Robust Bilayer Charge Pumping for Spin- and Density-Resolved Quantum Gas Microscopy

Quantum gas microscopy has emerged as a powerful new way to probe quantum many-body systems at the microscopic level. However, layered or efficient spin-resolved readout methods have remained scarce as they impose strong demands on the specific atomic species and constrain the simulated lattice geometry and size. Here we present a novel high-fidelity bilayer readout, which can be used for full spin- and density-resolved quantum gas microscopy of two-dimensional systems with arbitrary geometry. Our technique makes use of an initial Stern-Gerlach splitting into adjacent layers of a highly stable vertical superlattice and subsequent charge pumping to separate the layers by $21\mu \mathrm{m}$. This separation enables independent high-resolution images of each layer. We benchmark our method by spin- and density-resolving two-dimensional Fermi-Hubbard systems. Our technique furthermore enables the access to advanced entropy engineering schemes, spectroscopic methods, or the realization of tunable bilayer systems.

Figure 1

Schematics of setup and charge pump. (a) We use a bichromatic optical superlattice (red, green) in the vertical direction of our quantum gas microscope to control bilayer systems (gray) and their mutual tunnel couplings $t_z$ or energy offsets $\mathrm{\Delta }$. The two layers of a bilayer system are pumped to a separation of $21\mu \mathrm{m}$, which enables subsequent site-resolved microscopy of both layers by shifting the focal plane by $\mathrm{\Delta }z$ between the images. (b) Charge pumping is achieved by time-dependent modulation of superlattice parameters. Atoms initialized in opposite wells ($G$ and $E$) experience transport in opposite directions. For technical reasons we reset the superlattice phase after each adiabatic passage (see the Supplemental Material [36]). (c) Absorption images (side view) of an initially coupled bilayer system whose planes are subsequently pumped in opposite directions for 1, 2, and 3 pumping steps, leading to a final separation of $21\mu \mathrm{m}$ between the two layers.

Figure 2

Bilayer readout and charge pump fidelity. (a) An initially coupled Mott insulating bilayer system is separated over a distance of $21\mu \mathrm{m}$ using three charge pumping steps. (b),(c), Single-site resolved fluorescence images and reconstruction (inset) of the respective site occupations of the two separated layers. The images were obtained by shifting the high-resolution objective to sequentially image the two layers. (d) Summed occupation of vertically combined sites (supersites) relevant for bilayer systems. Here, the two vertically overlapping Mott insulators show a large region of double occupation on a supersite. (e) Averaged and normalized number of atoms in a monolayer system as a function of pumping steps. A fit to the data (black line) yields a transfer fidelity for each pumping step of $\eta =0.996(1)$. Error bars denote one standard error of the mean (s.e.m.).

Figure 3

Spin resolution of two-dimensional systems. (a) The two different spin states of a monolayer spin mixture (here a two-dimensional Fermi-Hubbard system) are split into different layers (red and blue) of a bilayer system with a vertical magnetic gradient. Subsequently, charge pumping and bilayer readout is applied with single-site resolution. (b),(c), Snapshot of the two spin components of a two-dimensional Fermi-Hubbard system after separation and the full spin and density reconstruction of the original single layer in (d). The correct recombination of the spin-layers is ensured by the unique minimization of reconstructed doublons (see the Supplemental Material [36]). (e) Number of atoms detected in the upper (red) or lower (blue) layer as a function of the superlattice splitting phase. The magnetic field gradient during the initial splitting process creates a broad plateau of superlattice phases ${\varphi }_{\mathrm{SL}}$, for which a balanced spin mixture is successfully split into its constituents.

Figure 4

Two-dimensional spin correlations. (a) Averaged spin correlations versus distance of undoped two-dimensional Fermi-Hubbard systems at $U/t=9.3(4)$ obtained by spin- and density-resolved imaging. Sites with density $n<0.84$ are excluded from the analysis. (b) Sign-corrected spin correlations versus radial distance. Error bars denote one s.e.m. (c) Spin structure-factor, exhibiting a strong peak at the antiferromagnetic momentum $(\pi ,\pi )$. (d) Full counting statistics of the staggered magnetization ${\widehat{m}}^z$. The figure is based on 150 experimental realizations.