Directly imaging spin polarons in a kinetically frustrated Hubbard system.

The emergence of quasiparticles in quantum many-body systems underlies the rich phenomenology in many strongly interacting materials. In the context of doped Mott insulators, magnetic polarons are quasiparticles that usually arise from an interplay between the kinetic energy of doped charge carriers and superexchange spin interactions1-8. However, in kinetically frustrated lattices, itinerant spin polarons-bound states of a dopant and a spin flip-have been theoretically predicted even in the absence of superexchange coupling9-14. Despite their important role in the theory of kinetic magnetism, a microscopic observation of these polarons is lacking. Here we directly image itinerant spin polarons in a triangular-lattice Hubbard system realized with ultracold atoms, revealing enhanced antiferromagnetic correlations in the local environment of a hole dopant. In contrast, around a charge dopant, we find ferromagnetic correlations, a manifestation of the elusive Nagaoka effect15,16. We study the evolution of these correlations with interactions and doping, and use higher-order correlation functions to further elucidate the relative contributions of superexchange and kinetic mechanisms. The robustness of itinerant spin polarons at high temperature paves the way for exploring potential mechanisms for hole pairing and superconductivity in frustrated systems10,11. Furthermore, our work provides microscopic insights into related phenomena in triangular-lattice moiré materials17-20.

Probing site-resolved correlations in a spin system of ultracold molecules.

Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in explaining fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising platform that combines several advantageous properties1-11. These include a large set of internal states with long coherence times12-17 and long-range, anisotropic interactions. These features could enable the exploration of intriguing phases of correlated quantum matter, such as topological superfluids18, quantum spin liquids19, fractional Chern insulators20 and quantum magnets21,22. Probing correlations in these phases is crucial to understanding their properties, necessitating the development of new experimental techniques. Here we use quantum gas microscopy23 to measure the site-resolved dynamics of quantum correlations of polar 23Na87Rb molecules confined in a two-dimensional optical lattice. By using two rotational states of the molecules, we realize a spin-1/2 system with dipolar interactions between particles, producing a quantum spin-exchange model21,22,24,25. We study the evolution of correlations during the thermalization process of an out-of-equilibrium spin system for both spatially isotropic and anisotropic interactions. Furthermore, we examine the correlation dynamics of a spin-anisotropic Heisenberg model engineered from the native spin-exchange model by using periodic microwave pulses26-28. These experiments push the frontier of probing and controlling interacting systems of ultracold molecules, with prospects for exploring new regimes of quantum matter and characterizing entangled states that are useful for quantum computation29,30 and metrology31.

Two-Dimensional Programmable Tweezer Arrays of Fermions.

We prepare high-filling two-component arrays of tens of fermionic ^{6}Li atoms in optical tweezers, with the atoms in the ground motional state of each tweezer. Using a stroboscopic technique, we configure the arrays in various two-dimensional geometries with negligible Floquet heating. A full spin- and density-resolved readout of individual sites allows us to postselect near-zero entropy initial states for fermionic quantum simulation. We prepare a correlated state in a two-by-two tunnel-coupled Hubbard plaquette, demonstrating all the building blocks for realizing a programmable fermionic quantum simulator.

Realization of a Fermi-Hubbard Optical Tweezer Array.

We use lithium-6 atoms in an optical tweezer array to realize an eight-site Fermi-Hubbard chain near half filling. We achieve single site detection by combining the tweezer array with a quantum gas microscope. By reducing disorder in the energy offsets to less than the tunneling energy, we observe Mott insulators with strong antiferromagnetic correlations. The measured spin correlations allow us to put an upper bound on the entropy of 0.26(4)k_{B} per atom, comparable to the lowest entropies achieved with optical lattices. Additionally, we establish the flexibility of the tweezer platform by initializing atoms on one tweezer and observing tunneling dynamics across the array for uniform and staggered 1D geometries.

Quench Dynamics of a Fermi Gas with Strong Nonlocal Interactions.

We induce strong nonlocal interactions in a 2D Fermi gas in an optical lattice using Rydberg dressing. The system is approximately described by a t - V model on a square lattice where the fermions experience isotropic nearest-neighbor interactions and are free to hop only along one direction. We measure the interactions using many-body Ramsey interferometry and study the lifetime of the gas in the presence of tunneling, finding that tunneling does not reduce the lifetime. To probe the interplay of nonlocal interactions with tunneling, we investigate the short-time-relaxation dynamics of charge-density waves in the gas. We find that strong nearest-neighbor interactions slow down the relaxation. Our work opens the door for quantum simulations of systems with strong nonlocal interactions such as extended Fermi-Hubbard models.

Bad metallic transport in a cold atom Fermi-Hubbard system.

Strong interactions in many-body quantum systems complicate the interpretation of charge transport in such materials. To shed light on this problem, we study transport in a clean quantum system: ultracold lithium-6 in a two-dimensional optical lattice, a testing ground for strong interaction physics in the Fermi-Hubbard model. We determine the diffusion constant by measuring the relaxation of an imposed density modulation and modeling its decay hydrodynamically. The diffusion constant is converted to a resistivity by using the Nernst-Einstein relation. That resistivity exhibits a linear temperature dependence and shows no evidence of saturation, two characteristic signatures of a bad metal. The techniques we developed in this study may be applied to measurements of other transport quantities, including the optical conductivity and thermopower.

Spin-imbalance in a 2D Fermi-Hubbard system.

The interplay of strong interactions and magnetic fields gives rise to unusual forms of superconductivity and magnetism in quantum many-body systems. Here, we present an experimental study of the two-dimensional Fermi-Hubbard model-a paradigm for strongly correlated fermions on a lattice-in the presence of a Zeeman field and varying doping. Using site-resolved measurements, we revealed anisotropic antiferromagnetic correlations, a precursor to long-range canted order. We observed nonmonotonic behavior of the local polarization with doping for strong interactions, which we attribute to the evolution from an antiferromagnetic insulator to a metallic phase. Our results pave the way to experimentally mapping the low-temperature phase diagram of the Fermi-Hubbard model as a function of both doping and spin polarization, for which many open questions remain.

Phase Separation and Pair Condensation in a Spin-Imbalanced 2D Fermi Gas.

We study a two-component quasi-two-dimensional Fermi gas with imbalanced spin populations. We probe the gas at different interaction strengths and polarizations by measuring the density of each spin component in the trap and the pair momentum distribution after time of flight. For a wide range of experimental parameters, we observe in-trap phase separation characterized by the appearance of a spin-balanced core surrounded by a polarized gas. Our momentum space measurements indicate pair condensation in the imbalanced gas even for large polarizations where phase separation vanishes, pointing to the presence of a polarized pair condensate. Our observation of zero momentum pair condensates in 2D spin-imbalanced gases opens the way to explorations of more exotic superfluid phases that occupy a large part of the phase diagram in lower dimensions.

Quantum-gas microscope for fermionic atoms.

We realize a quantum-gas microscope for fermionic ^{40}K atoms trapped in an optical lattice, which allows one to probe strongly correlated fermions at the single-atom level. We combine 3D Raman sideband cooling with high-resolution optics to simultaneously cool and image individual atoms with single-lattice-site resolution at a detection fidelity above 95%. The imaging process leaves the atoms predominantly in the 3D motional ground state of their respective lattice sites, inviting the implementation of a Maxwell's demon to assemble low-entropy many-body states. Single-site-resolved imaging of fermions enables the direct observation of magnetic order, time-resolved measurements of the spread of particle correlations, and the detection of many-fermion entanglement.

Heavy solitons in a fermionic superfluid.

Solitons-solitary waves that maintain their shape as they propagate-occur as water waves in narrow canals, as light pulses in optical fibres and as quantum mechanical matter waves in superfluids and superconductors. Their highly nonlinear and localized nature makes them very sensitive probes of the medium in which they propagate. Here we create long-lived solitons in a strongly interacting superfluid of fermionic atoms and directly observe their motion. As the interactions are tuned from the regime of Bose-Einstein condensation of tightly bound molecules towards the Bardeen-Cooper-Schrieffer limit of long-range Cooper pairs, the solitons' effective mass increases markedly, to more than 200 times their bare mass, signalling strong quantum fluctuations. This mass enhancement is more than 50 times larger than the theoretically predicted value. Our work provides a benchmark for theories of non-equilibrium dynamics of strongly interacting fermions.

Spin-injection spectroscopy of a spin-orbit coupled Fermi gas.

The coupling of the spin of electrons to their motional state lies at the heart of recently discovered topological phases of matter. Here we create and detect spin-orbit coupling in an atomic Fermi gas, a highly controllable form of quantum degenerate matter. We directly reveal the spin-orbit gap via spin-injection spectroscopy, which characterizes the energy-momentum dispersion and spin composition of the quantum states. For energies within the spin-orbit gap, the system acts as a spin diode. We also create a spin-orbit coupled lattice and probe its spinful band structure, which features additional spin gaps and a fully gapped spectrum. In the presence of s-wave interactions, such systems should display induced p-wave pairing, topological superfluidity, and Majorana edge states.

Evolution of fermion pairing from three to two dimensions.

We follow the evolution of fermion pairing in the dimensional crossover from three-dimensional to two-dimensional as a strongly interacting Fermi gas of ^{6}Li atoms becomes confined to a stack of two-dimensional layers formed by a one-dimensional optical lattice. Decreasing the dimensionality leads to the opening of a gap in radio-frequency spectra, even on the Bardeen-Cooper-Schrieffer side of a Feshbach resonance. The measured binding energy of fermion pairs closely follows the theoretical two-body binding energy and, in the two-dimensional limit, the zero-temperature mean-field Bose-Einstein-condensation to Bardeen-Cooper-Schrieffer crossover theory.

Orbital excitation blockade and algorithmic cooling in quantum gases.

Interaction blockade occurs when strong interactions in a confined, few-body system prevent a particle from occupying an otherwise accessible quantum state. Blockade phenomena reveal the underlying granular nature of quantum systems and allow for the detection and manipulation of the constituent particles, be they electrons, spins, atoms or photons. Applications include single-electron transistors based on electronic Coulomb blockade and quantum logic gates in Rydberg atoms. Here we report a form of interaction blockade that occurs when transferring ultracold atoms between orbitals in an optical lattice. We call this orbital excitation blockade (OEB). In this system, atoms at the same lattice site undergo coherent collisions described by a contact interaction whose strength depends strongly on the orbital wavefunctions of the atoms. We induce coherent orbital excitations by modulating the lattice depth, and observe staircase-like excitation behaviour as we cross the interaction-split resonances by tuning the modulation frequency. As an application of OEB, we demonstrate algorithmic cooling of quantum gases: a sequence of reversible OEB-based quantum operations isolates the entropy in one part of the system and then an irreversible step removes the entropy from the gas. This technique may make it possible to cool quantum gases to have the ultralow entropies required for quantum simulation of strongly correlated electron systems. In addition, the close analogy between OEB and dipole blockade in Rydberg atoms provides a plan for the implementation of two-quantum-bit gates in a quantum computing architecture with natural scalability.

Photon-assisted tunneling in a biased strongly correlated Bose gas.

We study the impact of coherently generated lattice photons on an atomic Mott insulator subjected to a uniform force. Analogous to an array of tunnel-coupled and biased quantum dots, we observe sharp, interaction-shifted photon-assisted tunneling resonances corresponding to tunneling one and two lattice sites either with or against the force and resolve multiorbital shifts of these resonances. By driving a Landau-Zener sweep across such a resonance, we realize a quantum phase transition between a paramagnet and an antiferromagnet and observe quench dynamics when the system is tuned to the critical point. Direct extensions will produce gauge fields and site-resolved spin flips, for topological physics and quantum computing.

Quantum simulation of antiferromagnetic spin chains in an optical lattice.

Understanding exotic forms of magnetism in quantum mechanical systems is a central goal of modern condensed matter physics, with implications for systems ranging from high-temperature superconductors to spintronic devices. Simulating magnetic materials in the vicinity of a quantum phase transition is computationally intractable on classical computers, owing to the extreme complexity arising from quantum entanglement between the constituent magnetic spins. Here we use a degenerate Bose gas of rubidium atoms confined in an optical lattice to simulate a chain of interacting quantum Ising spins as they undergo a phase transition. Strong spin interactions are achieved through a site-occupation to pseudo-spin mapping. As we vary a magnetic field, quantum fluctuations drive a phase transition from a paramagnetic phase into an antiferromagnetic phase. In the paramagnetic phase, the interaction between the spins is overwhelmed by the applied field, which aligns the spins. In the antiferromagnetic phase, the interaction dominates and produces staggered magnetic ordering. Magnetic domain formation is observed through both in situ site-resolved imaging and noise correlation measurements. By demonstrating a route to quantum magnetism in an optical lattice, this work should facilitate further investigations of magnetic models using ultracold atoms, thereby improving our understanding of real magnetic materials.

A quantum gas microscope for detecting single atoms in a Hubbard-regime optical lattice.

Recent years have seen tremendous progress in creating complex atomic many-body quantum systems. One approach is to use macroscopic, effectively thermodynamic ensembles of ultracold atoms to create quantum gases and strongly correlated states of matter, and to analyse the bulk properties of the ensemble. For example, bosonic and fermionic atoms in a Hubbard-regime optical lattice can be used for quantum simulations of solid-state models. The opposite approach is to build up microscopic quantum systems atom-by-atom, with complete control over all degrees of freedom. The atoms or ions act as qubits and allow the realization of quantum gates, with the goal of creating highly controllable quantum information systems. Until now, the macroscopic and microscopic strategies have been fairly disconnected. Here we present a quantum gas 'microscope' that bridges the two approaches, realizing a system in which atoms of a macroscopic ensemble are detected individually and a complete set of degrees of freedom for each of them is determined through preparation and measurement. By implementing a high-resolution optical imaging system, single atoms are detected with near-unity fidelity on individual sites of a Hubbard-regime optical lattice. The lattice itself is generated by projecting a holographic mask through the imaging system. It has an arbitrary geometry, chosen to support both strong tunnel coupling between lattice sites and strong on-site confinement. Our approach can be used to directly detect strongly correlated states of matter; in the context of condensed matter simulation, this corresponds to the detection of individual electrons in the simulated crystal. Also, the quantum gas microscope may enable addressing and read-out of large-scale quantum information systems based on ultracold atoms.