Third-order spatial correlations for ultracold atoms

Abstract

We present here the first measurement of the third-order spatial correlation function for atoms, made possible by cooling a metastable helium cloud to create an ultracold thermal ensemble just above the Bose-Einstein condensation point. The resulting large correlation length well exceeds the spatial resolution limit of the single-atom detection system, and enables extension of our earlier temporal measurements to evaluate the third-order correlation function in the spatial plane of the detector. The enhancement of the spatial third-order correlation function above a value of unity demonstrates the presence of spatial three-atom bunching, as expected for an incoherent source. Contents

A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas

“…We now focus in more detail on local correlation functions. We note that the local second-order coherence has recently been proposed as a measure of quantum criticality in the 1D boson system [102], while the local third-order correlations have received increasing attention both in theory [103] and experiment [47,[104][105][106]. The local fourth-order correlations for the Lieb-Liniger model have also been investigated [107].…”

Third-order momentum correlation interferometry maps for entangled quantal states of three singly trapped massive ultracold fermions

“…To put this development in context, we note here recent progress in the experimental processing of data and control and manipulation of ultracold atoms in colliding free-space beams or clouds (including free fall under the cloud's gravity) [10,11,23,25,[31][32][33] or in optical traps and tweezers (in situ or TOF) [34][35][36][37], which has motivated a growing number of both experimental [10,11,23,[31][32][33][34][35][36][37] and theoretical [12-15, 38, 39] studies concerning the analogies between quantum optics and matter-wave spectroscopy.…”

Observation of Transverse Bose-Einstein Condensation via Hanbury Brown–Twiss Correlations

“…The peak amplitude for the coldest cloud (c) is in good agreement with the maximum value of 2! [24] expected for the second-order correlation function for a thermal gas, while as the temperature increases and the correlation length shortens in (b) and (a), the finite bin sizes used in our data analysis result in a reduction of the peak bunching amplitude [11][12][13][14][15]. Note that differences between the peak bunching amplitude observed transversely and longitudinally can result from different bin choices in those axes.…”