Thermal counting statistics in an atomic two-mode squeezed vacuum state

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 submissio

Hanbury Brown Twiss effect for ultracold quantum gases

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 availabl

Pair correlations of scattered atoms from two colliding Bose-Einstein Condensates: Perturbative Approach

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 figure

Getting the elastic scattering length by observing inelastic collisions in ultracold metastable helium atoms

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

Observation of atom pairs in spontaneous four wave mixing of two colliding Bose-Einstein Condensates

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 correcte

Violation of the Cauchy-Schwarz inequality with matter waves

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 Materia

Theory for a Hanbury Brown Twiss experiment with a ballistically expanding cloud of cold atoms

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

Theory of an optical dipole trap for cold atoms

The theory of an atom dipole trap composed of a focused, far red-detuned, trapping laser beam, and a pair of red-detuned, counterpropagating, cooling beams is developed for the simplest realistic multilevel dipole interaction scheme based on a model of a (3+5)-level atom. The description of atomic motion in the trap is based on the quantum kinetic equations for the atomic density matrix and the reduced quasiclassical kinetic equation for atomic distribution function. It is shown that when the detuning of the trapping field is much larger than the detuning of the cooling field, and with low saturation, the one-photon absorption (emission) processes responsible for the trapping potential can be well separated from the two-photon processes responsible for sub-Doppler cooling atoms in the trap. Two conditions are derived that are necessary and sufficient for stable atomic trapping. The conditions show that stable atomic trapping in the optical dipole trap can be achieved when the trapping field has no effect on the two-photon cooling process and when the cooling field does not change the structure of the trapping potential but changes only the numerical value of the trapping potential well. It is concluded that the separation of the trapping and cooling processes in a pure optical dipole trap allows one to cool trapped atoms down to a minimum temperature close to the recoil temperature, keeping simultaneously a deep potential well

Mixing of magmatic-hydrothermal and metamorphic fluids and the origin of peribatholitic Sn vein-type deposits in Rwanda

The fluid sources of granite-related Sn-quartz vein deposits are commonly obscured by fluid mixing or fluid-rock interactions. As a result, fluid inclusions, minerals and isotopes in these veins indicate an intermediate composition between magmatic and metamorphic, but the degree of mixing between these endmembers is currently unquantified. This study presents a novel quantitative approach to assess the degree of mixing between magmatic-hydrothermal and external metamorphic fluids in the formation of peribatholitic Sn-quartz veins. In particular, fluid mixing in the Sn-mineralized Rwamagana-Musha-Ntunga pegmatite-quartz vein field in East Rwanda has been evaluated by the following four methods: quartz stable isotopes, muscovite geochemistry, fluid inclusion microthermometry and LA-ICP-MS, and geochemical modelling. The quartz stable isotope data (δ18O: +13.1 to +15.8 ‰ V-SMOW; δD: −27.6 to –59.7 ‰ V-SMOW) cannot uniquely differentiate between a metamorphic fluid origin or an initial magmatic hydrothermal fluid origin with subsequent metamorphic fluid mixing or host-rock interaction. However, granitophile element concentrations in magmatic muscovite from pegmatites and hydrothermal muscovite from associated Sn-quartz veins are equally high, indicating a close genetic link (Rb: 530 – 8740 ppm, Li: 110 – 1990 ppm, Sn: 87 – 810 ppm, Cs: 62 – 420 ppm). Primary H2O-CO2-N2-NaCl medium saline magmatic fluid inclusions in quartz of pegmatites (∼12.7 wt% NaCleq) and H2O-CO2-(N2)-NaCl low saline fluid inclusions in barren metamorphic quartz veins (∼4.9 wt% NaCleq) were analyzed by LA-ICP-MS. These results show an enrichment in Li, Rb, Sn and Cs for the magmatic fluid, while the metamorphic fluid is characterized by low granitophile element concentrations and high Sr and Ba contents. The expected Rb-Cs and Rb-Sn signature of the Sn-quartz vein muscovite was modelled using the measured fluid endmember compositions, confirming mixing between magmatic and metamorphic fluids in the formation of the veins. The quantification suggests that the hydrothermal Sn-quartz vein fluid contains 5 – 80 % of an external metamorphic fluid component