Session B9: High Resolution of Lattice-trapped Fermions

Spin-imbalance in a 2D Fermi-Hubbard system

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. A simple model for exploring this physics is a two-dimensional Fermi-Hubbard system in an effective Zeeman field. We investigate this model using site-resolved measurements of a spin-imbalanced Fermi gas in an optical lattice. We observe short-range canted antiferromagnetism at half-filling with stronger spin correlations in the direction orthogonal to the magnetization. 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. The realization of lattice Fermi gases with spin imbalance opens the door to studying exotic superconductivity in large magnetic fields.   

Realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms

Exotic phenomena in strongly correlated electron systems emerge from the interplay between spin and motional degrees of freedom. For example, doping an antiferromagnet is expected to give rise to pseudogap states and high-temperature superconductors. Ultracold fermions in optical lattices offer the potential to answer open questions about the doped Hubbard Hamiltonian. Here we report the realization and site-resolved observation of an antiferromagnet exhibiting long range order (LRO) in a repulsively interacting Fermi gas on a 2D square lattice of about 80 sites. Signatures of LRO manifest through the development of a peak in the spin structure factor and the divergence of the correlation length that reaches the size of the system. At our lowest temperature of $T/t=0.25(2)$ we find order spanning the entire sample, where the staggered magnetization approaches the ground-state value. Our experimental platform enables doping away from half filling, where interesting states are expected, but numerical analysis is challenging. We find that the antiferromagnetic LRO persists to hole dopings of about $15$\%, providing a guideline for computational studies. Our results show that quantum gas microscopy of ultracold fermions can address open questions on the low-temperature Hubbard model.   

Potential Engineering of Fermi-Hubbard Systems using a Quantum Gas Microscope

Arbitrary control of optical potentials has emerged as an important tool in manipulating ultracold atomic systems, especially when combined with the single-site addressing afforded by quantum gas microscopy. Already, experiments have used digital micromirror devices (DMDs) to initialize and control ultracold atomic systems in the context of studying quantum walks, quantum thermalization, and many-body localization. Here, we report on progress in using a DMD located in the image plane of a quantum gas microscope to explore static and dynamic properties of a 2D Fermi-Hubbard system. By projecting a large, ring-shaped anti-confining potential, we demonstrate entropy redistribution and controlled doping of the system. Moreover, we use the DMD to prepare localized holes, which upon release interact with and disrupt the surrounding spin environment. These techniques pave the way for controlled investigations of dynamics in the low-temperature phases of the Hubbard model.   

Observation of charge density wave correlations in the attractive Fermi-Hubbard model

The attractive Hubbard model is the simplest condensed matter model that gives rise to conventional superfluidity in a lattice. At half-filling, the ground state of the model has degenerate superfluid and charge density wave orders. Using quantum gas microscopy of fermionic lithium in an optical lattice, we detect charge-density wave correlations in attractive gases prepared either on the upper or lower branch of a Feshbach resonance. Away from half-filling, the correlations get weaker as the system favors superfluid order. These correlations serve as a low-temperature thermometer and are an indirect way to measure the strength of superfluid correlations in the gas. Our characterization of the entropy of spin-balanced attractive gases in lattices sets the stage for searching for signatures of non-zero momentum superfluids in spin-imbalanced lattice gases.   

Detecting correlations in deterministically prepared quantum states with single-atom imaging

We deterministically prepare quantum states consisting of few fermions in single and double-well potentials. Here we report on a new imaging scheme for $^{6}$Lithium with which we detect the correlations of the quantum state on a single-atom level and with spin resolution. The detection method uses fluorescence imaging at high magnetic field where the optical transitions for the used hyperfine states are almost closed. With a high-resolution objective we image about 15 scattered photons per atom on an EMCCD camera. This is sufficient to identify and locate single atoms in our imaging plane. We can perform this scheme in situ or after an expansion in time-of-flight and additionally resolve the spin by subsequently adressing the different hyperfine states. By combining this scheme with our deterministic preparation, we measure the two-point momentum correlations to probe the spatial symmetry of the two-particle wavefunction. The high contrast and the scalability of the detection technique allows us to go beyond measuring two-point correlations and characterize many-body quantum states.   

Site-Resolved Observation of Charge and Spin Correlations in the 2D Fermi-Hubbard Model

The application of quantum gas microscopy to fermionic systems has allowed for rapid advances in the field of ultracold fermionic atoms in optical lattices, including site-resolved studies of metallic, Mott insulating, and band insulating states of the two-dimensional Fermi-Hubbard model. In this talk, we extend these studies to explore spatial charge and spin correlations using spin sensitive fluorescence imaging of ultracold $^{\mathrm{40}}$K atoms trapped in a square optical lattice [1]. We observe nearest-neighbor antiferromagnetic spin correlations which are maximal at half-filling, and which weaken monotonically upon doping. Correlations between singly charged sites on the other hand display non-monotonic behavior as a function of doping. At low filling, these correlations are negative, revealing the effects of Pauli blocking and strong repulsive interactions. As the filling is increased beyond a critical value however, the correlations become positive, indicating an effective attraction between holes and doublons in the system. These findings agree well with numerical linked-cluster expansion (NLCE) and determinantal quantum Monte Carlo (DQMC) calculations. [1] Cheuk et al., Science 353, 1260 (2016)   

Revealing "Hidden" Antiferromagnetic Correlations in Doped Hubbard Chains via String Correlators

Topological phases, among them 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 1d systems due to the remarkable 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 microscopic manifestation of spin-charge separation. Our technique, which can be directly extended to higher dimensions, enable the study of the complex interplay between magnetic order and density fluctuations and show how topological order can be directly measured in experiments.   

Few-body interactions in a Fermi degenerate optical lattice clock

Alkaline-earth-like atoms trapped in optical lattices are at the forefront of both precision measurements, realizing record accuracy as an optical frequency standard, and quantum simulations. Recent advances have sought to use precision spectroscopy on the millihertz-linewidth optical transition to study many-body physics, including the discovery of an interorbital Feshbach resonance, demonstration of spin-orbit coupling, and the realization of a Fermi-degenerate 3D optical lattice clock. In this talk, I will discuss our recent work on resolving few-body interactions of SU(N) fermionic strontium in deep optical lattices with narrow-line optical spectroscopy. By combining spectroscopy with imaging, we can resolve the spatial structure of interacting atoms in a degenerate Fermi gas.   

Energy-resolved atomic scanning probe: Mapping local density of states of many-body systems

The density of states (DOS) is an important quantity for determining thermodynamic quantities and transport coefficients of many-body systems. The scanning tunneling microscope (STM) measures the product of DOS and the local weight of wavefunction at the measurement location, which is called the local density of states (LDOS). By connecting a narrow-band, noninteracting lattice as a probe to a lattice loaded with interacting particles, the tunneling current also reveals the LDOS of the interacting system. By tuning the relative energy between the probe and the system, the LDOS can be resolved in the energy domain, a task that would be much more difficult in conventional STM. We propose a heterogeneous lattice structure with confined interactions for realizing the energy-resolved atomic scanning probe (ERASP) using cold-atoms in magnetic or optical potentials. The ERASP is capable of mapping out the LDOS of complex interacting systems such as the Hubbard model and provides local information for inhomogeneous systems. Reference: D. Gruss, C. C. Chien, M. Di Ventra, and M. Zwolak, arXiv: 1610.01903.