Site-Resolved Imaging of Fermionic ${}^6\mathrm{Li}$ in an Optical Lattice

We demonstrate site-resolved imaging of individual fermionic ${}^6\mathrm{Li}$ atoms in a single layer of a 3D optical lattice. To preserve the density distribution during fluorescence imaging, we simultaneously cool the atoms with 3D Raman sideband cooling. This laser cooling technique, demonstrated here for the first time for ${}^6\mathrm{Li}$ atoms, also provides a pathway to rapid low-entropy filling of an optical lattice. We are able to determine the occupation of individual lattice sites with a fidelity $>95\%$, enabling direct, local measurement of particle correlations in Fermi lattice systems. This ability will be instrumental for creating and investigating low-temperature phases of the Fermi-Hubbard model, including antiferromagnets and $d$-wave superfluidity.

Figure 1

Fluorescence image of atoms in a single layer of a cubic lattice obtained using Raman sideband cooling. The filling fraction in the center of the cloud is 40%. We collect approximately 750 photons per atom during a 1.9 s exposure. The color bar is in arbitrary units.

Figure 2

A schematic of the microscope (a). $R1$ and $R2$ denote our Raman beams, and OP the optical pumping light which copropagates with $R2$. $L1$ and $L2$ are additionally retroreflected out of the schematic to create a 3D lattice as described in Ref. [29]. $L3$ forms a lattice along $\widehat{z}$, providing additional confinement during imaging. $L1$, $L2$, and $L3$ have waists of 80, 80, and $40\mu \mathrm{m}$, respectively. The measured point spread function, obtained by superimposing and averaging isolated atoms, is shown in panel (b). The black markers are an azimuthal average of the measured point spread function (PSF). The red curve is the expected diffraction-limited Airy disk for a NA of 0.87. The inset is an image of the PSF. A Gaussian fit to the PSF yields a full width at half maximum of 520 nm, compared to our lattice spacing of 569 nm.

Figure 3

Pulsed Raman sideband imaging. A Raman transition drives atoms into the $|2{{}^{2}S}_{1/2}(F=3/2)⟩$ hyperfine manifold, removing one vibrational excitation. Atoms are then optically pumped back into the $|2{{}^{2}S}_{1/2}(F=1/2)⟩$ manifold while simultaneously switching on the intensifier of an intensified CCD camera to collect the photons scattered during pumping (a). A spectrum, taken by driving a Raman transition with a $200\mu \mathrm{s}$ long pulse and then imaging the $|2{{}^{2}S}_{1/2}(F=1/2,m_F=-1/2)⟩$ state is shown in panel (b), with the red line denoting the two-photon detuning during imaging. The spectrum was taken at the same lattice depth that we use for Raman imaging. From the imbalance of red and blue sidebands we estimate the average number of motional quanta per axis at the start of the imaging sequence to be 1.0(3). The timing of two imaging pulses is shown in panel (c).

Figure 4

Site-resolved imaging with high fidelity. Images obtained by applying $6.4\times {10}^4$ Raman imaging pulses are fit to a lattice of the measured point spread function, with the amplitudes for each lattice site as fit parameters (a). Whether a site is occupied is determined by applying a threshold to the fitted amplitudes, with occupied sites denoted by white dots. A histogram of fitted amplitudes, accumulated from a fixed $20\times 20$-site region over 100 images is shown in panel (b). We optimize the imaging by taking two subsequent frames, with $6.4\times {10}^4$ additional imaging pulses in between, and looking at the fraction of atoms that remain pinned to their sites between the two images while varying the imaging parameters (c),(d). Each data point in (c) and (d) represents an average over 10 shots. By varying the number of pulses between frames and applying a linear fit to the pinned, hopping, and lost fractions, taken from single shots (e), we extract loss and hopping rates used to determine the imaging fidelity (see main text). The fit results are $f_p=(0.945\pm 0.022)-[(7.6\pm 1.9)\times {10}^{-7}]n$, $f_h=(0.085\pm 0.025)+[(3.7\pm 2.1)\times {10}^{-7}]n$, and $f_l=(-0.029\pm 0.031)+[(4.0\pm 2.7)\times {10}^{-7}]n$, where $n$ is the number of pulses between the two frames.