Self-Trapping in an Array of Coupled 1D Bose Gases

We study the transverse expansion of arrays of ultracold ${}^{87}\mathrm{Rb}$ atoms weakly confined in tubes created by a 2D optical lattice and observe that transverse expansion is delayed because of mutual atom interactions. A mean-field model of a coupled array shows that atoms become localized within a roughly square fortlike self-trapping barrier with time-evolving edges. But the observed dynamics are poorly described by the mean-field model. The theoretical introduction of random phase fluctuations among tubes improves the agreement with experiment but does not correctly predict the density at which the atoms start to expand with larger lattice depths. Our results suggest a new type of self-trapping, where quantum correlations suppress tunneling even when there are no density gradients.

Figure 1

(a) Experimental setup (not to scale): Atom clouds are confined in a crossed-dipole trap and partitioned by a blue-detuned optical lattice into a coupled array of vertical tubes. (b) Peak transversely integrated axial density as a function of time for $V_0=13E_R$. The linear density drops rapidly with time as the atoms expand axially, mostly driven initially by their mutual interaction energy.

Figure 2

Transverse rms widths of the directly measured density-squared distributions as a function of time for (a) $V_0=7.25E_R$, (b) $9.25E_R$, (c) $11E_R$, and (d) $13E_R$. Each data point is the average of 10 measurements. The error bars represent our random uncertainty and are the quadrature sum of the statistical noise and the uncertainty from the density dependence of the absorption beam lensing. There is an overall systematic uncertainty of $0.5\mu \mathrm{m}$ associated with the imaging resolution; comparable shifts of the initial size simply shift the theoretical curves at early times (below 10 ms), followed by a gradual divergence of the curves at longer times. The dashed blue line is the result of a mean-field calculation of the dynamics with no random phase between the tubes ($\eta =0$). The dotted purple line is for $\eta =0.2$, the dash-dotted green lines are for (a) $\eta =0.4$ and (b) $\eta =0.5$, and the solid orange line is for $\eta =1$. The horizontal red line is the mean of the $t<t_c$ data.

Figure 3

Transverse density distributions 12.4 ms after release for $V_0=13E_R$. (a) $\eta =0$; (b) $\eta =1$.