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arXiv:1007.3713 · Physical Review Letters

Probing Three-Body Correlations in a Quantum Gas Using the Measurement of the Third Moment of Density Fluctuations

Julien Armijo, T. Jacqmin, Karen V. Kheruntsyan, Isabelle Bouchoule

Published Nov 30, 2010• 125 citations
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Abstract

We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasicondensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state, and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three-body correlations in the system.

DOI
10.1103/physrevlett.105.230402

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We perform measurements of the third moment of atom number fluctuations in small slices of a very elongated weakly interacting degenerate Bose gas. We find a positive skewness of the atom number distribution in the ideal gas regime and a reduced skewness compatible with zero in the quasicondensate regime. For our parameters, the third moment is a thermodynamic quantity whose measurement constitutes a sensitive test of the equation of state, and our results are in agreement with a modified Yang-Yang thermodynamic prediction. Moreover, we show that the measured skewness reveals the presence of true three-body correlations in the system.
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By measuring the density fluctuations in a highly elongated weakly interacting Bose gas, we observe and quantify the transition from the ideal gas to a quasicondensate regime throughout the dimensional crossover from a purely one-dimensional (1D) to an almost three-dimensional (3D) gas. We show that that the entire transition region and the dimensional crossover are described surprisingly well by the modified Yang-Yang model. Furthermore, we find that at low temperatures the linear density at the quasicondensate transition scales according to an interaction-driven scenario of a longitudinally uniform 1D Bose gas, whereas at high temperatures it scales according to the degeneracy-driven critical scenario of transverse condensation of a 3D ideal gas.
We study, within the framework of the classical-field approximation, the density correlations of a weakly interacting expanding Bose gas for the whole range of temperatures across the Bose-Einstein condensation threshold. We focus on elongated quasi-one-dimensional systems where there is a huge discrepancy between the existing theory and experimental results [A. Perrin et al., Nat. Phys. 8, 195 (2012)]. We find that the density correlation function is not reduced for temperatures below the critical one as it is predicted for the ideal gas or for a weakly interacting system within the Bogoliubov approximation. This behavior of the density correlations agrees with the above-mentioned experiment with the elongated system. Although the system was much larger than that studied here, we believe that the behavior of the density correlation function found there is quite generic. Our theoretical study indicates also large density fluctuations in the trap in the quasicondensate regime where only phase fluctuations were expected. We argue that the enhanced density fluctuations can originate in the presence of interactions in the system, or more precisely in the presence of spontaneous dark solitons in the elongated gas at thermal equilibrium.
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.
We study the equilibrium correlations of a Bose gas in an elongated three-dimensional harmonic trap using a grand-canonical classical-field method. We focus in particular on the progressive transformation of the gas from the normal phase, through a phase-fluctuating quasicondensate regime to the so-called true-condensate regime, with decreasing temperature. Choosing realistic experimental parameters, we quantify the density fluctuations and phase coherence of the atomic field as functions of the system temperature. We identify the onset of Bose condensation through analysis of both the generalized Binder cumulant appropriate to the inhomogeneous system, and the suppression of the effective many-body TTT matrix that characterizes interactions between condensate atoms in the finite-temperature field. We find that the system undergoes a second-order transition to condensation near the critical temperature for an ideal Bose gas in the strongly anisotropic three-dimensional geometry but remains in a strongly phase-fluctuating quasicondensate regime until significantly lower temperatures. We characterize the crossover from a quasicondensate to a true condensate by a qualitative change in the form of the nonlocal first-order coherence function of the field and compare our results to those of previous works employing a density-phase Bogoliubov--de Gennes analysis.
Number fluctuations in a one-dimensional Bose gas consist of contributions from grainy fluctuations of localized domains (the density grains). We have derived a set of extended integral equations from the Yang–Yang solution for finite temperature that exactly determine all higher-order moments of number fluctuations. These moments are closely related to the statistics of the localized (but not zero-range) density grains. We directly calculate the mean occupation of these fluctuations, and the variance, skewness, and kurtosis of their distribution across the whole parameter space of the gas. Findings include: large mesoscopic density grains with a fat-tailed distribution in the thermal quasicondensate of the dilute gas and in the nonperturbative quantum turbulent regime; regions of negative skewness and below-Gaussian kurtosis in a part of the fermionized gas, and an unexplained crossover region along T ∼ T d / γ ; the existence of a peak in the density–density correlation function at finite interparticle spacing. We relate these density grain statistics to measurable behavior such as the statistics of coarse imaging bins, and finite-size scaling of number fluctuations. We propose how to experimentally test the relationship between thermodynamically independent density grains and density concentrations visible in single-shot images.