Momentum-Space Correlations of a One-Dimensional Bose Gas

Analyzing the noise in the momentum profiles of single realizations of one-dimensional Bose gases, we present the experimental measurement of the full momentum-space density correlations $⟨\delta n_p\delta n_{p^{\prime }}⟩$, which are related to the two-body momentum correlation function. Our data span the weakly interacting region of the phase diagram, going from the ideal Bose gas regime to the quasicondensate regime. We show experimentally that the bunching phenomenon, which manifests itself as super-Poissonian local fluctuations in momentum space, is present in all regimes. The quasicondensate regime is, however, characterized by the presence of negative correlations between different momenta, in contrast to the Bogolyubov theory for Bose condensates, predicting positive correlations between opposite momenta. Our data are in good agreement with ab initio calculations.

Figure 1

Momentum correlations $⟨\delta N_{\alpha }\delta N_{\beta }⟩$ for a gas in the IBG regime (data A, left column), in the QBEC regime (data C, right column), and in the QBEC-IBG crossover (data B, middle column). The pixel size is $\mathrm{\Delta }/\hslash =0.15\mu {\mathrm{m}}^{-1}$. The experimental data are shown in the top row. Data A, B, and C are compared with the IBG theory, QMC calculations, and QBEC theory, respectively, at the temperature of the data determined by independent thermometry methods [25]. The middle row gives the computed momentum correlations. The bottom row shows the diagonal cuts: the experimental data in circles for $\alpha =\beta$ (squares for $\alpha =-\beta$ for data B and C only) are compared with their respective theory model in dashed (dotted) lines. The error bars are statistical. The dash-dotted lines give the shot-noise limit.

Figure 2

$Ct{\gamma }_0^2$ versus ${\gamma }_0$, the interaction parameter at the center of the cloud. The theoretical predictions in the limit $\hslash /l_{\varphi }\gg \delta \gg \mathrm{\Delta }$ [25] are plotted for highly degenerate IBG (dashed line), QBEC (dotted line), and IBG (solid line, computed at $t=1000$). Circles are experimental results for data A–C (corresponding to $t=1170$, 1760, 920). The error bars account for both fitting (in $t$) and statistics (in $C$ and ${\gamma }_0$).