The repulsive Hubbard Hamiltonian is one of the foundational models describing strongly correlated electrons and is believed to capture essential aspects of high-temperature superconductivity. Ultracold fermions in optical lattices allow for the simulation of the Hubbard Hamiltonian with control over kinetic energy, interactions, and doping. A great challenge is to reach the required low entropy and to observe antiferromagnetic spin correlations beyond nearest neighbors, for which quantum gas microscopes are ideal. Here, we report on the direct, single-site resolved detection of antiferromagnetic correlations extending up to three sites in spin-1/2 Hubbard chains, which requires entropies per particle well below s* = ln(2). The simultaneous detection of spin and density opens the route toward the study of the interplay between magnetic ordering and doping in various dimensions.

The Pauli exclusion principle is one of the most fundamental manifestations of quantum statistics. Here, we report on its local observation in a spin-polarized degenerate gas of fermions in an optical lattice. We probe the gas with single-site resolution using a new generation quantum gas microscope avoiding the common problem of light induced losses. In the band insulating regime, we measure a strong local suppression of particle number fluctuations and a low local entropy per atom. Our work opens a new avenue for studying quantum correlations in fermionic quantum matter both in and out of equilibrium.Quantum statistics distinguishes between two fundamentally different kinds of particles: bosons, which condense into a single quantum state at zero temperature, and fermions, for which multiple occupancy of a single state is forbidden. As a result, identical fermions seem to repel each other, described by an effective Fermi pressure on a macroscopic level [1]. Microscopically, the Pauli blockade manifests itself in a strong suppression of density fluctuations [2,3] and in antibunching of densitydensity correlations [4][5][6][7][8][9]. Specifically, fermions in periodic potentials form a band insulating state with suppressed number fluctuations on each site when the chemical potential lies in the band gap. Measuring these number fluctuations can therefore be regarded as a direct probe of Pauli blocking.Local fluctuations in periodic potentials have been directly studied with ultracold bosonic atoms in optical lattices [10][11][12]. Some of these experiments featured siteresolved fluorescence detection with single atom sensitivity [13,14], which has proven to be a powerful method for probing quantum many-body systems. However, such quantum gas microscopy requires a specialized experimental setup with considerably increased technical complexity. In particular, the often used fermionic alkali atoms are difficult to laser cool, making the single-site and atom resolved detection even more challenging. First results have recently been reported on the imaging of single fermions in dilute thermal clouds [15][16][17][18]. However, microscopy of quantum degenerate fermions has so far remained out of reach.Here, we report on the site-resolved characterization of a spin-polarized degenerate Fermi gas in an optical lattice. In the band-insulating region, we measure a strong suppression of local atom number fluctuations, more than one order of magnitude below the Poisson limit expected for uncorrelated particles. Based on the measurement of the local occupation statistics, we reconstruct the spatial entropy distribution in the inhomogeneous samples. We obtained these results with a conceptionally novel quantum gas microscope based on an additional, dedicated optical lattice for detection. This provides high flexibility for future experiments and offers an alternative approach [19,20] to overcome the limitations due to parity detection [12,14].Our experiments started in a standard magneto-optical trap of 6 Li loaded from a Zeeman...

Topological phases, like the celebrated Haldane phase in spin-1 chains, defy characterization through local order parameters. Instead, non-local string order parameters can be employed to reveal their hidden order. Similar diluted magnetic correlations appear in doped one-dimensional lattice systems due to the phenomenon of spin-charge separation. Here we report on the direct observation of such hidden magnetic correlations via quantum gas microscopy of hole-doped ultracold Fermi-Hubbard chains. The measurement of non-local spin-density correlation functions reveals a hidden finite-range antiferromagnetic order, a direct consequence of spin-charge separation. Our technique demonstrates how topological order can directly be measured in experiments and it can be extended to higher dimensions to study the complex interplay between magnetic order and density fluctuations.The Fermi-Hubbard model, describing systems of strongly correlated fermions on a lattice, lies at the heart of our understanding of the Mott insulator-metal transitions and quantum magnetism [1]. The complexity of the interplay between hole doping and magnetic ordering in this model is believed to give rise to a rich phase diagram, including a High-Tc superconducting phase as, for example, observed in cuprate compounds [2]. In one dimension however, the competition between the spin and density sectors is largely absent due to the separation of the spin and density modes at low energy. This phenomenon of spin-charge separation, generally appearing in Luttinger liquids, is well understood theoretically [3], but there are only limited experimental observations. All experimental evidences of this foundational phenomenon are based so far on spectroscopic [4][5][6] or transport measurements [7,8] in condensed matter systems. Nevertheless, quasi long-range antiferromagnetic order at zero temperature, as conventionally measured by two-point spin correlation functions, gets suppressed by a finite hole density in the system. However, due to the independence of the spin and charge sectors the order is not truly reduced, but rather hidden [9][10][11]. It can be revealed by measurements over an extensive part of the system allowing to construct string correlation functions. In analogy to the spin-1 Haldane phase [12][13][14] this requires measuring all spins in the chain. A closely related way to unveil the hidden order is to work directly in "squeezed space", where empty sites are completely removed from the system [15][16][17][18]. In traditional condensed matter systems neither string order can be measured, nor is squeezed space accessible to experiments. Fermionic quantum gas microscopes [19][20][21][22][23][24], in contrast, give access to snapshots of the full spin and † Electronic address: timon.hilker@mpq.mpg.de density distribution with single site resolution [25], such that non-local correlation functions can be extracted [26]. Here we report on the direct measurement of string correlations in ultracold Fermi-Hubbard chains. The ability to locally dete...

Polarons are among the most fundamental quasiparticles emerging in interacting many-body systems, forming already at the level of a single mobile dopant [1]. In the context of the twodimensional Fermi-Hubbard model, such polarons are predicted to form around charged dopants in an antiferromagnetic background in the low doping regime close to the Mott insulating state [2][3][4][5][6][7][8]. Macroscopic transport and spectroscopy measurements related to high Tc materials have yielded strong evidence for the existence of such quasiparticles in these systems [9,10]. Here we report the first microscopic observation of magnetic polarons in a doped Fermi-Hubbard system, harnessing the full single-site spin and density resolution of our ultracold-atom quantum simulator. We reveal the dressing of mobile doublons by a local reduction and even sign reversal of magnetic correlations, originating 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 temperature [8]. We demonstrate that delocalization of the doublon is a necessary condition for polaron formation by contrasting this mobile setting to a scenario where the doublon is pinned to a lattice site. Our work paves the way towards probing interactions between polarons, which may lead to stripe formation, as well as microscopically exploring the fate of polarons in the pseudogap and bad metal phase. arXiv:1811.06907v1 [cond-mat.quant-gas]