Probing many-body states of ultracold atoms via noise correlations

We propose to utilize density-density correlations in the image of an expanding gas cloud to probe complex many-body states of trapped ultracold atoms. In particular, we show how this technique can be used to detect superfluidity of fermionic gases and to study spin correlations of multicomponent atoms in optical lattices. The feasibility of the method is investigated by analysis of the relevant signal to noise ratio including experimental imperfections.

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Figure 1

Fermionic superfluid. (a) Angle integrated weight of the correlation peak at diametrically opposite points. Solid line is the column integrated result relevant to experiment. (b) Weight of the correlation peak for $d_{x^2-y^2}$ pairing, which may be expected in a realization of the Hubbard model on an optical lattice. (c) and (d) depict $⟨\Delta n{(\mathbf{r},{\mathbf{r}}^{\prime })}^2⟩$ at $T>0$ (superfluid fraction 0.7). $\mathbf{r}$ is fixed on the Fermi surface. In (c) ${\mathbf{r}}^{\prime }$ is varied along the same diameter while in (d) ${\mathbf{r}}^{\prime }$ it is varied around the Fermi surface so that the relative angle between $\mathbf{r}$ and ${\mathbf{r}}^{\prime }$ is $\theta$. Dashed line corresponds to BEC of tightly bound pairs, whereas the solid line is the BCS limit at the same temperature. The width of the narrow dip $\sim \hslash t∕\left(mL\right)$ is limited by the system’s size.

Figure 2

(a) Normalized density correlations, in the Mott state for a chain of 2, 4, and 40 sites. (b) Density correlations for an antiferromagnetic Mott chain of two-component bosons. The weak singularities (broad peaks) reflect power-law correlations in the one-dimensional system.