A major advance in understanding the behavior of light was to describe the coherence of a light source by using correlation functions that define the spatio-temporal relationship between pairs and larger groups of photons. Correlations are also a fundamental property of matter. We performed simultaneous measurement of the second- and third-order correlation functions for atoms. Atom bunching in the arrival time for pairs and triplets of thermal atoms just above the Bose-Einstein condensation (BEC) temperature was observed. At lower temperatures, we demonstrated conclusively the long-range coherence of the BEC for correlation functions to third order, which supports the prediction that like coherent light, a BEC possesses long-range coherence to all orders.

In 1963 Glauber introduced the modern theory of quantum coherence 1 , which extended the concept of first-order (onebody) correlations, describing phase coherence of classical waves, to include higher-order (n-body) quantum correlations characterizing the interference of multiple particles. Whereas the quantum coherence of photons is a mature cornerstone of quantum optics, the quantum coherence properties of massive particles remain largely unexplored. To investigate these properties, here we use a uniquely correlated 2 source of atoms that allows us to observe n-body correlations up to the sixthorder at the ideal theoretical limit (n!). Our measurements constitute a direct demonstration of the validity of one of the most widely used theorems in quantum many-body theory-Wick's theorem 3 -for a thermal ensemble of massive particles. Measurements involving n-body correlations may play an important role in the understanding of thermalization of isolated quantum systems 4 and the thermodynamics of exotic many-body systems, such as Efimov trimers 5 .Glauber's modern theory of optical coherence and the famous Hanbury Brown-Twiss effect 6 were pivotal in the establishment of the field of quantum optics. Importantly, the definition of a coherent state required coherence to all orders, which for example distinguishes a monochromatic but incoherent thermal source of light from a truly coherent source such as a laser. Higher-order correlation functions therefore provide a more rigorous test of coherence.Higher-order correlations, characterized by an n-body correlation function g (n) , are of general interest and have been investigated in many fields of physics including astronomy 6 , particle physics 7 , quantum optics 8 , and quantum atom optics 9 . In particular they have been a fruitful area of research in the field of quantum optics, where they have been used to investigate the properties of laser light, including heralded single photons 10 , and the statistics of parametric down-conversion sources 11 . State-of-the-art quantum optics experiments have measured photon correlation functions up to sixth order for quasi-thermal sources 8 , allowing the possibility of performing full quantum state tomography 12 .Higher-order correlations experiments with massive particles are currently approaching the same level of maturity as with photons. So far, experiments have directly observed correlations up to fourth order with single-atom-sensitive detection techniques for ultracold atomic bosons 9,13,14 , and second-order correlations for an atomic source of fermions 15 demonstrating the uniquely quantum mechanical property of atom-atom antibunching. Alternative, indirect techniques have also been employed to investigate higher-order correlations, including the measurements of twobody (photoassociation 16 ) and three-body 17 loss rates that are sensitive, respectively, to second-and third-order correlation functions. Interestingly, fermionic atom pairs 18 and fermionic antibunching 19 have also been observed in the atomic shot no...

A power-balance model, with radiation losses from impurities and neutrals, gives a unified description of the density limit (DL) of the stellarator, the L-mode tokamak, and the reversed field pinch (RFP). The model predicts a Sudo-like scaling for the stellarator, a Greenwald-like scaling, , for the RFP and the ohmic tokamak, a mixed scaling, , for the additionally heated L-mode tokamak. In a previous paper (Zanca et al 2017 Nucl. Fusion 57 056010) the model was compared with ohmic tokamak, RFP and stellarator experiments. Here, we address the issue of the DL dependence on heating power in the L-mode tokamak. Experimental data from high-density disrupted L-mode discharges performed at JET, as well as in other machines, are taken as a term of comparison. The model fits the observed maximum densities better than the pure Greenwald limit.

The wave-particle dual nature of light and matter and the fact that the choice of measurement determines which one of these two seemingly incompatible behaviours we observe are examples of the counterintuitive features of quantum mechanics. They are illustrated by Wheeler's famous 'delayedchoice' experiment 1 , recently demonstrated in a single-photon experiment 2 . Here, we use a single ultracold metastable helium atom in a Mach-Zehnder interferometer to create an atomic analogue of Wheeler's original proposal. Our experiment confirms Bohr's view that it does not make sense to ascribe the wave or particle behaviour to a massive particle before the measurement takes place 1 . This result is encouraging for current work towards entanglement and Bell's theorem tests in macroscopic systems of massive particles 3 .The question of whether light behaves like a particle or wave had a long and strongly contested history until the advent of quantum mechanics, where it was accepted that it could indeed exhibit either behaviour. Conversely, it was de Broglie's hypothesis of matter waves 4 that deviated from the preceding view of massive bodies exclusively as particles, which was confirmed by the electron diffraction experiments of Davisson and Germer 5 . Even more bizarrely, the way in which an experiment is performed seems to induce one of these behaviours to the exclusion of the other. The question of whether a single photon in an interferometer passes through either one arm (as a particle) or both simultaneously (as a wave) led to Wheeler devising his famous gedanken experiment, which supposed that the decision of whether to attempt to measure particle or wave behaviour is made after the photon enters the interferometer. By removing the second beamsplitter of the interferometer (Fig. 1a), which-way information is revealed 6 , which precludes an interference measurement, while inserting the beamsplitter destroys information about the path taken by the photon and re-establishes a wave interference dependent on the phase difference φ between the arms.Although many experiments have shown particle-wave duality with photons 7 , including delayed-choice schemes 8-10 , delayed-choice quantum eraser experiments 11 and entanglement swapping using delayed choice 12 , only recently has the complete scheme proposed by Wheeler been realized experimentally 2 . By simultaneously ensuring that only a single photon is present in the interferometer at once, and that the decision of interferometer configuration is relativistically separated from the photon's entry to the interferometer, it was unambiguously shown that Wheeler's supposition that such a choice affects the 'past history' of the photon was correct.Recent advances in the trapping and cooling of atoms has led to the ability to readily observe wavelike phenomena with particles that have mass, such as the interference between two Bose-Einstein condensates 13 . However, progress towards demonstrating Wheeler's experiment with massive particles, such a QR NG b |0〉 |1〉 DLD φ π /2 π /2...