Transport of a Bose Gas in 1D Disordered Lattices at the Fluid-Insulator Transition

We investigate the momentum-dependent transport of 1D quasicondensates in quasiperiodic optical lattices. We observe a sharp crossover from a weakly dissipative regime to a strongly unstable one at a disorder-dependent critical momentum. In the limit of nondisordered lattices the observations suggest a contribution of quantum phase slips to the dissipation. We identify a set of critical disorder and interaction strengths for which such critical momentum vanishes, separating a fluid regime from an insulating one. We relate our observation to the predicted zero-temperature superfluid-Bose glass transition.

Figure 1

Transport in nondisordered lattices. (a) Time evolution of the peak momentum for $U=1.26J$ and $n=3.6$. The experimental data (dots) are fitted at short times with a damped oscillation with $\gamma /2\pi =135(10)\mathrm{Hz}$ (continuous line) and at later times with ${\gamma }^{\prime }/2\pi =600(50)\mathrm{Hz}$ (dashed line). The dash-dotted line is the expected oscillation in the absence of damping. (b) The difference between the fit to the initial damped motion and the experimental data (dots) is fitted (continuous line) to estimate the critical momentum. The inset shows $\rho (p)$ at three different times: $t=0$, $t=0.8\mathrm{ms}$, $t=3.5\mathrm{ms}$, from top to bottom. The error bars represent the squared sum of statistical and systematic uncertainties.

Figure 2

Critical momentum for nondisordered lattices (dots) versus the interaction energy. The continuous line is a linear fit, the arrow marks the critical $U/J$ for the superfluid-Mott insulator transition for $n=2$, and the dashed line is the estimated $p_c$ from the quantum phase-slips model. Inset: Initial damping rate $\gamma$.

Figure 3

Transport in disordered lattices. Time evolution of the peak momentum for $U=1.26J$ for $\Delta /J=0$ (dots), $\Delta /J=3.6$ (triangles), and $\Delta /J=10$ (squares). The lines are fits of the semiclassical motion to the initial oscillation. The fitted damping rates are $\gamma /2\pi =130(10)\mathrm{Hz}$, $\gamma /2\pi =250(30)\mathrm{Hz}$, and $\gamma /2\pi =1.1(6)\mathrm{kH}z$, respectively.

Figure 4

Critical momentum $p_c$ (full circles) and initial rms momentum width $\delta p$ (open circles) for a fixed interaction energy ($U/J=1.26$) and increasing disorder strength. A linear fit (continuous line) is used to estimate ${\Delta }_c$, while the dashed line is a sigmoidal fit of $\delta p$.

Figure 5

Critical disorder to enter the insulating phase versus interaction energy. The experimental data from the critical momentum (dots) are fitted with the model described in the text (line). The uncertainty is dominated by a 20% error on the calibration of $\Delta$ [34].