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.

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.

We propose an experimentally accessible, objective measure for the macroscopicity of superposition states in mechanical quantum systems. Based on the observable consequences of a minimal, macrorealist extension of quantum mechanics, it allows one to quantify the degree of macroscopicity achieved in different experiments.

Matter-wave interferometry performed with massive objects elucidates their wave nature and thus tests the quantum superposition principle at large scales. Whereas standard quantum theory places no limit on particle size, alternative, yet untested theories-conceived to explain the apparent quantum to classical transition-forbid macroscopic superpositions. Here we propose an interferometer with a levitated, optically cooled and then free-falling silicon nanoparticle in the mass range of one million atomic mass units, delocalized over 4150 nm. The scheme employs the near-field Talbot effect with a single standing-wave laser pulse as a phase grating. Our analysis, which accounts for all relevant sources of decoherence, indicates that this is a viable route towards macroscopic high-mass superpositions using available technology.

Quantum experiments with nanomechanical oscillators are regarded as a test bed for hypothetical modifications of the Schrödinger equation, which predict a breakdown of the superposition principle and induce classical behavior at the macroscale. It is generally believed that the sensitivity to these unconventional effects grows with the mass of the mechanical quantum system. Here we show that the opposite is the case for optomechanical systems in the presence of generic noise sources, such as thermal and measurement noise. We determine conditions for distinguishing these decoherence processes from possible collapse-induced decoherence in continuous optomechanical force measurements.

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In recent years substantial efforts have been expended in extending thermodynamics to single quantum systems. Quantum effects have emerged as a resource that can improve the performance of heat machines. However in the fully quantum regime their implementation still remains a challenge. Here, we report an experimental realization of a quantum absorption refrigerator in a system of three trapped ions, with three of its normal modes of motion coupled by a trilinear Hamiltonian such that heat transfer between two modes refrigerates the third. We investigate the dynamics and steady-state properties of the refrigerator and compare its cooling capability when only thermal states are involved to the case when squeezing is employed as a quantum resource. We also study the performance of such a refrigerator in the single shot regime made possible by coherence and demonstrate cooling below both the steady-state energy and a benchmark set by classical thermodynamics.

Matter-wave interferometry with atoms 1 and molecules 2 has attracted a rapidly growing level of interest over the past two decades, both in demonstrations of fundamental quantum phenomena and in quantum-enhanced precision measurements. Such experiments exploit the non-classical superposition of two or more position and momentum states that are coherently split and rejoined to interfere 3-11 . Here, we present the experimental realization of a universal nearfield interferometer built from three short-pulse single-photon ionization gratings 12,13 . We observe quantum interference of fast molecular clusters, with a composite de Broglie wavelength as small as 275 fm. Optical ionization gratings are largely independent of the specific internal level structure and are therefore universally applicable to different kinds of nanoparticle, ranging from atoms to clusters, molecules and nanospheres. The interferometer is sensitive to fringe shifts as small as a few nanometres and yet robust against velocitydependent phase shifts, because the gratings exist only for nanoseconds and form an interferometer in the time domain.Recent progress in atom interferometry has been driven by the development of wide-angle beam splitters 14 , large interferometer areas 15 and long coherence times 16 . Most interferometers operate in a Mach-Zehnder 5,17 , Ramsey-Bordé 18 or Talbot-Lau 19 configuration, some of them also in the time domain 20,21 . Here we ask how to generalize these achievements to atoms, molecules, clusters or nanoparticles-irrespective of their internal states.Mechanical nanomasks 22 could be considered as universal if it were not for their van der Waals attraction on the traversing matter waves, which induces sizable dispersive, that is, velocity-dependent, phase shifts even for gratings as thin as 10 nm.Optical 9,14 or measurement-induced 23 gratings eliminate this effect, but most methods so far relied on closed transitions and required an individual light source for every specific kind of atom or molecule.It is possible to circumvent this restriction by using the spatially periodic electric dipole potential in an off-resonant standing light wave. Its field then modulates the phase of the matter wave rather than the amplitude. This implies, however, that the spatial coherence of the incident matter wave needs to be prepared by other means before-such as by collimation, cooling 24 or the addition of another absorptive (material) mask 2 .Here, we demonstrate a new method for coherence experiments with a wide class of massive particles and show how a sequence of ionizing laser grating pulses 12 can form a generic matter-wave interferometer in the time domain 13 . Figure 1 shows a schematic of the layout of our experiment, which we here realize specifically for clusters of anthracene (Ac) molecules. The molecules are evaporated in an Even-Lavie valve 25 Faculty of Physics, University of Vienna, VCQ, Boltzmanngasse 5, A-1090 Vienna, Austria. *e-mail: markus.arndt@univie.ac.at.that injects the organic vapour with a pulse wi...