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Register a new userSite-resolved measurement of the spin-correlation function in the Hubbard model
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Exotic phases of matter can emerge from strong correlations in quantum many-body systems. Quantum gas microscopy affords the opportunity to study these correlations with unprecedented detail. Here we report site-resolved observations of antiferromagnetic correlations in a two-dimensional, Hubbard-regime optical lattice and demonstrate the ability to measure the spin-correlation function over any distance. We measure the in-situ distributions of the particle density and magnetic correlations, extract thermodynamic quantities from comparisons to theory, and observe statistically significant correlations over three lattice sites. The temperatures that we reach approach the limits of available numerical simulations. The direct access to many-body physics at the single-particle level demonstrated by our results will further our understanding of how the interplay of motion and magnetism gives rise to new states of matter.
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We coherently manipulate spin correlations in a two-component atomic Fermi gas loaded into an optical lattice using spatially and time-resolved Ramsey spectroscopy combined with high-resolution textit{in situ} imaging. This novel technique allows us not only to imprint spin patterns but also to probe the static magnetic structure factor at arbitrary wave vector, in particular the staggered structure factor. From a measurement along the diagonal of the $1^mathrm{st}$ Brillouin zone of the optical lattice, we determine the magnetic correlation length and the individual spatial spin correlators. At half filling, the staggered magnetic structure factor serves as a sensitive thermometer for the spin temperature, which we employ to study the thermalization of spin and density degrees of freedom during a slow quench of the lattice depth.
Elementary particles such as the electron carry several quantum numbers, for example, charge and spin. However, in an ensemble of strongly interacting particles, the emerging degrees of freedom can fundamentally differ from those of the individual constituents. Paradigmatic examples of this phenomenon are one-dimensional systems described by independent quasiparticles carrying either spin (spinon) or charge (holon). Here we report on the dynamical deconfinement of spin and charge excitations in real space following the removal of a particle in Fermi-Hubbard chains of ultracold atoms. Using space- and time-resolved quantum gas microscopy, we track the evolution of the excitations through their signatures in spin and charge correlations. By evaluating multi-point correlators, we quantify the spatial separation of the excitations in the context of fractionalization into single spinons and holons at finite temperatures.
For a Bose-Hubbard dimer, we study quenches of the site energy imbalance, taking a highly asymmetric Hamiltonian to a fully symmetric one. The ramp is carried out over a finite time that interpolates between the instantaneous and adiabatic limits. We provide results for the excess energy of the final state compared to the ground state energy of the final Hamiltonian, as a function of the quench rate. This excess energy serves as the analog of the defect density that is considered in the Kibble-Zurek picture of ramps across phase transitions. We also examine the fate of quantum `self-trapping when the ramp is not instantaneous.
We analyze real-time dynamics of the two-dimensional Bose-Hubbard model after a sudden quench starting from the Mott insulator by means of the two-dimensional tensor-network method. Calculated single-particle correlation functions are found to be in good agreement with a recent experiment [Y. Takasu {it et al.}, Sci. Adv. {bf 6}, eaba9255 (2020)], which cross validates the experiment and the numerical simulation. By estimating the phase and group velocities from the single-particle and density-density correlation functions, we predict how these velocities vary in the moderate interaction region, which will be useful for future experiments.
Entanglement is an essential property of quantum many-body systems. However, its local detection is challenging and was so far limited to spin degrees of freedom in ion chains. Here we measure entanglement between the spins of atoms located on two lattice sites in a one-dimensional Bose-Hubbard chain which features both local spin- and particle-number fluctuations. Starting with an initially localized spin impurity, we observe an outwards propagating entanglement wave and show quantitatively how entanglement in the spin sector rapidly decreases with increasing particle-number fluctuations in the chain.
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