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arXiv:1710.00785 · The European Physical Journal D

Polaronic and dressed molecular states in orbital Feshbach resonances

Junjun Xu, Ran Qi

Published Apr 1, 2018• 4 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2018-90010-6

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Classification of Feshbach resonances in electron-molecule scattering

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•Jan 1, 1976•1 citation
We study the impurity problem in a gas of 173Yb^{173}\mathrm{Yb}173Yb atoms near the recently discovered orbital Feshbach resonance. In an orbital Feshbach resonance, atoms in the electronic ground state 1S0^{1}S_{0}1S0​ interact with those in the long-lived excited 3P0^{3}P_{0}3P0​ state with magnetically tunable interactions. We consider an impurity atom with a given hyperfine spin in the 3P0^{3}P_{0}3P0​ state interacting with a single-component Fermi sea of atoms in the ground 1S0^{1}S_{0}1S0​ manifold. Close to the orbital Feshbach resonance, the impurity can induce collective particle-hole excitations out of the Fermi sea, which can be regarded as the polaron state. As the magnetic field decreases, a molecular state becomes the ground state of the system. We show that a polaron to molecule transition exists in 173Yb^{173}\mathrm{Yb}173Yb atoms close to the orbital Feshbach resonance. Furthermore, due to the spin-exchange nature of the orbital Feshbach resonance, the formation of both the polaron and the molecule involve spin-flipping processes with interesting density distributions among the relevant hyperfine spin states. We show that the polaron to molecule transition can be detected using Raman spectroscopy.
We show that the essential properties of a Feshbach resonance in cold atomic gases can be tuned by dressing the atomic states in different scattering channels through inter-channel couplings. Such a scheme can be readily implemented in the orbital Feshbach resonance of alkaline-earth-metal-like atoms by coupling hyperfine states in the clock-state manifolds. Using 173Yb^{173}\mathrm{Yb}173Yb atoms as an example, we find that both the resonance position and the two-body bound-state energy depend sensitively on the inter-channel coupling strength, which offers control parameters in tuning the inter-atomic interactions. We also demonstrate the dramatic impact of the dressed Feshbach resonance on many-body processes such as the polaron to molecule transition and the BCS-BEC crossover.
The properties of impurities immersed in a large Fermi sea are naturally described in terms of dressed quasiparticles: attractive and repulsive polarons, and dressed molecules. Motivated by recent experiments on narrow Feshbach resonances, we analyze here how the quasiparticle properties are affected by a non-zero resonance range. We find two interesting analytic results. For large range, the ground-state energy close to resonance is shown to become perturbative in the inverse range. In the limit of broad resonance instead, we provide a new Tan's relation linking the impurity ground-state energy E ↓ to the number of atoms in its dressing cloud Δ N . As a corollary, at unitarity one finds Δ N =− E ↓ / F , with F the Fermi energy of the bath.