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We demonstrate the effect of pulse shaping in momentum selective atomic Bragg diffraction. We compare temporal square pulses, which produce sidelobes in momentum space, with other shapes which can produce more nearly square momentum distributions. We produce pulses that simultaneously address two sets of velocity classes and demonstrate that we can control the differential phase imprinted on them in a way that is insensitive to laser phase fluctuations. Our work marks a significant step forward in testing Bell inequalities using massive particles entangled in momentum.

Tomography of single-particle-resolved detectors is of primary importance for characterizing particle correlations with applications in quantum metrology, quantum simulation and quantum computing. However, it is a non-trivial task in practice due to the unavoidable presence of noise that affects the measurement but does not originate from the detector. In this work, we address this problem for a three-dimensional single-atom-resolved detector where shot-to-shot atom number fluctuations are a central issue to perform a quantum detector tomography. We overcome this difficulty by exploiting the parallel measurement of counting statistics in sub-volumes of the detector, from which we evaluate the effect of shot-to-shot fluctuations and perform a local tomography of the detector. In addition, we illustrate the validity of our method from applying it to Gaussian quantum states with different number statistics. Finally, we show that the response of Micro-Channel Plate detectors is well-described from using a binomial distribution with the detection efficiency as a single parameter., Comment: 7 pages, 5 figures

We study the feasibility of sub-shot-noise interferometry with imperfect detectors, starting from twin-Fock states and two mode squeezed vacuum states. We derive analytical expressions for the corresponding phase uncertainty. We find that one can achieve phase shift measurements below the standard quantum limit, as long as the losses are smaller than a given threshold, and that the measured phase is close enough to an optimal value. We provide our analytical formulae in a Python package, accessible online.

A collision of Bose-Einstein condensates is a useful source of single nonclassically correlated pairs of atoms. Here, we consider elastic scattering of atoms from elongated clouds taking into account an effective, finite duration of the collision due to the expansion of the condensates. Also, we include the quasicondensate nature of the degenerate quantum gases, due to a finite temperature of the system. We evaluate the pair correlation function measured experimentally in K. V. Kheruntsyan, et. al. Phys. Rev. Lett. 108, 260401 (2012). We show that the finite duration of the collision is an important factor determining the properties of the correlations. Our analytic calculations are in agreement with the measurements. The analytical model we provide, useful for identifying physical processes that influence the correlations, is relevant for experiments with nonclassical pairs of atoms.

We measure the population distribution in one of the atomic twin beams generated by four-wave mixing in an optical lattice. Although the produced two-mode squeezed vacuum state is pure, each individual mode is described as a statistical mixture. We confirm the prediction that the particle number follows an exponential distribution when only one spatio-temporal mode is selected. We also show that this distribution accounts well for the contrast of an atomic Hong--Ou--Mandel experiment. These experiments constitute an important validation of our twin beam source in view of a future test of a Bell inequalities., Comment: SciPost submission

We present a free-space interferometer to observe two-particle interference of a pair of atoms with entangled momenta. The source of atom pairs is a Bose--Einstein condensate subject to a dynamical instability, and the interferometer is realized using Bragg diffraction on optical lattices, in the spirit of our recent Hong--Ou--Mandel experiment. We report an observation consistent with an entangled state at the input of the interferometer. We explain how our current setup can be extended to enable a test of a Bell inequality on momentum observables.

The prose storyboard language is a formal language for describing movies shot by shot, where each shot is described with a unique sentence. The language uses a simple syntax and limited vocabulary borrowed from working practices in traditional movie-making, and is intended to be readable both by machines and humans. The language is designed to serve as a high-level user interface for intelligent cinematography and editing systems., Comment: 20 pages, extended version includes new figures and references

The celebrated Hong, Ou and Mandel (HOM) effect is one of the simplest illustrations of two-particle interference, and is unique to the quantum realm. In the original experiment, two photons arriving simultaneously in the input channels of a beam-splitter were observed to always emerge together in one of the output channels. Here, we report on the realisation of a closely analogous experiment with atoms instead of photons. This opens the prospect of testing Bell's inequalities involving mechanical observables of massive particles, such as momentum, using methods inspired by quantum optics, with an eye on theories of the quantum-to-classical transition. Our work also demonstrates a new way to produce and benchmark twin-atom pairs that may be of interest for quantum information processing and quantum simulation.

We consider a sonic analog of a black hole realized in the one-dimensional flow of a Bose-Einstein condensate. Our theoretical analysis demonstrates that one- and two-body momentum distributions accessible by present-day experimental techniques provide clear direct evidence (i) of the occurrence of a sonic horizon, (ii) of the associated acoustic Hawking radiation and (iii) of the quantum nature of the Hawking process. The signature of the quantum behavior persists even at temperatures larger than the chemical potential.

We report the experimental realization of a single-species atomic four-wave mixing process with BEC collisions for which the angular distribution of scattered atom pairs is not isotropic, despite the collisions being in the $s$-wave regime. Theoretical analysis indicates that this anomalous behavior can be explained by the anisotropic nature of the gain in the medium. There are two competing anisotropic processes: classical trajectory deflections due to the mean-field potential, and Bose enhanced scattering which bears similarity to super-radiance. We analyse the relative importance of these processes in the dynamical buildup of the anisotropic density distribution of scattered atoms, and compare to optically pumped super-radiance., Comment: 13 pages, 10 figures, added a fuller discussion of timescales, otherwise some minor changes in the text and the formatting of Figures 5-7

We have measured the 2-particle correlation function of atoms from a Bose--Einstein condensate participating in a superradiance process, which directly reflects the 2nd order coherence of the emitted light. We compare this correlation function with that of atoms undergoing stimulated emission. Whereas the stimulated process produces correlations resembling those of a coherent state, we find that superradiance, even in the presence of strong gain, shows a correlation function close to that of a thermal state, just as for ordinary spontaneous emission.

We use a one-dimensional optical lattice to modify the dispersion relation of atomic matter waves. Four-wave mixing in this situation produces atom pairs in two well defined beams. We show that these beams present a narrow momentum correlation, that their momenta are precisely tunable, and that this pair source can be operated both in the regime of low mode occupancy and of high mode occupancy.

We present a study of two di fferent sets of Micro-Channel Plates used for time and space resolved single particle detection. We investigate the eff ects of the gold coating and that of introducing an interplate voltage between the spatially separated plates. We fi nd that the gold coating increases the count rate of the detector and the pulse amplitude as previously reported for non-spatially resolved setups. The interplate voltage also increases count rates. In addition, we nd that a non-zero interplate voltage improves the spatial accuracy in determining the arrival position of incoming single particles (by 20%) while the gold coating has a negative e ect (by 30%).

We have realized an acoustic analog to the Dynamical Casimir effect. The density of a trapped Bose-Einstein condensate is modulated by changing the trap stiffness. We observe the creation of correlated excitations with equal and opposite momenta, and show that for a well defined modulation frequency, the frequency of the excitations is half that of the trap modulation frequency., Comment: Includes supplemental information

The Cauchy-Schwarz (CS) inequality -- one of the most widely used and important inequalities in mathematics -- can be formulated as an upper bound to the strength of correlations between classically fluctuating quantities. Quantum mechanical correlations can, however, exceed classical bounds.Here we realize four-wave mixing of atomic matter waves using colliding Bose-Einstein condensates, and demonstrate the violation of a multimode CS inequality for atom number correlations in opposite zones of the collision halo. The correlated atoms have large spatial separations and therefore open new opportunities for extending fundamental quantum-nonlocality tests to ensembles of massive particles., Comment: Final published version (with minor changes). 5 pages, 3 figures, plus Supplementary Material

We present an rf gas discharge apparatus which provides an atomic frequency reference for laser manipulation of metastable helium. We discuss the biasing and operation of a Colpitts oscillator in which the discharge coil is part of the oscillator circuit. Radiofrequency radiation is reduced by placing the entire oscillator in a metal enclosure., Comment: 9 pages, 5 figures

We review experimental and theoretical work on cold, trapped metastable noble gases. We em- phasize the aspects which distinguish work with these atoms from the large body of work on cold, trapped atoms in general. These aspects include detection techniques and collision processes unique to metastable atoms. We describe several experiments exploiting these unique features in fields including atom optics and statistical physics. We also discuss precision measurements on these atoms including fine structure splittings, isotope shifts, and atomic lifetimes.

We demonstrate sub-Poissonian number differences in four-wave mixing of Bose-Einstein condensates of metastable helium. The collision between two Bose-Einstein condensates produces a scattering halo populated by pairs of atoms of opposing velocities, which we divide into several symmetric zones. We show that the atom number difference for opposing zones has sub-Poissonian noise fluctuations whereas that of nonopposing zones is well described by shot noise. The atom pairs produced in a dual number state are well adapted to sub shot-noise interferometry and studies of Einstein-Podolsky-Rosen-type nonlocality tests., Comment: 4 pages, 3 figures

This paper discusses our recent work on developing the matter wave analogs to the Hanbury Brown Twiss experiment. We discuss experiments using cold atoms, both bosons and fermions, both coherent and incoherent. Simple concepts from classical and quantum optics suffice to understand most of the results, but the ideas can also be traced back to the work of Einstein on the thermodynamics of Bose gases., Comment: also available at http://pos.sissa.it/

We report the realization of a BEC of metastable helium-4 atoms (4He*) in an all optical potential. Up to 10^5 spin polarized 4He* atoms are condensed in an optical dipole trap formed from a single, focused, vertically propagating far off-resonance laser beam. The vertical trap geometry is chosen to best match the resolution characteristics of a delay-line anode micro-channel plate detector capable of registering single He* atoms. We also confirm the instability of certain spin state combinations of 4He* to two-body inelastic processes, which necessarily affects the scope of future experiments using optically trapped spin mixtures. In order to better quantify this constraint, we measure spin state resolved two-body inelastic loss rate coefficients in the optical trap.

We investigate the atom-optical analog of degenerate four-wave mixing of photons by colliding two Bose-Einstein condensates (BECs) of metastable helium and measuring the resulting momentum distribution of the scattered atoms with a time and space resolved detector. For the case of photons, phase matching conditions completely define the final state of the system, and in the case of two colliding BECs, simple analogy implies a spherical momentum distribution of scattered atoms. We find, however, that the final momenta of the scattered atoms instead lie on an ellipsoid whose radii are smaller than the initial collision momentum. Numerical and analytical calculations agree well with the measurements, and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.

We apply an analytical model for anisotropic, colliding Bose-Einstein condensates in a spontaneous four wave mixing geometry to evaluate the second order correlation function of the field of scattered atoms. Our approach uses quantized scattering modes and the equivalent of a classical, undepleted pump approximation. Results to lowest order in perturbation theory are compared with a recent experiment and with other theoretical approaches., Comment: 9 pages, 3 figures

Atom optics, a field which takes much inspiration from traditional optics, has advanced to the point that some of the fundamental experiments of quantum optics, involving photon correlations, have found atomic analogs. We discuss some recent experiments on atom bunching and anti-bunching as well as some prospects for extending them to the field of many body physics., Comment: English version of "Optique atomique quantique : apr\`es les bosons, les fermions"

We perform a theoretical analysis of atomic four-wave mixing via a collision of two Bose-Einstein condensates of metastable helium atoms, and compare the results to a recent experiment. We calculate atom-atom pair correlations within the scattering halo produced spontaneously during the collision. We also examine the expected relative number squeezing of atoms on the sphere. The analysis includes first-principles quantum simulations using the positive P-representation method. We develop a unified description of the experimental and simulation results.

Low energy elastic scattering between clouds of Bose condensed atoms leads to the well known s-wave halo with atoms emerging in all directions from the collision zone. In this paper we discuss the emergence of Hanbury Brown and Twiss coincidences between atoms scattered in nearly parallel directions. We develop a simple model that explains the observations in terms of an interference involving two pairs of atoms each associated with the elementary s wave scattering process., Comment: Minor corrections. reference updated

We study atom scattering from two colliding Bose-Einstein condensates using a position sensitive, time resolved, single atom detector. In analogy to quantum optics, the process can also be thought of as spontaneous, degenerate four wave mixing of de Broglie waves. We find a clear correlation between atoms with opposite momenta, demonstrating pair production in the scattering process. We also observe a Hanbury Brown and Twiss correlation for collinear momenta, which permits an independent measurement of the size of the pair production source and thus the size of the spatial mode. The back to back pairs occupy very nearly two oppositely directed spatial modes, a promising feature for future quantum optics experiments., Comment: A few typos have been corrected

Fifty years ago, Hanbury Brown and Twiss (HBT) discovered photon bunching in light emitted by a chaotic source, highlighting the importance of two-photon correlations and stimulating the development of modern quantum optics . The quantum interpretation of bunching relies upon the constructive interference between amplitudes involving two indistinguishable photons, and its additive character is intimately linked to the Bose nature of photons. Advances in atom cooling and detection have led to the observation and full characterisation of the atomic analogue of the HBT effect with bosonic atoms. By contrast, fermions should reveal an antibunching effect, i.e., a tendency to avoid each other. Antibunching of fermions is associated with destructive two-particle interference and is related to the Pauli principle forbidding more than one identical fermion to occupy the same quantum state. Here we report an experimental comparison of the fermion and the boson HBT effects realised in the same apparatus with two different isotopes of helium, 3He (a fermion) and 4He (a boson). Ordinary attractive or repulsive interactions between atoms are negligible, and the contrasting bunching and antibunching behaviours can be fully attributed to the different quantum statistics. Our result shows how atom-atom correlation measurements can be used not only for revealing details in the spatial density, or momentum correlations in an atomic ensemble, but also to directly observe phase effects linked to the quantum statistics in a many body system. It may thus find applications to study more exotic situations >., Comment: Nature 445, 402 (2007). V2 includes the supplementary information

We discuss experiments to produce and detect atom correlations in a degenerate or nearly degenerate gas of neutral atoms. First we treat the atomic analog of the celebrated Hanbury Brown Twiss experiment, in which atom correlations result simply from interference effects without any atom interactions.We have performed this experiment for both bosons and fermions. Next we show how atom interactions produce correlated atoms using the atomic analog of spontaneous four-wavemixing. Finally, we briefly mention experiments on a one dimensional gas on an atom chip in which correlation effects due to both interference and interactions have been observed., Comment: to appear in conference proceedings "Atomic Physics 20"

We have studied one-body and two-body correlation functions in a ballistically expanding, non-interacting atomic cloud in the presence of gravity. We find that the correlation functions are equivalent to those at thermal equilibrium in the trap with an appropriate rescaling of the coordinates. We derive simple expressions for the correlation lengths and give some physical interpretations. Finally a simple model to take into account finite detector resolution is discussed.

We have studied the atomic density of a cloud confined in an isotropic harmonic trap at the vicinity of the Bose-Einstein transition temperature. We show that, for a non-interacting gas and near this temperature, the ground-state density has the same order of magnitude as the excited states density at the centre of the trap. This holds in a range of temperatures where the ground-state population is negligible compared to the total atom number. We compare the exact calculations, available in a harmonic trap, to semi-classical approximations. We show that these latter should include the ground-state contribution to be accurate..

We have studied 2-body correlations of atoms in an expanding cloud above and below the Bose-Einstein condensation threshold. The observed correlation function for a thermal cloud shows a bunching behavior, while the correlation is flat for a coherent sample. These quantum correlations are the atomic analogue of the Hanbury Brown Twiss effect. We observe the effect in three dimensions and study its dependence on cloud size., Comment: Figure 1 available

We report an experiment measuring simultaneously the temperatureand the flux of ions produced by a cloud of triplet metastablehelium atoms at the Bose-Einstein critical temperature. The onsetof condensation is revealed by a sharp increase of the ion fluxduring evaporative cooling. Combining our measurements withprevious measurements of ionization in a pure BEC,we extract an improved value of the scattering length$a=11.3^{+2}_{-1}$ nm. The analysis includes corrections takinginto accountthe effect of atomic interactions on the criticaltemperature, and thus an independent measurement of the scatteringlength would allow a new test of these calculations.

We discuss observations of the ion flux from a cloud of trapped metastable helium atoms. Both Bose-Einstein condensates and thermal clouds were investigated. The ion flux is compared to time-of-flight observations of the expanded cloud. We show data concerning BEC formation and decay, as well as measurements of two- and three-body ionization rate constants. We also discuss possible improvements and extensions of our results., Comment: 14 pages, 9 figures, submitted to Journal of Optics B (special issue, cold quantum gases)

We have studied ionizing collisions in a BEC of He*. Measurements of the ion production rate combined with measurements of the density and number of atoms for the same sample allow us to estimate both the 2 and 3-body contributions to this rate. A comparison with the decay of the number of condensed atoms in our magnetic trap, in the presence of an rf-shield, indicates that ionizing collisions are largely or wholly responsible for the loss. Quantum depletion makes a substantial correction to the 3-body rate constant., Comment: 4 pages, 3 figures

We describe our recent realization of BEC using metastable helium. All detection is done with a micruchannel plate which detects the metastables or ions coming from the trapped atom cloud. This discussion emphasizes some of the diagnostic experiments which were necessary to quantitatively analyse our results., Comment: 5 pages, 3 figures