Two-Dimensional Programmable Tweezer Arrays of Fermions

We prepare high-filling two-component arrays of tens of fermionic ${}^6\mathrm{Li}$ atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. A full spin- and density-resolved readout of individual sites allows us to postselect near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator.

Figure 1

2D stroboscopic tweezer technique and lifetimes. (a) Two crossed acousto-optic modulators spaced in a $4f$ configuration generate the array. (b) Illustration of the principle of stroboscopic array generation of an eight-site ring. For a strobe frequency $f_s$, each column of the array is turned on for a quarter of the period $1/f_s$, generating a time-averaged potential shown in (c). (d) Lifetime of an atom in the ground vibrational state of a tweezer versus strobe frequency, with the red point at 0 kHz indicating the nonstrobed lifetime. The dashed line shows the theoretical prediction, and gray shading indicates the systematic uncertainties on the tweezer waist. The inset shows an example of a decay curve of population in the ground state for $f_s=513\mathrm{kHz}$ with an exponential fit.

Figure 2

Examples of band insulators of different geometries, showing (a) rectangular $5\times 5$, (b) 21-site Lieb plaquette, (c) $4\times 5$ triangular, and (d) octagonal ring arrays. Only $|\uparrow ⟩$ atoms are imaged, and the sites here are not tunnel coupled. The top row shows single shots with perfect filling of the $|\uparrow ⟩$ state, and the bottom row shows average images. Deviations of the atom positions in the single-shot images are due to quantization onto the lattice for imaging. Average fillings of $|\uparrow ⟩$ are (93, 92, 91, 89)%, accounting for imaging fidelity of 98.5%, out of (411, 254, 275, 100) shots.

Figure 3

Bilayer imaging procedure and entropy reduction through postselection. (a) Atoms in $|\uparrow ⟩$ (yellow) and $|\downarrow ⟩$ (blue) are initially trapped in the tweezers, then adiabatically loaded into (b) a 2D lattice with vertical waist of $75\mu \mathrm{m}$, where $|\uparrow ⟩$ is transferred to $|\tilde{\uparrow }⟩$ (red). (c) A magnetic field gradient is applied to separate the spins in the vertical direction, after which (d) two lightsheet potentials turn on to fix the $z$ positions. (e) The lightsheets are further separated to $25\mu \mathrm{m}$ separation. Raman sideband imaging commences, producing simultaneous images of both spin states. (f) Single-shot image of $|\downarrow ⟩$ and $|\tilde{\uparrow }⟩$ originally from a $3\times 5$ rectangular array. (g) Probability distribution versus number of atoms in each spin state over 972 shots. Here, all images with doublons (65 shots) were not used. (h) By postselecting on the maximum number of holes, effective entropy can be reduced by varying amounts.

Figure 4

Low entropy preparation of a $2\times 2$ array. (a) We load two atoms per site on one diagonal of the array. (b) We create a correlated state by ramping on the additional lattice sites and increasing the scattering length to introduce on site interactions. For the following data, we work with $t_x/h=140(5)\mathrm{Hz}$, $t_y/h=220(5)\mathrm{Hz}$, and $U/\overline{t}=3.4(2)$. (c) Measured spin-spin correlations enabled by the bilayer imaging scheme. (d) Best fit (purple bars) and measured (black dots) microstate populations for 671 postselected experimental shots. The fit gives an entropy in the range [0,0.09] $k_B$ per particle. Insets: the two most common states.