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This corrects the article DOI: 10.1103/PhysRevLett.117.235303.
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Two-particle interference is a fundamental feature of quantum mechanics, and is even less intuitive than wave-particle duality for a single particle. In this duality, classical concepts--wave or particle--are still referred to, and interference happens in ordinary space-time. On the other hand, two-particle interference takes place in a mathematical space that has no classical counterpart. Entanglement lies at the heart of this interference, as it does in the fundamental tests of quantum mechanics involving the violation of Bell's inequalities. The Hong, Ou and Mandel experiment is a conceptually simpler situation, in which the interference between two-photon amplitudes also leads to behaviour impossible to describe using a simple classical model. Here we report the realization of the Hong, Ou and Mandel experiment using atoms instead of photons. We create a source that emits pairs of atoms, and cause one atom of each pair to enter one of the two input channels of a beam-splitter, and the other atom to enter the other input channel. When the atoms are spatially overlapped so that the two inputs are indistinguishable, the atoms always emerge together in one of the output channels. This result opens the way to testing Bell's inequalities involving mechanical observables of massive particles, such as momentum, using methods inspired by quantum optics, and to testing theories of the quantum-to-classical transition. Our work also demonstrates a new way to benchmark non-classical atom sources that may be of interest for quantum information processing and quantum simulation.
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We report on the single-atom-resolved measurement of the distribution of momenta âk in a weakly interacting Bose gas after a 330 ms time of flight. We investigate it for various temperatures and clearly separate two contributions to the depletion of the condensate by their k dependence. The first one is the thermal depletion. The second contribution falls off as k^{-4}, and its magnitude increases with the in-trap condensate density as predicted by the Bogoliubov theory at zero temperature. These observations suggest associating it with the quantum depletion. How this contribution can survive the expansion of the released interacting condensate is an intriguing open question.
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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.
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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 on 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 characterization of the atomic analogue of the HBT effect with bosonic atoms. By contrast, fermions should reveal an antibunching effect (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 fermionic and bosonic HBT effects in the same apparatus, using two different isotopes of helium: (3)He (a fermion) and 4He (a boson). Ordinary attractive or repulsive interactions between atoms are negligible; therefore, the contrasting bunching and antibunching behaviour that we observe can be fully attributed to the different quantum statistics of each atomic species. Our results show how atom-atom correlation measurements can be used to reveal details in the spatial density or momentum correlations in an atomic ensemble. They also enable the direct observation of phase effects linked to the quantum statistics of a many-body system, which may facilitate the study of more exotic situations.
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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.
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We have modulated the density of a trapped Bose-Einstein condensate by changing the trap stiffness, thereby modulating the speed of sound. 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.
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We investigate the atom-optical analog of degenerate four-wave mixing by colliding two Bose-Einstein condensates of metastable helium. The momentum distribution of the scattered atoms is measured in three dimensions. A simple analogy with photon phase matching conditions suggests a spherical final distribution. We find, however, that it is an ellipsoid with radii smaller than the initial collision momenta. Numerical and analytical calculations agree with this and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.
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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.
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We report the realization of a Bose-Einstein condensate of metastable atoms (helium in the lowest triplet state). The excitation energy of each atom with respect to the ground state is 20 electron volts, but inelastic processes that would destroy the sample are suppressed strongly enough in a spin-polarized sample to allow condensation. Our detection scheme takes advantage of the metastability to achieve detection of individual atoms as well as of the decay products of inelastic processes. This detection opens the way toward new studies in mesoscopic quantum statistical physics, as well as in atomic quantum optics.
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We report on the development of a novel FPGA-based time-to-digital converter and its implementation in a detection chain that records the coordinates of single particles along three dimensions. The detector is composed of micro-channel plates mounted on top of a cross delay line and connected to fast electronics. We demonstrate continuous recording of the timing signals from the cross delay line at rates up to 4.1 × 10(6) s(-1) and three-dimensional reconstruction of the coordinates up to 3.2 × 10(6) particles per second. From the imaging of a calibrated structure we measure the in-plane resolution of the detector to be 140(20) µm at a flux of 3 × 10(5) particles per second. In addition, we analyze a method to estimate the resolution without placing any structure under vacuum, a significant practical improvement. While we use UV photons here, the results of this work apply to the detection of other kinds of particles.
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We present a study of two different sets of Micro-Channel Plates used for time and space resolved single particle detection. We investigate the effects of the gold coating and that of introducing an interplate voltage between the spatially separated plates. We find 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 find 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 effect (by ~30%).
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We present a 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.
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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-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.
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We present a method to suppress the roughness of the potential of a wire-based, magnetic atom guide: modulating the wire current at a few tens of kHz, the potential roughness, which is proportional to the wire current, averages to zero. Using ultracold 87Rb clouds, we show experimentally that modulation reduces the roughness by at least a factor five without measurable heating or atom loss. This roughness suppression results in a dramatic reduction of the damping of center-of-mass oscillations.
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We investigate the physics underlying the presence of a quasicondensate in a nearly one dimensional, weakly interacting trapped atomic Bose gas. We show that a Hartree-Fock (mean-field) approach fails to predict the existence of the quasicondensate in the center of the cloud: the quasicondensate is generated by interaction-induced correlations between atoms and not by a saturation of the excited states. Numerical calculations based on Bogoliubov theory give an estimate of the crossover density in agreement with experimental results.
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We report in situ measurements of density fluctuations in a quasi-one-dimensional 87Rb Bose gas at thermal equilibrium in an elongated harmonic trap. We observe an excess of fluctuations compared to the shot-noise level expected for uncorrelated atoms. At low atomic density, the measured excess is in good agreement with the expected "bunching" for an ideal Bose gas. At high density, the measured fluctuations are strongly reduced compared to the ideal gas case. We attribute this reduction to repulsive interatomic interactions. The data are compared with a calculation for an interacting Bose gas in the quasicondensate regime.
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We have studied two-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, whereas the correlation is flat for a coherent sample. These quantum correlations are the atomic analog of the Hanbury Brown Twiss effect. We observed the effect in three dimensions and studied its dependence on cloud size.
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We have studied ionizing collisions in a BEC of metastable 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 two- and three-body contributions to this rate. A comparison with the decay of the atom number indicates that ionizing collisions are largely or wholly responsible for the loss. Quantum depletion makes a substantial correction to the three-body rate constant.
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We present a high resolution study of the specularity of the atomic reflection from an evanescent wave mirror using velocity selective Raman transitions. We observed a double structure in the velocity distribution after reflection: a peak consistent with specular reflection and a diffuse reflection pedestal whose contribution decreases rapidly with increasing detuning. The diffuse reflection is due to two distinct effects: spontaneous emission in the evanescent wave and roughness in the evanescent wave potential whose amplitude is smaller than the de Broglie wavelength of the reflected atoms.