Experimental Evidence for the Breakdown of a Hartree-Fock Approach in a Weakly Interacting Bose Gas

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.

Figure 1

In situ longitudinal distributions for different temperatures (circles). Long dashed lines: ideal Bose gas profile at the shown temperature $T$ and chemical potential ${\mu }_0$ obtained from a fit to the wings. Solid lines: profiles obtained in the Hartree-Fock approximation for the same $T$ and ${\mu }_0$. Short dashed lines: quasicondensate profiles with the same peak density as the experimental data. Horizontal solid lines: crossover density estimated using a Bogoliubov calculation (see text).

Figure 2

Chemical potential ${\mu }_0$, obtained by fitting the wings of profile (b) to an ideal Bose gas distribution, as a function of the number of excluded pixels $N_{\mathrm{ex}}$ on either side of the distribution, for four different trial temperatures. The arrow indicates ${\mu }_{\mathrm{qc}}=\hslash {\omega }_{\perp }\sqrt{1+4n_{0}a}$, which is the chemical potential found from the measured peak linear density $n_0$.

Figure 3

Ratio between the effective chemical potential and $\Delta E$, the energy splitting between the ground state and the first excited state as a function of the chemical potential for the temperature of profile (b). The dashed lines correspond to the measured chemical potential.