We review recent progress and future prospects of matter wave interferometry with complex organic molecules and inorganic clusters. Three variants of a near-field interference effect, based on diffraction by material nanostructures, at optical phase gratings, and at ionizing laser fields are considered. We discuss the theoretical concepts underlying these experiments and the experimental challenges. This includes optimizing interferometer designs as well as understanding the role of decoherence. The high sensitivity of matter wave interference experiments to external perturbations is demonstrated to be useful for accurately measuring internal properties of delocalized nanoparticles. We conclude by investigating the prospects for probing the quantum superposition principle in the limit of high particle mass and complexity.

Research on matter waves is a thriving field of quantum physics and has recently stimulated many investigations with electrons 1 , neutrons 2 , atoms 3 , Bose-condensed ensembles 4 , cold clusters 5 and hot molecules 6 . Coherence experiments with complex objects are of interest for exploring the transition to classical physics 7-9 , for measuring molecular properties 10 , and they have even been proposed for testing new models of space-time 11 . For matter-wave experiments with complex molecules, the strongly dispersive effect of the interaction between the diffracted molecule and the grating wall is a major challenge because it imposes enormous constraints on the velocity selection of the molecular beam 12 . Here, we describe the first experimental realization of a new set-up that solves this problem by combining the advantages of a so-called Talbot-Lau interferometer 13 with the benefits of an optical phase grating.Several methods have been developed in the past for the coherent manipulation of matter waves with de Broglie wavelengths in the nanometre and picometre range. For instance, free-standing material gratings were used in the diffraction of electrons 14 , atoms 15,16 and molecules 5,6,17 . In addition, coherent beam splitting at non-resonant standing light waves, often designated the KapitzaDirac effect, has been observed for all of these species [18][19][20] . Recent implementations of near-field interferometry 13,[21][22][23] underlined the particular advantages of the Talbot-Lau concept for experiments with massive objects: the required grating period scales only weakly (d ∼ √ l) with the de Broglie wavelength, and the design accepts beams of low spatial coherence, which makes high signals possible even for weak sources.A symmetric Talbot-Lau interferometer (TLI) consists of three identical gratings. The first one prepares the transverse coherence of the weakly collimated beam. Quantum near-field diffraction at the second nanostructure generates a periodic molecular density distribution at the position of the third mask, which represents a self-image of the second grating, if the grating separation equals a multiple of the Talbot length L T = d 2 /l. The mask can be laterally shifted to transform the molecular interference pattern into a modulation of the molecular beam intensity that is recorded behind the interferometer.In the established TLI design with three nanofabricated gratings 23 , the molecule-wall interaction with the grating bars imprints a further phase shift ϕ on the matter wave, which depends on the molecular polarizability α, the velocity v z and the distance r to the wall within the grating slit. Because of its strongly nonlinear r-dependence, this interaction restricts the interference contrast to very narrow bands of de Broglie wavelengths, as we show in Fig. 1a for the example of the fullerene C 70 . In this simulation, we use the full Casimir-Polder potential 24 , even though the long-distance (retarded) approximation, decaying as α/r 4 , closely reproduces the results. The sha...

The wave nature of matter is a key ingredient of quantum physics and yet it defies our classical intuition. First proposed by Louis de Broglie a century ago, it has since been confirmed with a variety of particles from electrons up to molecules. Here we demonstrate new high-contrast quantum experiments with large and massive tailor-made organic molecules in a near-field interferometer. Our experiments prove the quantum wave nature and delocalization of compounds composed of up to 430 atoms, with a maximal size of up to 60 Å, masses up to m=6,910 AMU and de Broglie wavelengths down to λdB=h/mv≃1 pm. We show that even complex systems, with more than 1,000 internal degrees of freedom, can be prepared in quantum states that are sufficiently well isolated from their environment to avoid decoherence and to show almost perfect coherence.