Erratum: Thermodynamics and Magnetic Properties of the Anisotropic 3D Hubbard Model [Phys. Rev. Lett. 112, 115301 (2014)]

Imriška, Jakub; Iazzi, Mauro; Wang, Lei; Gull, Emanuel; Greif, Daniel; Uehlinger, Thomas; Jotzu, Gregor; Tarruell, Leticia; Esslinger, Tilman; Troyer, Matthias

doi:10.1103/physrevlett.112.159903

Cited by 11 publications

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“…66, 70 We point out that questions addressed in this paper are generally important for the many ongoing experimental efforts for realizing quantum simulators of the fermionic Hubbard model. Inelastic losses in the vicinity of Feshbach resonances are fast and the experiments need to be performed rapidly to avoid strong heating of the atoms.…”

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confidence: 99%

Dynamical instabilities and transient short-range order in the fermionic Hubbard model

2015

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We study the dynamics of magnetic correlations in the half-filled fermionic Hubbard model following a fast ramp of the repulsive interaction. We use Schwinger-Keldysh self-consistent second-order perturbation theory to investigate the evolution of single-particle Green's functions and solve the non-equilibrium Bethe-Salpeter equation to study the dynamics of magnetic correlations. This approach gives us new insights into the interplay between single-particle relaxation dynamics and the growth of antiferromagnetic correlations. Depending on the ramping time and the final value of the interaction, we find different dynamical behavior which we illustrate using a dynamical phase diagram. Of particular interest is the emergence of a transient short-range ordered regime characterized by the strong initial growth of antiferromagnetic correlations followed by a decay of correlations upon thermalization. The discussed phenomena can be probed in experiments with ultracold atoms in optical lattices.

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confidence: 99%

Dynamical instabilities and transient short-range order in the fermionic Hubbard model

2015

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“…The same experiment achieved temperatures as low as T = 0.95t 2.6 T N when the lattice was configured to be isotropic [17], where T N = 0.36t is the maximal value of the Néel transition temperature [12,18,19]. Our experiments are performed with an all-optically produced [20], quantum degenerate, two-state mixture of the two lowest hyperfine ground states of fermionic 6 Li atoms, which we label | ↑ and | ↓ .…”

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“…In the context of quantum simulations, AFM phases of Ising spins have been previously engineered with bosonic atoms in an optical lattice [13] and with spin-anisotropic lattice [16]. The same experiment achieved temperatures as low as T = 0.95t 2.6 T N when the lattice was configured to be isotropic [17], where T N = 0.36t is the maximal value of the Néel transition temperature [12,18,19].…”

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Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Hart

Duarte

Yang

et al. 2015

Nature

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Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-temperature (high-Tc) superconductivity [1]. Thirty years ago, Anderson suggested that the Hubbard model, a simplified representation of fermions moving on a periodic lattice, may contain the essence of copper oxide superconductivity [2]. The Hubbard model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realise the Hubbard model with readily tunable parameters, and thus provide a platform for the systematic exploration of its phase diagram [3,4]. Realisation of strongly correlated phases, however, has been hindered by the need to cool the atoms to temperatures as low as the magnetic exchange energy, and also by the lack of reliable thermometry [5]. Here we demonstrate spin-sensitive Bragg scattering of light to measure AFM spin correlations in a realisation of the three-dimensional (3D) Hubbard model at temperatures down to 1.4 times that of the AFM phase transition. This temperature regime is beyond the range of validity of a simple high-temperature series expansion, which brings our experiment close to the limit of the capabilities of current numerical techniques. We reach these low temperatures using a unique compensated optical lattice technique [6], in which the confinement of each lattice beam is compensated by a blue-detuned laser beam. The temperature of the atoms in the lattice is deduced by comparing the light scattering to determinantal quantum Monte Carlo [7] (DQMC) and numerical linked-cluster expansion [8] (NLCE) calculations. Further refinement of the compensated lattice may produce even lower temperatures which, along with light scattering thermometry, would open avenues for achieving and characterising other novel quantum states of matter, such as the pseudogap regime of the 2D Hubbard model.A two-spin-component Fermi gas in a simple cubic optical lattice may be described by a single-band Hubbard model with nearest-neighbour tunnelling t and on-site interaction U > 0. At a density n of one atom per site, and for sufficiently large U/t there is a crossover from a 'metallic' state to a Mott insulating regime [9] as the temperature T is reduced below U . The Mott regime has been demonstrated with ultracold atoms in an optical lattice by observing the reduction of doubly occupied sites [10] and the related reduction of the global compressibility [11]. For T below the Néel ordering temperature T N , which for U t is approximately equal to the exchange energy J = 4t 2 /U , the system undergoes a phase transition to an AFM state [12]. In the context of quantum simulations, AFM phases of Ising spins have been previously engineered with bosonic atoms in an optical lattice [13] and with spin-1 2 ions [14,15]. Also, nearest-neighbour AFM correlat...

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“…In particular, fermions trapped in optical lattices can directly simulate the physics of electrons in a crystalline solid, shedding light on novel physical phenomena in materials with strong electron correlations. A major effort is devoted to the realization of the Fermi-Hubbard model at low entropies, believed to capture the essential aspects of high-T c superconductivity [6][7][8][9][10][11][12]. For bosonic atoms, a new set of experimental probes ideally suited for the observation of magnetic order and correlations has become available with the advent of quantum-gas microscopes [13][14][15], enabling high-resolution imaging of Hubbardtype lattice systems at the single-atom level.…”

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Quantum-Gas Microscope for Fermionic Atoms

et al. 2015

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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-latticesite 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. DOI: 10.1103/PhysRevLett.114.193001 PACS numbers: 37.10.De, 03.75.Ss, 37.10.Jk, 67.85.Lm The collective behavior of fermionic particles governs the structure of the elements, the workings of hightemperature superconductors and colossal magnetoresistance materials, and the properties of nuclear matter. Yet our understanding of strongly interacting Fermi systems is limited, due in part to the antisymmetry requirement on the many-fermion wave function and the resulting "fermion sign problem" [1]. In recent years, ultracold atomic quantum gases have enabled quantitative experimental tests of theories of strongly interacting fermions [2][3][4][5]. In particular, fermions trapped in optical lattices can directly simulate the physics of electrons in a crystalline solid, shedding light on novel physical phenomena in materials with strong electron correlations. A major effort is devoted to the realization of the Fermi-Hubbard model at low entropies, believed to capture the essential aspects of high-T c superconductivity [6][7][8][9][10][11][12]. For bosonic atoms, a new set of experimental probes ideally suited for the observation of magnetic order and correlations has become available with the advent of quantum-gas microscopes [13][14][15], enabling high-resolution imaging of Hubbardtype lattice systems at the single-atom level. They allowed the direct observation of spatial structures and ordering in the Bose-Hubbard model [14,16] and of the intricate correlations and dynamics in these systems [17,18]. A longstanding goal has been to realize such a quantum-gas microscope for fermionic atoms. This would enable the direct probing and control at the single-lattice-site level of strongly correlated fermion systems, in particular the Fermi-Hubbard model, in regimes that cannot be described by current theories. These prospects have sparked significant experimental efforts to realize site-resolved, highfidelity imaging of ultracold fermions, but this goal has so far remained elusive.In the present work, we realize a quantum-gas microscope for fermionic 40 K atoms by combining 3D Raman sideband cooling with a high-resolution imaging system. The imaging setup incorporates a hemispherical solid immersion lens optically contacted to the vacuum window [ Fig. 1(a)]. In ...

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Erratum: Thermodynamics and Magnetic Properties of the Anisotropic 3D Hubbard Model [Phys. Rev. Lett. 112, 115301 (2014)]

Cited by 11 publications

References 0 publications

Dynamical instabilities and transient short-range order in the fermionic Hubbard model

Dynamical instabilities and transient short-range order in the fermionic Hubbard model

Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms

Quantum-Gas Microscope for Fermionic Atoms

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