Site-resolved imaging of a fermionic Mott insulator

Greif, Daniel; Parsons, Maxwell F.; Mazurenko, Anton; Chiu, Christie; Blatt, Sebastian; Huber, Florian; Ji, Geoffrey; Greiner, Markus

doi:10.1126/science.aad9041

Cited by 192 publications

(207 citation statements)

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“…Within the past few months, Pauli blocking was directly observed in a spin-polarized gas of 6 Li [26], and the metallic, Mott-insulating and band-insulating states of the 2D Fermi-Hubbard model have been directly detected, both in 6 Li [27], and, as reported in this paper, in 40 K. In this work, we also demonstrate the formation of local moments at half-filling as the temperature is lowered.…”

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confidence: 52%

Observation of 2D Fermionic Mott Insulators ofK40with Single-Site Resolution

et al. 2016

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We report on the site-resolved observation of characteristic states of the two-dimensional repulsive Fermi-Hubbard model, using ultracold 40 K atoms in an optical lattice. By varying the tunneling, interaction strength, and external confinement, we realize metallic, Mott-insulating, and bandinsulating states. We directly measure the local moment, which quantifies the degree of on-site magnetization, as a function of temperature and chemical potential. Entropies per particle as low as 0.99( 6) kB indicate that nearest-neighbor antiferromagnetic correlations should be detectable using spin-sensitive imaging.

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confidence: 52%

Observation of 2D Fermionic Mott Insulators ofK40with Single-Site Resolution

et al. 2016

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“…Already, Mott-insulating phases and short-range antiferromagnetic correlations have been observed, but temperatures were too high to create an antiferromagnet [12][13][14][15]. A new perspective is afforded by quantum gas microscopy [16][17][18][19][20][21][22][23][24][25][26][27][28], which allows readout of magnetic correlations at the site-resolved level [25][26][27][28]. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice of approximately 80 sites.…”

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A cold-atom Fermi–Hubbard antiferromagnet

Mazurenko

Chiu

et al. 2017

Nature

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Many exotic phenomena in strongly correlated electron systems emerge from the interplay between spin and motional degrees of freedom [1, 2]. For example, doping an antiferromagnet gives rise to interesting phases including pseudogap states and high-temperature superconductors [3]. A promising route towards achieving a complete understanding of these materials begins with analytic and computational analysis of simplified models. Quantum simulation has recently emerged as a complementary approach towards understanding these models [4][5][6][7][8]. Ultracold fermions in optical lattices offer the potential to answer open questions on the lowtemperature regime of the doped Hubbard model [9][10][11], which is thought to capture essential aspects of the cuprate superconductor phase diagram but is numerically intractable in that parameter regime. Already, Mott-insulating phases and short-range antiferromagnetic correlations have been observed, but temperatures were too high to create an antiferromagnet [12][13][14][15]. A new perspective is afforded by quantum gas microscopy [16][17][18][19][20][21][22][23][24][25][26][27][28], which allows readout of magnetic correlations at the site-resolved level [25][26][27][28]. Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice of approximately 80 sites. Using site-resolved imaging, we detect (finite-size) antiferromagnetic long-range order (LRO) 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 strong order across the entire sample, where the staggered magnetization approaches the ground-state value. Our experimental platform enables doping away from half filling, where pseudogap states and stripe ordering are expected, but theoretical methods become numerically intractable. In this regime we find that the antiferromagnetic LRO persists to hole dopings of about 15%, providing a guideline for computational methods. Our results demonstrate that quantum gas microscopy of ultracold fermions in optical lattices can now address open questions on the low-temperature Hubbard model.The Hubbard Hamiltonian is a fundamental model for spinful lattice electrons describing a competition between kinetic energy t and interaction energy U [29]. In the limiting case of half-filling (average one particle per site) and dominant interactions (U/t 1) the Hubbard model maps to the Heisenberg model [1]. There, the exchange energy J = 4t 2 /U can give rise to antiferromagnetically ordered states at low temperatures [30]. This order persists for all finite U/t, where charge fluctuations reduce the ordering strength [31]. Away from half-filling, the coupling between motional and spin degrees of freedom is expected to give rise to a rich many-body phase diagram (see Fig. 1a), which is challenging to understand theoretically due to the fermion sign problem [32]. Even so, in the thermodynamic limit com...

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“…In contrast to traditional solid state systems, quantum gases feature tunable spin polarization, dimensionality, and interaction strength. This enables the separation of quantum statistical effects from interaction-driven effects, and invites the exploration of rich phase diagrams, for example bulk Fermi gases in the BEC-BCS crossover [3][4][5][6][7][8][9][10] and Fermi-Hubbard models in optical lattices [11][12][13][14][15][16][17][18][19][20].…”

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confidence: 99%

Homogeneous Atomic Fermi Gases

et al. 2017

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We report on the creation of homogeneous Fermi gases of ultracold atoms in a uniform potential. In the momentum distribution of a spin-polarized gas, we observe the emergence of the Fermi surface and the saturated occupation of one particle per momentum state: the striking consequence of Pauli blocking in momentum space for a degenerate gas. Cooling a spin-balanced Fermi gas at unitarity, we create homogeneous superfluids and observe spatially uniform pair condensates. For thermodynamic measurements, we introduce a hybrid potential that is harmonic in one dimension and uniform in the other two. The spatially resolved compressibility reveals the superfluid transition in a spin-balanced Fermi gas, saturation in a fully polarized Fermi gas, and strong attraction in the polaronic regime of a partially polarized Fermi gas.

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Site-resolved imaging of a fermionic Mott insulator

Cited by 192 publications

References 47 publications

Observation of 2D Fermionic Mott Insulators ofK40with Single-Site Resolution

Observation of 2D Fermionic Mott Insulators ofK40with Single-Site Resolution

A cold-atom Fermi–Hubbard antiferromagnet

Homogeneous Atomic Fermi Gases

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