Local Observation of Antibunching in a Trapped Fermi Gas

Local density fluctuations and density profiles of a Fermi gas are measured in situ and analyzed. In the quantum degenerate regime, the weakly interacting ${}^6\mathrm{Li}$ gas shows a suppression of the density fluctuations compared to the nondegenerate case, where atomic shot noise is observed. This manifestation of antibunching is a direct result of the Pauli principle and constitutes a local probe of quantum degeneracy. We analyze our data using the predictions of the fluctuation-dissipation theorem and the local density approximation, demonstrating a fluctuation-based temperature measurement.

Figure 1

(a) Setup for high-resolution imaging of the trapped ${}^6\mathrm{Li}$ gas. The shadow cast by the atoms held in the dipole trap is imaged through the microscope objective and a telephoto objective onto an EMCCD chip. The resolution ($1/e^2$ radius) is $1.8\mu \mathrm{m}$ [30] at a wavelength of 671 nm and the magnification is 54. (b) Density distribution (atoms per pixel) of the trapped atoms obtained by averaging over 20 realizations. The effective pixel size measures $1.2\mu \mathrm{m}$ [20], the maximum optical density is $\sim 2$. The images which we evaluate are $\sim 40\mu \mathrm{m}$ wide showing the center of the cloud, which has a total length of $500\mu \mathrm{m}$.

Figure 2

Observed variance versus mean of the atom number detected on a pixel. Red squares show the data for a nondegenerate and blue circles for a quantum degenerate gas. The solid red line is a linear fit to the nondegenerate gas, yielding a slope of $0.20\pm 0.02$. For the data shown, 80 experiments were performed, 60 for the degenerate case and 20 for the nondegenerate case. About 30% of the experiments were excluded. The error bars shown are estimated from the subtraction of photon shot noise which is the dominant contribution.

Figure 3

Spatially resolved measurement of antibunching. The black line shows the mean atom number and the blue circles the corresponding variance along the $x_1$ axis for a degenerate gas. The variance is rescaled using the slope fitted in Fig. 2. Error bars are estimated from the subtraction of photon shot noise, which is the dominant contribution. The dashed line shows the variance derived from theory. The shaded region indicates the uncertainty originating from uncertainties in the trap parameters. The inset shows corresponding data for a nondegenerate gas.

Figure 4

Fluctuation-based temperature measurement. Variance of atom number detected on an effective pixel versus dimensionless compressibility. The blue circles and red squares show the data for the quantum degenerate and the nondegenerate case, respectively. The dashed red line is fitted to the red squares, giving the temperature according to (4).