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arXiv:1912.02637 · Physical Review A

High-precision analysis of Feshbach resonances in a Mott insulator

T. Secker, Jesse Amato-Grill, Wolfgang Ketterle, S. J. J. M. F. Kokkelmans

Published Apr 15, 2020• 6 citations
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Abstract

A coupled-channel model is developed to analyze the interaction energy shift of ultracold lithium atoms in a Mott insulator state. This refined treatment shows a better agreement with the experimental data than the standard Hubbard model.
DOI
10.1103/physreva.101.042703

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Ultracold atomic gas experiments have proven to be a versatile ground for studying quantum mechanics, quantum many-body physics, quantum simulation and computation. A precise model for two-body collisions in those systems is essential. Coupled-channels models can accurately describe the two-atom system at ultracold temperatures by detailed interaction potentials that are finetuned by just a few parameters, determined from experiment. We extend such a coupled-channels model to include the situation in a Mott insulator phase of ultracold bosonic atoms, where two atoms are confined to one lattice site. Of particular importance is the specific conversion between the on-site interaction energy, which remains finite in the lattice, and the scattering length around a Feshbach resonance that diverges. Recently spectroscopic techniques allowed for a precise experimental determination of the on-site interaction energy in a system of 7Li atoms, we analyze this data with our model to improve the precision of current lithium interaction potentials.
We perform precision measurements on a Mott-insulator quantum state of ultracold atoms with tunable interactions. We probe the dependence of the superfluid-to-Mott-insulator transition on the interaction strength and explore the limits of the standard Bose-Hubbard model description. By tuning the on-site interaction energies to values comparable to the interband separation, we are able to quantitatively measure number-dependent shifts in the excitation spectrum caused by effective multibody interactions.
Resonant interactions associated with the emergence of a bound state constitute one of the cornerstones of modern many-body physics, ranging from Kondo physics, BEC-BCS crossover, to tunable interactions at Feshbach resonances in ultracold atoms or 2D semiconductors. Here we present a Feshbach perspective on the origin of strong pairing in Fermi-Hubbard type models. We perform a theoretical analysis of interactions between charge carriers in doped Mott insulators, modeled by a near-resonant two-channel scattering problem, and find strong evidence for Feshbach-type interactions in the dx2−y2d_{x^2-y^2}dx2−y2​ channel that can support strong pairing, consistent with the established phenomenology of cuprates. Existing experimental and numerical results on hole-doped cuprates lead us to conjecture the existence of a light, long-lived, low-energy excited state of two holes with bipolaron character in these systems, which enables near-resonant interactions and can thus provide a microscopic foundation for theories of high-temperature superconductivity involving strong attraction, as assumed e.g. in BEC-BCS crossover scenarios. To put our theory to a direct test we suggest to use coincidence angle-resolved photoemission spectroscopy (cARPES), pair-tunneling measurements or less direct pump-probe experiments. The emergent Feshbach resonance we propose could also underlie superconductivity in other doped antiferromagnetic Mott insulators, as recently proposed for bilayer nickelates, highlighting its potential as a unifying strong-coupling pairing mechanism rooted in quantum magnetism.
The quantum phase transition from the Mott insulator to the superfluid phases of the bosonic atoms trapped in an optical lattice, in which the on-site interaction can be tuned by a Feshbach resonance, is investigated by a variational approach within mean-field theory. We derive an extended Bose-Hubbard model to describe this ultracold atomic system. By theoretical calculation and analysis, the phase diagram is shown clearly, and we find an exciting and novel phenomenon that is the appearance of the Mott insulator-sea (MI-sea). Meanwhile, the experimental feasibility of observing the MI-sea is discussed by analyzing the published data related to the Fashbach resonance at present. Finally, the potential application of the MI-sea for quantum information processing and quantum computation is also discussed in detail.