Atom Interferometry with Trapped Fermi Gases

We realize an interferometer with an atomic Fermi gas trapped in an optical lattice under the influence of gravity. The single-particle interference between the eigenstates of the lattice results in macroscopic Bloch oscillations of the sample. The absence of interactions between fermions allows a time-resolved study of many periods of the oscillations, leading to a sensitive determination of the acceleration of gravity. The experiment proves the superiority of noninteracting fermions with respect to bosons for precision interferometry and offers a way for the measurement of forces with microscopic spatial resolution.

Figure 1

Momentum distribution of a coherent superposition of Wannier-Stark states. Although the single state fills completely the first Brillouin zone (thin line), the interference of several states gives narrow momentum peaks. Shown are the cases of a phase difference between successive states of $\Delta \varphi =0$ (continuous line) and $\Delta \varphi =\pi$ (dashed line). The inset shows the square of Wannier-Stark wave functions calculated for ${}^{40}\mathrm{K}$ atoms in a lattice with $U=2E_R$ subjected to gravity (for clarity, the states shown are separated by four lattice sites).

Figure 2

Evolution of the interference pattern of the Fermi gas for increasing holding times in the vertical lattice. The spatial distribution of the cloud detected after 8 ms of free expansion reflects the momentum distribution in the trap at the time of release.

Figure 3

Bloch oscillation of the Fermi gas driven by gravity: the peak of the momentum distribution of the sample scans periodically the first Brillouin zone of the lattice. More than 100 oscillations can be followed with large contrast.

Figure 4

(a) Momentum distribution of fermions at two different holding times in the lattice: 1 ms (continuous line) and 252 ms (dashed line). (b) Momentum distribution of bosons at 0.6 ms (continuous line) and 3.8 ms (dashed line). The much faster broadening for bosons is due to the presence of interactions.