Quantum-Gas Microscope for Fermionic Atoms

We realize a quantum-gas microscope for fermionic ${}^{40}\mathrm{K}$ atoms trapped in an optical lattice, which allows one to probe strongly correlated fermions at the single-atom level. We combine 3D Raman sideband cooling with high-resolution optics to simultaneously cool and image individual atoms with single-lattice-site resolution at a detection fidelity above 95%. The imaging process leaves the atoms predominantly in the 3D motional ground state of their respective lattice sites, inviting the implementation of a Maxwell’s demon to assemble low-entropy many-body states. Single-site-resolved imaging of fermions enables the direct observation of magnetic order, time-resolved measurements of the spread of particle correlations, and the detection of many-fermion entanglement.

Figure 1

(a) High-resolution imaging setup. A solid immersion lens is formed by a spherical cap and a superpolished substrate contacted on either side of the vacuum window. Using an objective with $\mathrm{NA}=0.60$, the system achieves an effective $\mathrm{NA}=0.87$. The substrate reflects 1064-nm light while transmitting $D_1$ and $D_2$ light of ${}^{40}\mathrm{K}$. The lattice beams are shown in red; the optical pumping and $x$ Raman beams are shown in blue. (b) Top view of Raman beams (blue) and optical pumping beam (green). (c) Raman cooling scheme. The Raman beams detuned near the $D_2$ line (solid blue) drive vibration-lowering transitions. The optical $F$-pumping beam (dashed green) is tuned to the $D_1$ line. Not shown is the $m_F$-pumping beam.

Figure 2

(a) Electronic ground ($|g,N⟩$) and excited ($|e,N⟩$) states dressed by optical pumping photons. (b) On resonance, all dressed states are equally populated and experience an antitrapping potential. The four decay channels between the dressed states are equal. (c) The dressed states with $\mathrm{\Omega }/\delta =0.175$, shown with the dark state $|D⟩$. Only a small fraction ${\mathrm{\Omega }}^4/{\delta }^4$ of the steady-state population resides in antitrapping states. For the atoms in the trapping state, the branching ratios between trapping transitions (solid arrows) and antitrapping transitions (dashed arrow) are shown.

Figure 3

(a) Site-resolved imaging of fermonic atoms on a densely filled 541-nm-period optical lattice, with an exposure time of 2 s; one can clearly discern the lattice structure and individual atoms. (b) Raman spectrum after cooling. The lattice depths are chosen such that the vibrational sidebands are well resolved. The heating sidebands for the three lattice axes are labeled $Z$, $X$, and $Y$. We observe a large sideband asymmetry, from which we extract a 3D ground-state occupation of 72(3)% [19].

Figure 4

(a) Radially averaged PSF extracted from isolated atoms; the FWHM is 640 nm. (b) Intensity histogram after binning the deconvoluted images by lattice site. The threshold for reconstruction is shown by the dashed line. (c) Loss and hopping rates, shown in red squares and blue circles, respectively, as extracted from 20 consecutive 1-s exposures. (d) Correlation measurement $g^{(2)}(r)$ of a thermal cloud with filling of 0.19, showing the absence of distance-dependent loss. (e) Image of sparsely filled lattice with grid lines showing lattice spacing and orientation. The exposure time is 1 s. (f),(g) The same image after deconvolution and with the filled sites identified.