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 6 Li in a 2D 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 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 develop here may be applied to measurements of other transport quantities, including the optical conductivity and thermopower. arXiv:1802.09456v2 [cond-mat.quant-gas]
Simulating the real-time evolution of quantum spin systems far out of equilibrium poses a major theoretical challenge, especially in more than one dimension. We experimentally explore quench dynamics in a two-dimensional Ising spin system with transverse and longitudinal fields. We realize the system with a near unit-occupancy atomic array of over 200 atoms obtained by loading a spin-polarized band insulator of fermionic lithium into an optical lattice and induce short-range interactions by direct excitation to a lowlying Rydberg state. Using site-resolved microscopy, we probe antiferromagnetic correlations in the system after a sudden quench from a paramagnetic state and compare our measurements to numerical calculations using state-of-the-art techniques. We achieve many-body states with longer-range antiferromagnetic correlations by implementing a near-adiabatic quench of the longitudinal field and study the buildup of correlations as we vary the rate with which we change the field. Lattice quantum spin models serve as a paradigm for exploring a range of many-body phenomena, including quantum phase transitions [1,2], equilibration and thermalization [3,4], and quench dynamics [5][6][7][8][9][10]. While there exists a variety of well-developed theoretical techniques to study the equilibrium properties of quantum spin systems [11][12][13][14][15][16][17], the toolkit for simulating real-time dynamics of these systems is rather limited and can only capture the evolution accurately for short times, especially for systems in more than one dimension [11,[18][19][20]. Recent advances in the field of quantum simulation have introduced several experimental platforms where the dynamics of quantum spin systems can be measured over long evolution times, providing much needed benchmarks for testing uncontrolled theoretical approximations. Examples of such platforms include trapped ions [21-23], polar molecules [24], Rydberg atoms [25][26][27][28][29], magnetic atoms [30,31], and atoms interacting through superexchange in optical lattices [32][33][34][35][36][37].In this work, we explore the dynamics of a two-dimensional quantum Ising model using a nearly defect-free array of neutral atoms which are coupled with laser light to a lowlying Rydberg state in an optical lattice [38]. The spin coupling in the model arises due to a van der Waals interaction between atoms in the Rydberg state. If one atom is in a Rydberg state, the excitation of another atom to a Rydberg state is strongly suppressed within a blockade radius R b [39][40][41][42][43]. This is because the interaction between the Rydberg atoms within this radius is much larger than the laser coupling strength. Previous experiments in 2D arrays have studied the regime R b ≫ a l , where a l is the lattice spacing [25,28]. In this regime, the Rydberg blockade makes it difficult to access many-body states with a large Rydberg fraction. This significantly reduces the size of the relevant Hilbert space of the system from the maximum possible size of 2 N , where N is the numb...
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 [1]. The essential physics of these materials is believed to be captured by the Fermi-Hubbard model [2], a minimal model that has been realized with cold atoms in optical lattices [3, 4]. 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 [5]. We compare our measurements to predictions from Determinantal Quantum Monte Carlo (DQMC) [6] and Numerical Linked Cluster Expansion (NLCE) [7] 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.Ultracold quantum gases have emerged as a powerful tool to study strongly correlated many-body physics. A two-component Fermi gas in an optical lattice can realize the repulsive Hubbard model, which describes fermions in a periodic potential with onsite interaction U and tunneling matrix element t between neighboring sites [8]. The recent introduction of quantum gas microscopes for fermionic atoms [9][10][11][12][13][14][15] has led to rapid development in the experimental study of the 2D Hubbard model. The number-squeezed nature of the Mott insulating phasepreviously inferred from bulk measurements [3, 4]-has been explicitly revealed. Furthermore, site-resolved measurements probe antiferromagnetic correlations beyond the nearest neighbor [16][17][18], which was not possible in previous studies [19][20][21].In this work, we investigate the Fermi-Hubbard model with imbalanced spin populations described by the HamiltonianHere c † i,σ is the creation operator for a fermion with spin σ on site i and n i,σ = c † i,σ c i,σ . Theoretical studies of spin-imbalance in the Hubbard model have predicted an interesting magnetic structure in trapped gases arising from the interplay of spin-imbalance and antiferromagnetic and Stoner instabilities [22][23][24]. Experimentally, * wbakr@princeton.edu the polarization of our two-component atomic Fermi gas is a controllable quantity that is conserved due to the absence of spin-relaxation mechanisms. Thermodynamically, a non-zero polarization corresponds to the introduction of an effective Zeeman field h = (µ ↑ − µ ↓ )/2, wh...
Using quantum gas microscopy we study the late-time effective hydrodynamics of an isolated cold-atom Fermi-Hubbard system subject to an external linear potential (a "tilt"). The tilt is along one of the principal directions of the two-dimensional (2D) square lattice and couples mass transport to local heating through energy conservation. We study transport and thermalization in our system by observing the decay of prepared initial density waves as a function of wavelength λ and tilt strength and find that the associated decay time τ crosses over as the tilt strength is increased from characteristically diffusive to subdiffusive with τ ∝ λ 4 . In order to explain the underlying physics we develop a hydrodynamic model that exhibits this crossover. For strong tilts, the subdiffusive transport rate is set by a thermal diffusivity, which we are thus able to measure as a function of tilt in this regime. We further support our understanding by probing the local inverse temperature of the system at strong tilts, finding good agreement with our theoretical predictions. Finally, we discuss the relation of the strongly tilted limit of our system to recently studied 1D models which may exhibit nonergodic dynamics. arXiv:1909.05848v1 [cond-mat.quant-gas]
The attractive Fermi-Hubbard model is the simplest theoretical model for studying pairing and superconductivity of fermions on a lattice [1]. Although its s-wave pairing symmetry excludes it as a microscopic model for high-temperature superconductivity, it exhibits much of the relevant phenomenology, including a short-coherence length at intermediate coupling and a pseudogap regime with anomalous properties [2][3][4][5]. Here we study an experimental realization of this model using a two-dimensional (2D) atomic Fermi gas in an optical lattice. Our site-resolved measurements on the normal state reveal checkerboard charge-density-wave correlations close to half-filling. A "hidden" SU(2) pseudo-spin symmetry of the Hubbard model at half-filling guarantees superfluid correlations in our system [6], the first evidence for such correlations in a single-band Hubbard system of ultracold fermions. Compared to the paired atom fraction, we find the charge-density-wave correlations to be a much more sensitive thermometer, useful for optimizing cooling into superfluid phases in future experiments.
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