Entanglement can improve the measurement precision of quantum sensors beyond the shot noise limit. Neutral atoms, the basis of some of the most precise and accurate optical clocks and interferometers, do not naturally exhibit the all-to-all interactions traditionally used to generate such entangled states. On the other hand, these systems exhibit exceedingly high degrees of experimental control over parameters such as temperature, spatial entropy, and itinerancy. In this work, we investigate spin squeezing in a highly coherent itinerant system of neutral atoms with magnetic dipole-dipole interactions. We achieve 7.1 dB of metrologically useful squeezing using finite-range spin-exchange interactions in an erbium quantum gas microscope, and we demonstrate that introducing atomic motion, realizing a dipolar $t$-$J$ model, protects the spin sector coherence at low fillings, significantly improving the achievable spin squeezing in a 2D dipolar system. This work’s protocol can be implemented with most neutral atoms, opening the door to quantum-enhanced metrology in other itinerant dipolar systems, such as molecules or optical lattice clocks, and serves as a novel method for studying itinerant quantum magnetism with long-range interactions.
Figures
34 panels with data across 7 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.
Fig. 1
panel (c): Qubit frequency shift (Hz) against magnetic field $B$ (G) near the magnetically insensitive point (bottom-right inset of (c)): points with SEM error bars and the quadratic fit (line). data.csv
Fig. 2
panel (a-1): Mean-field shearing after 100 ms: $\langle \hat{S}_y/|\hat{S}|\rangle$ against the initial-state angle $\theta$ (rad), points with SEM error bars and the DTWA simulation as a band (mean $\pm$ one standard deviation) (left) of (a)). data.csv
panel (a-2): Mean-field shearing after 1000 ms: $\langle \hat{S}_y/|\hat{S}|\rangle$ against the initial-state angle $\theta$ (rad), points with SEM error bars and the DTWA simulation as a band (mean $\pm$ one standard deviation) (left is 100 ms; this is the right, 1000 ms part) of (a)). data.csv
panel (b): Ramsey contrast against wait time (s) for 1000 atoms at about 85% peak filling (blue) and 85 atoms at about 20% center filling (orange), points with 16th to 84th percentile bootstrap error bars joined by dashed lines; red: fitted interaction-free $T_2$ decay; shaded: DTWA. The inset is fig2/b-inset. data.csv
panel (b-inset): Inset of (b): Ramsey fringe $S_z/S$ against phase (rad) at one wait time of the blue data set, points with SEM error bars and the sine fit (line) whose amplitude is the plotted contrast. data.csv
Fig. 3
panel (a): Histogram of $S_z/\sqrt{N/4}$ at the most squeezed point of (e) (counts per bin, bars), with Gaussians of the measured variance (blue) and the SQL variance (red). The Bloch spheres and pulse sequence of (a) are not shown. data.csv
panel (b): Mean filling of the two spatially separated clouds used for differential measurement against lattice site $x$ and $y$; sites outside the analysed region are blank. The dashed dividing line of the print is not drawn. data.csv
panel (c-1): Measured noise squeezing $\xi^2$ (dB) against evolution time $\tau$ (s) and readout angle $\theta$ (deg), left square of (c). The DTWA square on the right is not shown here. data.csv
panel (c-2): DTWA simulation of the noise squeezing $\xi^2_{\mathrm{DTWA}}$ (dB) against evolution time $\tau$ (s) and readout angle $\theta$ (deg), right square of (c). data.csv
panel (d): Ramsey contrast against evolution time $\tau$ (s), points with 16th to 84th percentile bootstrap error bars joined by a dashed line, and the DTWA simulation as a shaded band. data.csv
panel (e): Wineland squeezing parameter $\xi^2_R$ (dB) after $\tau = 0.27$ s against readout angle $\theta$ (deg): points with 16th to 84th percentile bootstrap error bars, the sin fit (red), the SQL (dashed, 0 dB) and DTWA (shaded band). data.csv
panel (f-1): Spin correlation $\langle \hat{\sigma}^z_{x,y}\hat{\sigma}^z_{0,0}\rangle - \langle \hat{\sigma}^z_{x,y}\rangle\langle \hat{\sigma}^z_{0,0}\rangle$ against the site offsets $x$ and $y$ at readout angle $\theta = 13$ deg (left) of (f)), on a symmetric-log colour scale (linear within $\pm$0.02). data.csv
panel (f-2): Spin correlation $\langle \hat{\sigma}^z_{x,y}\hat{\sigma}^z_{0,0}\rangle - \langle \hat{\sigma}^z_{x,y}\rangle\langle \hat{\sigma}^z_{0,0}\rangle$ against the site offsets $x$ and $y$ at readout angle $\theta = 89$ deg (left is 13 deg; this is the right, 89 deg map) of (f)), on a symmetric-log colour scale (linear within $\pm$0.02). data.csv
Fig. 4
panel (b-1): Measured noise squeezing $\xi^2$ (dB) against evolution time $\tau$ (s) and readout angle $\theta$ (deg) at tunneling $t = 0$ Hz (top row of (b)). The DTWA row below it is not shown here. data.csv
panel (b-2): Measured noise squeezing $\xi^2$ (dB) against evolution time $\tau$ (s) and readout angle $\theta$ (deg) at tunneling $t = 10$ Hz (top row of (b)). The DTWA row below it is not shown here. data.csv
panel (b-3): Measured noise squeezing $\xi^2$ (dB) against evolution time $\tau$ (s) and readout angle $\theta$ (deg) at tunneling $t = 50$ Hz (top row of (b)). The DTWA row below it is not shown here. data.csv
panel (b-dtwa-1): DTWA simulation of the noise squeezing $\xi^2_{\mathrm{DTWA}}$ (dB) against evolution time $\tau$ (s) and readout angle $\theta$ (deg) at tunneling $t = 0$ Hz (bottom row of (b)). data.csv
panel (b-dtwa-2): DTWA simulation of the noise squeezing $\xi^2_{\mathrm{DTWA}}$ (dB) against evolution time $\tau$ (s) and readout angle $\theta$ (deg) at tunneling $t = 10$ Hz (bottom row of (b)). data.csv
panel (b-dtwa-3): DTWA simulation of the noise squeezing $\xi^2_{\mathrm{DTWA}}$ (dB) against evolution time $\tau$ (s) and readout angle $\theta$ (deg) at tunneling $t = 50$ Hz (bottom row of (b)). data.csv
panel (c): Ramsey contrast against evolution time $\tau$ (s) at tunneling $t = 0$, 10 and 50 Hz: points with 16th to 84th percentile bootstrap error bars joined by dashed lines, and DTWA bands (blue, red, yellow; green: stochastic hopping at 50 Hz). data.csv
panel (d): Wineland parameter $\xi^2_R$ (dB) after 0.53 s against readout angle $\theta$ (deg) at $t = 0$, 10 and 50 Hz: points with 16th to 84th percentile bootstrap error bars, quadratic fits (lines), DTWA (bands) and the SQL (dashed). The fits' thin uncertainty outlines are not drawn. data.csv
panel (e-1): Spin correlation $\langle \hat{\sigma}^z_i\hat{\sigma}^z_j\rangle - \langle \hat{\sigma}^z_i\rangle\langle \hat{\sigma}^z_j\rangle$ against the site offsets $x$ and $y$ at readout angle $\theta = 19$ deg and tunneling $t = 0$ Hz (row 1, column 1 of (e)), on a symmetric-log colour scale (linear within $\pm$0.01). data.csv
panel (e-2): Spin correlation $\langle \hat{\sigma}^z_i\hat{\sigma}^z_j\rangle - \langle \hat{\sigma}^z_i\rangle\langle \hat{\sigma}^z_j\rangle$ against the site offsets $x$ and $y$ at readout angle $\theta = 19$ deg and tunneling $t = 10$ Hz (row 1, column 2 of (e)), on a symmetric-log colour scale (linear within $\pm$0.01). data.csv
panel (e-3): Spin correlation $\langle \hat{\sigma}^z_i\hat{\sigma}^z_j\rangle - \langle \hat{\sigma}^z_i\rangle\langle \hat{\sigma}^z_j\rangle$ against the site offsets $x$ and $y$ at readout angle $\theta = 19$ deg and tunneling $t = 50$ Hz (row 1, column 3 of (e)), on a symmetric-log colour scale (linear within $\pm$0.01). data.csv
panel (e-4): Spin correlation $\langle \hat{\sigma}^z_i\hat{\sigma}^z_j\rangle - \langle \hat{\sigma}^z_i\rangle\langle \hat{\sigma}^z_j\rangle$ against the site offsets $x$ and $y$ at readout angle $\theta = 120$ deg and tunneling $t = 0$ Hz (row 2, column 1 of (e)), on a symmetric-log colour scale (linear within $\pm$0.01). data.csv
panel (e-5): Spin correlation $\langle \hat{\sigma}^z_i\hat{\sigma}^z_j\rangle - \langle \hat{\sigma}^z_i\rangle\langle \hat{\sigma}^z_j\rangle$ against the site offsets $x$ and $y$ at readout angle $\theta = 120$ deg and tunneling $t = 10$ Hz (row 2, column 2 of (e)), on a symmetric-log colour scale (linear within $\pm$0.01). data.csv
panel (e-6): Spin correlation $\langle \hat{\sigma}^z_i\hat{\sigma}^z_j\rangle - \langle \hat{\sigma}^z_i\rangle\langle \hat{\sigma}^z_j\rangle$ against the site offsets $x$ and $y$ at readout angle $\theta = 120$ deg and tunneling $t = 50$ Hz (row 2, column 3 of (e)), on a symmetric-log colour scale (linear within $\pm$0.01). data.csv
Fig. 5
panel (b): Maximum nearest-neighbour transverse interaction strength $J_\perp$ (Hz) against $\min\{I, J\}$ for fermionic isotopes and $^{87}$Rb, each point labelled with its species, and the value used in this work (orange); lattice spacing 266 nm. data.csv
Fig. 6
Illustrative figure, no extractable data. Shown in the paper PDF.
Fig. 7
Illustrative figure, no extractable data. Shown in the paper PDF.
Fig. 8
panel (a): Interaction-decoupled $T_2$ coherence: normalized polarization against wait time (s) for a cloud of 900 atoms under spin echo and WAHUHA decoupling, points with SEM error bars and the exponential fit (line). data.csv
panel (b): Single-particle lattice loss: atom number against wait time (s), points with SEM error bars and the exponential fit (line). data.csv
Fig. 9
Illustrative figure, no extractable data. Shown in the paper PDF.
Fig. 10
panel (a): Rabi oscillation of the hyperfine qubit: spin polarization $S_z/S$ against microwave pulse length (ms), points with SEM error bars and the sine fit (line). data.csv
panel (b): Spin polarization $S_z/S$ after 400 consecutive $\pi$ pulses against $\pi$ pulse length (ms), points with SEM error bars and the Gaussian fit (line). data.csv
panel (c): Drift of the fitted $\pi$ pulse length (ms) over a 12-hour period against shot index, with the fit parameter's standard deviation as error bars. data.csv
panel (d): Drift of the $\pi$-pulse infidelity over a 12-hour period against shot index, with error bars from the fit parameter's standard deviation. data.csv
Cite
Alec Douglas, Vassilios Kaxiras, Lin Su, Michal Szurek, Vikram Singh, Ognjen Marković, Markus Greiner. Spin Squeezing with Itinerant Magnetic Dipoles. Phys. Rev. X 15, 041021 (2025). https://doi.org/10.1103/shj7-9kb3
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