In quantum many-body theory, all physical observables are described in terms of correlation functions between particle creation or annihilation operators. Measurement of such correlation functions can therefore be regarded as an operational solution to the quantum many-body problem. Here, we demonstrate this paradigm by measuring multiparticle momentum correlations up to third order between ultracold helium atoms in an s-wave scattering halo of colliding Bose-Einstein condensates, using a quantum manybody momentum microscope. Our measurements allow us to extract a key building block of all higherorder correlations in this system-the pairing field amplitude. In addition, we demonstrate a record violation of the classical Cauchy-Schwarz inequality for correlated atom pairs and triples. Measuring multiparticle momentum correlations could provide new insights into effects such as unconventional superconductivity and many-body localization. DOI: 10.1103/PhysRevLett.118.240402 In quantum physics, fully understanding and characterizing complex systems, comprising a large (often macroscopic) number of interacting particles, is an extremely challenging problem. Solutions within the standard framework of (first-quantized) quantum mechanics generally require the knowledge of the full quantum many-body wave function. This necessitates an exponentially large amount of information to be encoded and simulated using the many-body Schrödinger equation. In an equivalent (second-quantized) quantum field theory formulation, the fundamental understanding of quantum many-body systems comes through the description of all physical observables via correlation functions between particle creation and annihilation operators. Here, the exponential complexity of the quantum many-body problem is converted into the need to know all possible multiparticle correlation functions, starting from two-, three-, and increasing to arbitrary N-particle (or higher-order) correlations.From an experimental viewpoint, an operational solution to the quantum many-body problem is therefore equivalent to measuring all multiparticle correlations. In certain cases, however, knowing only a specific set of (few-body or lower-order) correlations is sufficient to allow a solution of the many-body problem to be constructed. This was recently shown for phase correlations between two coupled one-dimensional (1D) Bose gases [1]. Apart from facilitating the description of physical observables, characterizing multiparticle correlations is important for introducing controlled approximations in many-body physics, such as the virial-and related cluster-expansion approaches that rely on truncation of the Bogolyubov-Born-GreenKirkwood-Yvon hierarchy [2,3] Correlations between multiple photons are also routinely used in numerous quantum optics experiments including ghost imaging [15,16], defining criteria for nonclassicality [17,18], analyzing entangled states generated by parametric down conversion [19], and characterizing single photon sources [20].Here, we demonstrate an e...

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...

Ghost imaging is a counter-intuitive phenomenon-first realized in quantum optics-that enables the image of a two-dimensional object (mask) to be reconstructed using the spatio-temporal properties of a beam of particles with which it never interacts. Typically, two beams of correlated photons are used: one passes through the mask to a single-pixel (bucket) detector while the spatial profile of the other is measured by a high-resolution (multi-pixel) detector. The second beam never interacts with the mask. Neither detector can reconstruct the mask independently, but temporal cross-correlation between the two beams can be used to recover a 'ghost' image. Here we report the realization of ghost imaging using massive particles instead of photons. In our experiment, the two beams are formed by correlated pairs of ultracold, metastable helium atoms, which originate from s-wave scattering of two colliding Bose-Einstein condensates. We use higher-order Kapitza-Dirac scattering to generate a large number of correlated atom pairs, enabling the creation of a clear ghost image with submillimetre resolution. Future extensions of our technique could lead to the realization of ghost interference, and enable tests of Einstein-Podolsky-Rosen entanglement and Bell's inequalities with atoms.

We present the first measurement for helium atoms of the tune-out wavelength at which the atomic polarizability vanishes. We utilise a novel, highly sensitive technique for precisely measuring the effect of variations in the trapping potential of confined metastable (2 3 S1) helium atoms illuminated by a perturbing laser light field. The measured tune-out wavelength of 413.0938(9Stat.)(20Syst.) nm compares well with the value predicted by a theoretical calculation (413.02(9) nm) which is sensitive to finite nuclear mass, relativistic, and quantum electro-dynamic (QED) effects. This provides motivation for more detailed theoretical investigations to test QED. 11 level with differences of several standard deviations.Of much lower precision are the experimental and theoretical determinations of transition rates, which are both inherently difficult to measure and predict respectively. Nevertheless, theory and experiment appear to be in good agreement within the (typically of order a few per cent) uncertainty. In helium, we have previously verified theoretical QED predictions in a series of measurements of the transition rates to the ground state for the 2 3 P manifold [5,6] and the 2 3 S 1 metastable level [7]. Recently, QED has been challenged by experiments that determine the proton radius via spectroscopy of muonic hydrogen [8,9], whose values differ by seven standard deviations (7σ) from those measured by precision hydrogen spectroscopy (combined with QED theory [10]), and by proton-electron scattering experiments [11]. This has created the so-called proton radius puzzle [12]. More stringent tests of QED using different experiments are therefore important to provide independent validation or otherwise of QED.One such example is the precision measurement of tune-out (or magic-zero [13]) wavelengths that can provide independent verification of QED predictions for transition rate ratios. At excitation energies above the lowest excited state, the contribution to the dynamic polarizability from the lowest excited state is negative. There will then occur a series of wavelengths, each associated with a further excited state, where positive contributions to the polarizability from other states will exactly cancel the negative polarizability contributions, thereby creating so-called tune-out wavelengths.Mitroy and Tang [14] have estimated theoretically the tune-out wavelengths for transitions from the helium 2 3 S 1 metastable state (He*) to near the 2 3 P , 3 3 P and 4 3 P triplet manifolds (at 1083, 389 and 319 nm respectively). These approximate calculations (at around the 0.02% level) were designed to provide guidance for the first experimental measurements which we present here. Their calculations were based on a composite theory utilizing state-of-the-art transition rate data by Morton and Drake [15] for the low lying transitions, and model potential oscillator strengths for higher excitations. From a theoretical perspective, it should be noted that the same QED contributions to the dynamic polarizability are als...

Ghost imaging is a technique -first realized in quantum optics [1,2] -in which the image emerges from cross-correlation between particles in two separate beams. One beam passes through the object to a bucket (single-pixel) detector, while the second beam's spatial profile is measured by a high resolution (multi-pixel) detector but never interacts with the object. Neither detector can reconstruct the image independently. However, until now ghost imaging has only been demonstrated with photons.Here we report the first realisation of ghost imaging of an object using massive particles. In our experiment, the two beams are formed by correlated pairs of ultracold metastable helium atoms [3], originating from two colliding Bose-Einstein condensates (BECs) via s-wave scattering [4,5]. We use the higher-order Kapitza-Dirac effect [6] to generate the large number of correlated atom pairs required, enabling the creation of a ghost image with good visibility and sub-millimetre resolution. Future extensions could include ghost interference as well as tests of EPR entantlement [7] and Bell's inequalities [8].