Site-resolved measurement of the spin-correlation function in the Fermi-Hubbard model

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.PACS numbers: 37.10. Jk, 67.85.Lm, 71.10.Fd, 75.10.Jm, Quantum many-body systems exhibiting magnetic correlations underlie a wide variety of phenomena. Hightemperature superconductivity, for example, can arise from the correlated motion of holes on an antiferromagnetic (AFM) Mott insulator [1,2]. It is possible to probe physical analogs of such systems using ultracold atoms in lattices, which introduce a degree of control that is not available in conventional solid-state systems [3,4]. Recent experiments exploring the Hubbard model with cold atoms are accessing temperatures where AFM correlations form, but have only observed these correlations via measurements that were averages over inhomogeneous systems [5,6]. The recent development of site-resolved imaging for fermionic quantum gases [7][8][9][10][11][12][13] provides the ability to directly detect the correlations and fluctuations present in a fermionic quantum many-body state. As demonstrated in experiments with both bosons [14,15] and fermions [12,13,16], microscopy gives access to the spatial variation in observables that occurs in an inhomogeneous system, yielding precise comparisons with theory. The low energy scales in cold atom systems also allow for time-resolved observations of many-body dynamics, which typically occur on millisecond timescales. In bosonic systems temporal and spatial resolution have been combined to observe strongly correlated quantum walks [17], to measure entanglement entropy [18], and to study the dynamics of magnetic correlations [19,20].Here we report the first trap-resolved observations of magnetic correlations in a Fermi-lattice system. Fermionic atoms in a two-dimensional optical lattice can be well described by the Hubbard Hamiltonian, a simple model in which there is a competition between the nearest-neighbor tunneling energy t and the on-site interaction energy U . Despite the apparent simplicity of the Hubbard model it has a rich phase diagram, containing for example the transition from a metal to a Mott insulator. AFM spin correlations begin to appear near half-filling when the temperature scale becomes comp...

A cold-atom Fermi–Hubbard antiferromagnet

“…We extract this quantity using the alternative method described in previous work [25], due to it having lower uncertainty for small values of C d . Displacement vectors that have less than 100 total pairs of sites across all images are discarded.…”

“…The system is well described by the Hubbard model with t/h = 0.90(2) kHz and U/h = 6.50(3) kHz where h is the Planck constant, leading to U/t = 7.2(2). Similar to previous work, our detection method is based on selective spin removal followed by site-resolved imaging of the remaining atomic distribution [25], see Fig. 1c.…”

“…The low-temperature Fermi gas is prepared using a sequence similar to previous work, where a balanced mixture of the two lowest hyperfine states of 6 Li with repulsive interactions is loaded into a 2D optical dipole trap [25]. Prior to loading the lattice from the dipole trap we ramp to the final magnetic bias field used in the experiment, 576 G, corresponding to a scattering length of 210 a 0 , and interaction energy U/h = 6.50(3) kHz.…”

“…Details regarding the spin-removal process, site-resolved imaging, and analysis of site-resolved images can be found in previous work [20,25]. Spin removal begins by rapidly reducing the tunnelling through increasing the lattice depth to 50 E r .…”

“…Already, Mott-insulating phases and short-range antiferromagnetic correlations have been observed, but temperatures were too high to create an antiferromagnet [12][13][14][15]. A new perspective is afforded by quantum gas microscopy [16][17][18][19][20][21][22][23][24][25][26][27][28], which allows readout of magnetic correlations at the site-resolved level [25][26][27][28]. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice of approximately 80 sites.…”