Programmable Assembly of Ground State Fermionic Tweezer Arrays

Abstract

We demonstrate deterministic preparation of arbitrary two-component product states of fermionic $^6$Li atoms in an 8$\times$8 optical tweezer array, achieving motional ground-state fidelities above $98.5\,\%$. Leveraging the large differential magnetic moments for spin-resolution, with parallelized site- and number-resolved control, our approach addresses key challenges for low-entropy quantum state engineering. Combined with high-fidelity spin-, site-, and density-resolved readout within a single $20\,\mathrm{μs}$ exposure, and $3\,\mathrm{s}$ experimental cycles, these advances establish a fast, scalable, and programmable architecture for fermionic quantum simulation.

Figures (8)

• Figure 1: Arbitrary product state preparation and high-fidelity detection of fermionic atoms. (a) Schematic of the setup. A high-NA objective creates 2D tweezer arrays via orthogonal AODs, with superimposed DMD potentials, while collecting 671 fluorescence for detection. Spin information is encoded in orthogonally polarized fluorescence photons and separated via polarization optics onto distinct EMCCD regions. (b) Simultaneous spin detection of $^6$Li ($\ket{3}$: red, $\ket{6}$: blue), shown in an averaged raw image. Example pattern demonstrates arbitrary product state preparation on an 8$\times$8 array; target pattern is shown on the right. The lower panel highlights the programmability of our platform using tweezers (purple) and DMD potentials (green, meshed grid). (c) Representative assembled states for Hubbard physics with overlapped spin sectors. Left: classical anti-ferromagnet (AFM) with a vertical domain wall (green). Right: hole-doped AFM. Top: averaged raw images; bottom: processed single-shot realizations, in arrays loaded at 4, and imaged at 33 separation.
• Figure 2: Rapid single-exposure quantum state readout of $^6$Li. (a) Averaged single-exposure image of a fully filled array with representative histograms demonstrating high-fidelity 0-1 atom discrimination for both spins. (b) The addressed cycling $D2$ transitions, $\ket{6}\to\ket{10'}$ and $\ket{3}\to\ket{1'}$ enable spin-resolved detection. Zeeman energies (solid) and magnetic moments $\mu$ (Inset, dashed) for $\ket{1}$ (blue) and $\ket{2}$ (red), leveraged for state-dependent potentials. Shaded bands denote the RF and MW antenna-driven transitions. (c) Repeated $\pi$-pulse fidelity ($F$) for the state transfers: $\ket{1} - \ket{2}$ (24.3, blue) for spin-resolved preparation at 27, $\ket{2}-\ket{3}$ (84.6, green), and $\ket{1}-\ket{6}$ (1.64, orange) utilized for detection at 527. Insets show the measured coherent oscillations with Rabi frequency $\Omega_R$.
• Figure 3: Deterministic singlet preparation in tweezer arrays. (a) Homogeneous loading is achieved in the tweezer array by translating it across a cold $\ket{1}-\ket{2}$ reservoir formed by a 1070 ODT. Site occupations are detected after array expansion. (b) Typical spilling curves at $\nabla B \,$= 21.5 / for individual tweezers (light lines) closely follow the array-average trend (dark line), demonstrating power uniformity (Inset). The even-atom plateaus characterize strong two-component Fermi degeneracy. The schematic illustrates selective removal of excited motional states via spilling. (c) Heatmap depicting single-particle preparation fidelities for individual tweezers across the 8$\times$8 array with best tweezers reaching $99.7\%$.
• Figure 4: Arbitrary product state preparation. (a) Schematic of the protocol for preparing a $\ket{2}-\ket{1}$ spin-patterned 'L-i'. Left: representative DMD potentials (showing only the first addressed column for clarity; green) with spin-resolved images. Right: axial potential schematic summarizing the concept. First, a global, spin-agnostic spill removes excited motional states, while a repulsive DMD mask, Mask($H$), simultaneously creates site-resolved holes. A second DMD pattern Mask($\ket{1}$) targets sites designated for $\ket{1}$ occupation, followed by a $\ket{1}-\ket{2}$ population swap, and a final pattern Mask($\ket{2}$) that imprints the complementary spin structure, realizing arbitrary spin-charge configurations. (b) Measured spin-selective survival probabilities at fixed $\nabla B \,$= 50 / . Sigmoid fits yield centers $a_{\ket{1}}$=19.83± 0.03, $a_{\ket{2}}$=3.54± 0.02, and widths $\varepsilon_{\ket{1}}$= 1.3 ± 0.06, $\varepsilon_{\ket{2}}$= 0.70 ± 0.02. (c) Experimental sequence mapping key parameters. (d) Local spin-selective spilling using the DMD at fixed tweezer power ($\approx \,$16) and $\nabla B \,$= 21.5 / . Operational fidelities correspond to the probability of retaining (removing) a specific spin at addressed (non-addressed) sites in the 3D ground state, evaluated at DMD power marked by the dashed line.
• Figure S1: Deterministic state preparation with varying potential gradients. (a) Heatmap of the mean atom number as a function of tweezer power and applied magnetic field gradient. The dashed lines delineate the plateaus where even atom numbers can be deterministically prepared, following an approximately linear relation. (b) With gravity as the only potential slope, tweezer power ramps yield clear 2- and 4-atom plateaus. Light traces show individual tweezer spilling trends, following the 8$\times$8 array-averaged trend (dark trace). A double sigmoid fit separates the 0-2 and 2-4 transitions by $5 (\sigma_{0-2} + \sigma_{2-4})$, enabling robust spilling. The corresponding atom number variance is shown on the right.