Observation of a Fragmented, Strongly Interacting Fermi Gas

We study the emergence of a fragmented state in a strongly interacting Fermi gas subject to a tunable disorder. We investigate its properties using a combination of high-resolution in situ imaging and conductance measurements. The fragmented state exhibits saturated density modulations, a strongly reduced density percolation threshold, lower than the average density, and a resistance equal to that of a noninteracting Fermi gas in the same potential landscape. The transport measurements further indicate that this state is connected to the superfluid state as disorder is reduced. We propose that the fragmented state consists of unpercolated islands of bound pairs, whose binding energy is enhanced by the disorder.

Figure 1

Evolution of the column density $n$ (in units of ${\sigma }^{-2}$) as the disorder strength is increased. (a)–(e) High-resolution images of size $21\mu \mathrm{m}\times 72\mu \mathrm{m}$ of the in situ density distribution in the channel for increasing $\overline{V}/\mu$. The saturated column density on top and bottom marks the beginning of the reservoirs, which extend far beyond the field of view. The systematic uncertainty in $\overline{V}/\mu$ is estimated to be 25%. (f) Image of the projected speckle pattern. The density ripples, gradually appearing from (a) to (e) can be matched one to one to bright (potential hills) and dark spots (potential valleys) in the image. (g) Local column density as a function of disorder strength for three specific points indicated in the potential landscape of (f) (point $A$, red; point $B$, blue; point $C$, cyan), each computed within a region of size $1.2\mu \mathrm{m}\times 1.2\mu \mathrm{m}$ marked as red squares in (c). The gray data points are the mean column density in the channel, computed in a central region of size $18\mu \mathrm{m}\times 7\mu \mathrm{m}$. (h) Variance of the density computed in the same central region. The dashed line represents the theoretical percolation threshold for the potential seen by pointlike pairs.

Figure 2

Percolation properties of the density distribution. (a) Shortest connecting path between the two ends of the reservoirs (indicated by the red dashed lines) for $\overline{V}/\mu =1.39$ and a density level of $\tilde{n}=0.6/{\sigma }^2$ close to the percolation threshold. The path displays strong deviations from a straight line and has a length of $1.5L$. (b) Shortest path length as a function of density level $\tilde{n}$ (in units of ${\sigma }^{-2}$), for $\overline{V}/\mu =0.12,0.58,1.39,2.78$ in blue, cyan, green, red, respectively. (c) Percolation threshold as a function of disorder strength. The solid line is a linear fit to the first 9 points. (d) Percolation threshold normalized to the average density as a function of disorder strength. Error bars represent the statistical error in the measurement of $n$. (e) Map of the relative path length as a function of $\tilde{n}$ and $\overline{V}/\mu$. The dashed lines in (c) and (e) represent the theoretical percolation threshold of the potential seen by pointlike pairs of atoms.

Figure 3

Resistance of the thin film. (a) Dimensionless resistance as a function of disorder strength for the strongly interacting Fermi gas (blue squares) and for a weakly interacting Fermi gas (gray circles) for comparison. (b) Ratio of absolute resistances of the strongly and weakly interacting Fermi gas. The dash-dotted horizontal red line emphasizes that the ratio is close to 1 in the strongly disordered regime. The dashed vertical black line indicates the theoretical percolation threshold for the potential seen by tightly bound, pointlike pairs.