For strong interactions, we find evidence for an emergent incompressible Mott insulating phase.

Transport properties are among the defining characteristics of many important phases in condensed matter physics. In the presence of strong correlations they are difficult to predict even for model systems like the Hubbard model. In real materials they are in general obscured by additional complications including impurities, lattice defects or multi-band effects. Ultracold atoms in contrast offer the possibility to study transport and out-of-equilibrium phenomena in a clean and well-controlled environment and can therefore act as a quantum simulator for condensed matter systems. Here we studied the expansion of an initially confined fermionic quantum gas in the lowest band of a homogeneous optical lattice. While we observe ballistic transport for non-interacting atoms, even small interactions render the expansion almost bimodal with a dramatically reduced expansion velocity. The dynamics is independent of the sign of the interaction, revealing a novel, dynamic symmetry of the Hubbard model.In solid state physics, transport properties are among the key observables, the most prominent example being the electrical conductivity, which e.g. allows to distinguish normal conductors from insulators or superconductors. Furthermore, many of today's most intriguing solid state phenomena manifest themselves in transport properties, examples including high-temperature superconductivity, giant magnetoresistance, quantum hall physics, topological insulators and disorder phenomena. Especially in strongly correlated systems, where the interactions between the conductance electrons are important, transport properties are difficult to calculate beyond the linear response regime. In general, predicting out-of-equilibrium fermionic dynamics represents an even harder problem than the prediction of static properties like the nature of the ground state. In real solids further complications arise due to the effects of e.g. impurities, lattice defects and phonons. These complications render an experimental investigation in a clean and well controlled ultracold atom system highly desirable. While the last years have seen dramatic progress in the control of quantum gases in optical lattices [1-3], a thorough understanding of the dynamics in these systems is still lacking. Genuine dynamical experiments can not only uncover new dynamic phenomena but are also essential to gain insight into the timescales needed to achieve equilibrium in the lattice [4,5] or to adiabatically load into the lattice [6,7].Using both bosonic and fermionic [8-10] atoms, it has become possible to simulate models of strongly interacting quantum particles, for which the Hubbard model [11] * ulrich.schneider@lmu.de is probably the most important example. A major advantage of these systems compared to real solids is the possibility to change all relevant parameters in real-time by e.g. varying laser intensities or magnetic fields. While first studies of dynamical properties of both bosonic and fermionic quantum gases [12][13][14] have already been performed, a remaining...

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Interactions lie at the heart of correlated many-body quantum phases. Typically, the interactions between microscopic particles are described as two-body interactions. However, it has been shown that higher-order multi-body interactions could give rise to novel quantum phases with intriguing properties. So far, multi-body interactions have been observed as inelastic loss resonances in three- and four-body recombinations of atom-atom and atom-molecule collisions. Here we demonstrate the presence of effective multi-body interactions in a system of ultracold bosonic atoms in a three-dimensional optical lattice, emerging through virtual transitions of particles from the lowest energy band to higher energy bands. We observe such interactions up to the six-body case in time-resolved traces of quantum phase revivals, using an atom interferometric technique that allows us to precisely measure the absolute energies of atom number states at a lattice site. In addition, we show that the spectral content of these time traces can reveal the atom number statistics at a lattice site, similar to foundational experiments in cavity quantum electrodynamics that yield the statistics of a cavity photon field. Our precision measurement of multi-body interaction energies provides crucial input for the comparison of optical-lattice quantum simulators with many-body quantum theory.

Emergent quantum technologies have led to increasing interest in decoherence -the processes that limit the appearance of quantum effects and turn them into classical phenomena. One important cause of decoherence is the interaction of a quantum system with its environment, which 'entangles' the two and distributes the quantum coherence over so many degrees of freedom as to render it unobservable. Decoherence theory [1][2][3][4] has been complemented by experiments using matter waves coupled to external photons [5][6][7] or molecules [8], and by investigations using coherent photon states [9], trapped ions [10] and electron interferometers [11,12]. Large molecules are particularly suitable for the investigation of the quantumclassical transition because they can store much energy in numerous internal degrees of freedom; the internal energy can be converted into thermal radiation and thus induce decoherence. Here we report matter wave interferometer experiments in which C 70 molecules lose their quantum behaviour by thermal emission of radiation. We find good quantitative agreement between our experimental observations and microscopic decoherence theory. Decoherence by emission of thermal radiation is a general mechanism that should be relevant to all macroscopic bodies.In this Letter we investigate the decoherence of molecular matter waves. We change the internal temperature of the molecules in a controlled way before they enter a near-field interferometer, and observe the corresponding reduction of the interference contrast. The idea behind this effort is to demonstrate a most fundamental decoherence mechanism that we encounter in the macroscopic world: All large objects, but also molecules of sufficient complexity, are able to store energy and to interact with their environment via thermal emission of photons. It is generally believed that warm macroscopic bodies emit far too many photons to allow the observation of de Broglie interferences, whereas individual atoms or molecules can be sufficiently well isolated to exhibit their quantum nature. However, there must be a transition region between these two limiting cases. Interestingly, as we show in this study, C 70 fullerene molecules have just the right amount of complexity to exhibit perfect quantum interference in our experiments [13] at temperatures below 1000 K, and to gradually lose all their quantum behaviour when the internal temperature is increased up to 3000 K. We can thus trace the quantum-to-classical transition in a controlled and quantitative way. The complexity of large molecules adds a novel quality with respect to previously performed experiments with atoms [5][6][7]: the energy in molecules may be equilibrated in many internal degrees of freedom during the free flight, and a fraction of the vibrational energy will eventually be reconverted into emitted photons. Therefore the internal dynamics of the molecule is also relevant for the quantum behaviour of the centre-of-mass state. In contrast to resonance fluorescence, which was investigated wit...

We study the loss of spatial coherence in the extended wave function of fullerenes due to collisions with background gases. From the gradual suppression of quantum interference with increasing gas pressure we are able to support quantitatively both the predictions of decoherence theory and our picture of the interaction process. We thus explore the practical limits of matter wave interferometry at finite gas pressures and estimate the required experimental vacuum conditions for interferometry with even larger objects.PACS numbers: 03.65.Yz,39.20.+q Matter wave interferometers are based on quantum superpositions of spatially separated states of a single particle. However, as is well known, the concept of wave-particle duality does not apply to a classical object which by definition never occupies macroscopically distinct states simultaneously. By performing interference experiments with particles of increasing complexity one can therefore probe the borderline between these incompatible descriptions.It is still a matter of debate how to explain the quantum-to-classical transition in a unified framework. Some theories contain an element beyond the unitary evolution of quantum mechanics [1, 2] -which includes the 'collapse' of the wave function as taught in many standard textbooks. Decoherence theory, on the other hand, remains within the framework of the quantum theory [3,4,5]. It explains the decay of quantum coherences as being caused by the interaction of the quantum object with its environment.So far, several decoherence experiments in atom interferometry focused on the loss of coherence due to scattering of a single [6,7] or a few [8] laser photons by an atom. Other authors proposed or realized schemes to encode which-path information in internal atomic degrees of freedom, thereby reducing the interference contrast as well, in spite of a negligible change in the atomic centerof-mass state [9,10]. These studies are complemented by experiments which quantitatively followed the decoherence of a coherent photon state in a high-finesse microwave cavity [11] or of the motional state of a trapped ion [12]. However, all these experiments worked with few-level systems and engineered environments.In the present letter we quantitatively investigate a mechanism which seems to be among the most natural and most effective sources of decoherence in our macroscopic world, namely collisions with gas particles. From the controlled suppression of quantum interference as a function of the gas pressure we are able to test both the predictions of decoherence theory and our picture of the collisional interaction.We note that the effect of atomic collisions in an atom interferometer was already investigated in [13]. How- ever, decoherence effects were not observed in these experiments, since the detected atoms did not change the state of the colliding gas sufficiently to leave behind the required path information for decoherence. In contrast to that, our experiment uses massive C 70 -fullerene molecules, and is based on a Talbot-L...

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...

We demonstrate quantum interference for tetraphenylporphyrin, the first biomolecule exhibiting wave nature, and for the fluorofullerene C60F48 using a near-field Talbot-Lau interferometer. For the porphyrins, which are distinguished by their low symmetry and their abundant occurence in organic systems, we find the theoretically expected maximal interference contrast and its expected dependence on the de Broglie wavelength. For C60F48 the observed fringe visibility is below the expected value, but the high contrast still provides good evidence for the quantum character of the observed fringe pattern. The fluorofullerenes therefore set the new mark in complexity and mass (1632 amu) for de Broglie wave experiments, exceeding the previous mass record by a factor of two.PACS numbers: 03.65.Ta,39.20.+q The wave-particle duality of massive objects is one of the corner stones of quantum physics. Nonetheless this quantum property is never observed in our everyday world. The current experiments are aiming at exploring the limits to which one can still observe the quantum wave nature of massive objects and to understand the role of the internal molecular structure and symmetry.Coherent molecule optics was already initiated as early as in 1930 when Estermann and Stern confirmed de Broglie's wave hypothesis [1] in a diffraction experiment with He atoms and H 2 molecules [2]. In contrast to the rapidly evolving field of electron and neutron optics, atom optics became only feasible about twenty years ago and has led from experiments with thermal atoms to coherent ensembles of ultra-cold atoms forming Bose-Einstein condensates. Molecule interferometry was only taken up again in 1994 with the first observation of Ramsey-Bordé interferences for I 2 [3] and with the proof of the existence of the weakly bound He 2 in a farfield diffraction experiment [4]. Experiments with alkali dimers in the far-field [5] and in near-field [6] interferometers followed. Recent interest in molecule optics has been stimulated by the quest for demonstrations of fundamental quantum mechanical effects with mesoscopic objects [7,8,9].In the present letter, we report the first demonstration of the wave nature of both tetraphenylporphyrin (TPP) and of fluorinated fullerenes using near-field interference. The porphyrin structure is at the heart of many complex biomolecules, serving as a color center for instance in chlorophyll and in hemoglobin. The fluorofullerene C 60 F 48 is the most massive (1632 amu) and most complex (composed of 108 atoms) molecule for which the de Broglie wave-nature has been shown so far (see fig.1).In order to demonstrate the wave property of a massive object with a short de Broglie wavelength it is advisable to use a near-field diffraction scheme. In particular a Talbot-Lau-interferometer (TLI, for details see [11,12,13,14]) is compact and rugged, has favorable3D Structure of tetraphenylporphyrin (TPP) C44H30N4 (left) and the fluorofullerene C60F48 (right) [10]. TPP (m=614 amu) is composed of four tilted phenyl rings attached t...