusive evidence for wave-type behavior, Otto Stern and his coworkers conceived two matter-wave diffraction experiments employing their innovative molecular-beam method. The first concept assumed the molecular ray to coherently scatter off a plane ruled grating at grazing incidence conditions, while the second one was based on the coherent scattering from a cleaved crystal surface. The latter concept allowed Stern and his associates to demonstrate the wave behavior of atoms and molecules and to validate de Broglie’s formula. The former experiment, however, fell short of providing evidence for diffraction of matter waves. It was not until 2007 that the grating diffraction experiment was retried with a modern molecular-beam apparatus. Fully resolved matter-wave diffraction patterns were observed, confirming the viability of Otto Stern’s experimental concept. The correct explanation of the experiment accounts for quantum reflection, another wave effect incompatible with the particle picture, which was not foreseen by Stern and his contemporaries.