We report on the observation of nearest-neighbor antiferromagnetic spin correlations of a Fermi gas with SU(
N) symmetry trapped in an optical dimerized lattice. Quantum magnetism originates from the superexchange interaction between quantum-mechanical spins. By using a dimerized cubic configuration, we enhance the superexchange coupling within the dimer, which gives rise to an excess of singlets compared with triplets consisting of two different spins. The precise control of the spin degrees of freedom provided by an optical pumping technique enables us a straightforward comparison between the cases of SU(2) and SU(4). Our important finding is that the antiferromagnetic correlation is enhanced for the SU(4)-spin system compared with SU(2) as a consequence of a Pomeranchuk cooling effect. This work is an important step towards the realization of novel SU(
N>2) quantum magnetism.
The exchange coupling between quantum mechanical spins lies at the origin of quantum magnetism. We report on the observation of nearest-neighbor magnetic spin correlations emerging in the many-body state of a thermalized Fermi gas in an optical lattice. The key to obtaining short-range magnetic order is a local redistribution of entropy within the lattice structure. This is achieved in a tunable-geometry optical lattice, which also enables the detection of the magnetic correlations. We load a low-temperature two-component Fermi gas with repulsive interactions into either a dimerized or an anisotropic simple cubic lattice. For both systems the correlations manifest as an excess number of singlets as compared to triplets consisting of two atoms with opposite spins. For the anisotropic lattice, we determine the transverse spin correlator from the singlet-triplet imbalance and observe antiferromagnetic correlations along one spatial axis. Our work paves the way for addressing open problems in quantum magnetism using ultracold fermions in optical lattices as quantum simulators.
Understanding the magnetic response of the normal state of the cuprates is considered a key piece in solving the puzzle of their high-temperature superconductivity. The essential physics of these materials is believed to be captured by the Fermi-Hubbard model, a minimal model that has been realized with cold atoms in optical lattices. Here we report on site-resolved measurements of the Fermi-Hubbard model in a spin-imbalanced atomic gas, allowing us to explore the response of the system to large effective magnetic fields. We observe short-range canted antiferromagnetism at half-filling with stronger spin correlations in the direction orthogonal to the magnetization, in contrast with the spin-balanced case where identical correlations are measured for any projection of the pseudospin. The rotational anisotropy of the spin correlators is found to increase with polarization and with distance between the spins. Away from half-filling, the polarization of the gas exhibits non-monotonic behavior with doping for strong interactions, resembling the behavior of the magnetic susceptibility in the cuprates. We compare our measurements to predictions from Determinantal Quantum Monte Carlo (DQMC) and Numerical Linked Cluster Expansion (NLCE) algorithms and find good agreement. Calculations on the doped system are near the limits of these techniques, illustrating the value of cold atom quantum simulations for studying strongly-correlated materials.
Quantum magnetism originates from the exchange coupling between quantum mechanical spins. Here, we report on the observation of nearest-neighbor magnetic correlations emerging in the many-body state of a thermalized Fermi gas in an optical lattice. The key to obtaining short-range magnetic order is a local redistribution of entropy, which allows temperatures below the exchange energy for a subset of lattice bonds. When loading a repulsively interacting gas into either dimerized or anisotropic simple cubic configurations of a tunable-geometry lattice, we observe an excess of singlets as compared with triplets consisting of two opposite spins. For the anisotropic lattice, the transverse spin correlator reveals antiferromagnetic correlations along one spatial axis. Our work facilitates addressing open problems in quantum magnetism through the use of quantum simulation.
Quantum-gas microscopes provide direct access to the phases of the Hubbard model, bringing microscopic insight into the complex competition between interactions, SU(2) magnetism, and doping. Alkaline-earth(-like) fermions extend this spin-1/2 paradigm by realizing higher symmetries and giving access to SU(
N) Hubbard models, with rich phase diagrams to be unveiled. Despite its fundamental interest, a microscopic exploration of SU(
N) quantum systems has remained elusive. Here we report the realization of a quantum-gas microscope for fermionic
87Sr. Our imaging scheme, based on cooling and fluorescence on the narrow intercombination line at 689 nm, enables spin-resolved single-atom detection. By implementing a spin-selective optical pumping protocol, we determine the occupation of each of the 10 spin states in a single experimental realization, a crucial capability for probing site-resolved magnetic correlations. We benchmark our method by observing single-particle Larmor precession across the full spin-9/2 ground-state manifold and use numerical simulations of SU(
N) Fermi-Hubbard chains, incorporating the measured detection fidelities, to demonstrate its capability to resolve many-body spin correlations. Our results establish
87Sr quantum-gas microscopy as a powerful approach to study exotic magnetism in the SU(
N) Fermi-Hubbard model, and provide a new detection tool for studies in quantum simulation, computation, and metrology.
We study antiferromagnetic systems with enhanced “nearly-SU(N)” symmetry, which can be realized in systems of ultracold spinor atoms in optical lattices. Examples of N = 3 (for S = 1 bosons) and N = 4 (for S=32 fermions) are considered. Near the SU(N) point, the low-energy physics can be described by the CPN−1 model with an additional symmetry-breaking term lowering the symmetry down to SU(2) and favoring the Néel ordering. We show that the effective theory of such systems can be cast in the form of a nonlinear sigma model with the SO(3) matrix-valued field, which is typically obtained for frustrated magnets with non-collinear order. Further, we show that those systems possess a peculiar effect of topological binding: for a system with the underlying spin S, lowering of the symmetry from SU(2S + 1) to SU(2) leads to binding of topological unit-charge excitations of the CP2S model (skyrmions for space dimension d = 2, instantons for d = 1, and hedgehogs for d = 3) into 2S-multiplets.