Realizing the symmetry-protected Haldane phase in Fermi-Hubbard ladders.

Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain1,2. Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterized by vanishing two-point spin correlations, gapped excitations and a characteristic non-local order parameter3,4. More recently it has been understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry-protected topological phases of matter, which is based on ideas connected to quantum information and entanglement5-7. Here, we realize a finite-temperature version of such a topological Haldane phase with Fermi-Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements, as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system enables us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model, using a novel correlator.

Imaging magnetic polarons in the doped Fermi-Hubbard model.

Polarons-electronic charge carriers 'dressed' by a local polarization of the background environment-are among the most fundamental quasiparticles in interacting many-body systems, and emerge even at the level of a single dopant1. In the context of the two-dimensional Fermi-Hubbard model, polarons are predicted to form around charged dopants in an antiferromagnetic background in the low-doping regime, close to the Mott insulating state2-7; this prediction is supported by macroscopic transport and spectroscopy measurements in materials related to high-temperature superconductivity8. Nonetheless, a direct experimental observation of the internal structure of magnetic polarons is lacking. Here we report the microscopic real-space characterization of magnetic polarons in a doped Fermi-Hubbard system, enabled by the single-site spin and density resolution of our ultracold-atom quantum simulator. We reveal the dressing of doublons by a local reduction-and even sign reversal-of magnetic correlations, which originates from the competition between kinetic and magnetic energy in the system. The experimentally observed polaron signatures are found to be consistent with an effective string model at finite temperature7. We demonstrate that delocalization of the doublon is a necessary condition for polaron formation, by comparing this setting with a scenario in which a doublon is pinned to a lattice site. Our work could facilitate the study of interactions between polarons, which may lead to collective behaviour, such as stripe formation, as well as the microscopic exploration of the fate of polarons in the pseudogap and 'bad metal' phases.

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 µm. 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.

Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid.

The competition between antiferromagnetism and hole motion in two-dimensional Mott insulators lies at the heart of a doping-dependent transition from an anomalous metal to a conventional Fermi liquid. We observe such a crossover in Fermi-Hubbard systems on a cold-atom quantum simulator and reveal the transformation of multipoint correlations between spins and holes upon increasing doping at temperatures around the superexchange energy. Conventional observables, such as spin susceptibility, are furthermore computed from the microscopic snapshots of the system. Starting from a magnetic polaron regime, we find the system evolves into a Fermi liquid featuring incommensurate magnetic fluctuations and fundamentally altered correlations. The crossover is completed for hole dopings around 30%. Our work benchmarks theoretical approaches and discusses possible connections to lower-temperature phenomena.

Time-resolved observation of spin-charge deconfinement in fermionic Hubbard chains.

Elementary particles carry several quantum numbers, such as charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. For example, one-dimensional systems are described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here, we report on the dynamical deconfinement of spin and charge excitations in real space after the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we tracked the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multipoint correlators, we quantified the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.

Thermally robust spin correlations between two 85Rb atoms in an optical microtrap.

The complex collisional properties of atoms fundamentally limit investigations into a range of processes in many-atom ensembles. In contrast, the bottom-up assembly of few- and many-body systems from individual atoms offers a controlled approach to isolating and studying such collisional processes. Here, we use optical tweezers to individually assemble pairs of trapped 85Rb atoms, and study the spin dynamics of the two-body system in a thermal state. The spin-2 atoms show strong pair correlation between magnetic sublevels on timescales exceeding one second, with measured relative number fluctuations 11.9 ± 0.3 dB below quantum shot noise, limited only by detection efficiency. Spin populations display relaxation dynamics consistent with simulations and theoretical predictions for 85Rb spin interactions, and contrary to the coherent spin waves witnessed in finite-temperature many-body experiments and zero-temperature two-body experiments. Our experimental approach offers a versatile platform for studying two-body quantum dynamics and may provide a route to thermally robust entanglement generation.