Superfluidity with disorder in a thin film of quantum gas

We investigate the properties of a strongly interacting superfluid gas of ${}^6\mathrm{Li}_2$ Feshbach molecules forming a thin film confined in a quasi-two-dimensional channel with a tunable random potential, creating a microscopic disorder. We measure the atomic current, extract the resistance of the film in a two-terminal configuration, and identify a superfluid state at low disorder strength, which evolves into a normal poorly conducting state for strong disorder. The transition takes place when the chemical potential reaches the percolation threshold of the disorder. The evolution of the conduction properties contrasts with the smooth behavior of the density and compressibility across the transition, measured in situ at equilibrium. These features suggest the emergence of a glasslike phase at strong disorder.

Figure 1

Sketch of the experimental configuration. (a) Top view. (b) Side view. Two ${}^6\mathrm{Li}_2$ Feshbach molecule reservoirs (gray regions) are connected by a narrow quasi-2D channel, created by a laser beam (regions in blue) at 532 nm with a $1/e^2$ waist of $30\mu \mathrm{m}$ along $y$, having a nodal line at the center. When a number imbalance between the reservoirs is present, a molecule current sets in through the channel. A speckle pattern (green curve and grains) of variable intensity is projected onto the channel along the $z$ axis through a microscope objective (not shown).

Figure 2

Conduction properties of the disordered gas of molecules (red squares) and of a weakly interacting Fermi gas (gray dots) as a function of disorder strength normalized by $\mu =400\mathrm{nK}$, the chemical potential of the molecular gas in the channel without disorder. (a) Initial current for a fixed driving (see the text). (b) Dimensionless resistance. The dotted green line represents the classical percolation threshold of the speckle pattern. The dash-dotted line indicates the correlation energy $E_{\sigma }$. Note that the first two points of the BEC data in (a) have no resistance counterpart in (b) (see the text). The error bars are statistical.

Figure 3

$B$ parameter (see the text) as a function of disorder strength. The dotted green line represents the percolation threshold of the speckle potential and coincides with the change of behavior from superfluid to single-particle transport. The dash-dotted line shows the correlation energy $E_{\sigma }$. The error bars represent statistical errors.

Figure 4

Equilibrium properties of the disordered gas as a function of disorder strength. The dotted green line indicates the percolation threshold. The solid black line indicates the prediction of the Thomas-Fermi approximation. (a) Average density at the center of the channel. The dashed line indicates the expected decrease of density from the compressibility measurement without speckle (see the text). (b) Reduced compressibility (see the text) estimated from the shape of the cloud. (c), (d) Density profiles in the channel (open circles) and quadratic fit to the central part (solid line) used to extract the compressibility, for $\overline{V}/\mu =0$ and 1.6.