Site-resolved measurement of the spin-correlation function in the Hubbard model (1605.02704v2)

Abstract: Exotic phases of matter can emerge from strong correlations in quantum many-body systems. Quantum gas microscopy affords the opportunity to study these correlations with unprecedented detail. Here we report site-resolved observations of antiferromagnetic correlations in a two-dimensional, Hubbard-regime optical lattice and demonstrate the ability to measure the spin-correlation function over any distance. We measure the in-situ distributions of the particle density and magnetic correlations, extract thermodynamic quantities from comparisons to theory, and observe statistically significant correlations over three lattice sites. The temperatures that we reach approach the limits of available numerical simulations. The direct access to many-body physics at the single-particle level demonstrated by our results will further our understanding of how the interplay of motion and magnetism gives rise to new states of matter.

Overview of Site-resolved Measurement of the Spin-correlation Function in the Hubbard Model

This paper focuses on the site-resolved measurements of antiferromagnetic (AFM) correlations in a two-dimensional Hubbard-regime optical lattice. The research offers pivotal advancements in understanding quantum many-body systems, primarily utilizing quantum gas microscopy to achieve unparalleled precision in examining AFM correlations.

Methodology

The paper employs a sophisticated experimental setup that harnesses quantum gas microscopy to directly observe spin-correlations at the single-particle level within a Fermi-lattice system. The technique involves adiabatically loading fermionic atoms into an optical lattice and leveraging spin removal to translate spin correlations into charge correlations that can be detected with high fidelity using site-resolved imaging. The spin removal technique maps spin correlations onto charge correlations by ejecting atoms of a specific spin state, thereby enabling the measurement of these correlations over distance scales.

Experimental Results

The paper presents significant observations of spin-correlations, reporting statistically notable correlations extending to three lattice sites. Specifically, the experiments demonstrate the ability to measure AFM correlations for nearest-neighbors and diagonal next-nearest neighbors, with the correlation length increasing as the system temperature decreases. Notably, at temperatures as low as $k_{B}T/t < 0.45(2)$, the measured nearest-neighbor correlation reaches 53% of the largest predicted value, marking a critical achievement in cold atom systems operating in the Hubbard regime.

Temperature and Interaction Dependence

Through meticulous experiments, the authors demonstrate a methodical evaluation of the temperature dependence of AFM correlations. They observe that spin-correlations are profoundly sensitive to temperature changes, with a stark reduction in correlator values with increasing temperature. Additionally, the paper examines interaction strength by varying the scattering length, finding that maximal AFM correlations occur near $U/t = 8$. This observation aligns with theoretical predictions, showing suppressed correlations both at large $U/t$ due to diminished exchange energy and at lower $U/t$ where charge fluctuations interfere with magnetic correlations.

Implications and Future Directions

This research not only provides critical insights into the AFM phase near half-filling in two-dimensional systems governed by the Hubbard model but also validates experimental setups against theoretical predictions, paving the way for future exploration of entropy redistribution techniques. Such techniques hold potential for achieving finite-system-size long-range order, which is an essential step toward exploring low-temperature phases like $d$-wave superconductivity in the hole-doped 2D Hubbard model. Additionally, the systematic characterization of spin-correlation functions through quantum gas microscopy may soon permit experimental exploration of pseudogap phenomena and non-equilibrium many-body dynamics, contributing substantively to the theoretical toolkit available for these intricate systems.

Conclusion

The paper effectively showcases the integration of advanced microscopy and precise control over quantum gases, setting a standard for detailed explorations of AFM correlations in strongly correlated quantum systems. The findings enhance understanding of how correlations underpin emergent phenomena in quantum many-body physics, with promising applications in elucidating complex phases such as superconductivity and pseudogap behaviors in cold atom systems.