Polarons and molecules in a Fermi gas with orbital Feshbach resonance

Jin-Ge Chen, Tian-Shu Deng, Wei Yi, and Wei Zhang

Phys. Rev. A 94, 053627 – Published 28 November 2016

Abstract

We study the impurity problem in a gas of ${}^{173}{Yb}$ atoms near the recently discovered orbital Feshbach resonance. In an orbital Feshbach resonance, atoms in the electronic ground state ${}^{1}S_{0}$ interact with those in the long-lived excited ${}^{3}P_{0}$ state with magnetically tunable interactions. We consider an impurity atom with a given hyperfine spin in the ${}^{3}P_{0}$ state interacting with a single-component Fermi sea of atoms in the ground ${}^{1}S_{0}$ 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 ${}^{173}{Yb}$ 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.

Received 11 August 2016

DOI:https://doi.org/10.1103/PhysRevA.94.053627

Physics Subject Headings (PhySH)

Fermi gases Quantum fluids & solids Ultracold gases

Atomic, Molecular & Optical

Authors & Affiliations

Jin-Ge Chen^1,2, Tian-Shu Deng^3,4, Wei Yi^3,4,*, and Wei Zhang^1,2,†

¹Department of Physics, Renmin University of China, Beijing 100872, China
²Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing 100872, China
³Key Laboratory of Quantum Information, University of Science and Technology of China, Chinese Academy of Sciences, Hefei, Anhui 230026, China
⁴Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

^*wyiz@ustc.edu.cn
^†wzhangl@ruc.edu.cn

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Issue

Vol. 94, Iss. 5 — November 2016

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Images

Figure 1
Level diagram of orbital Feshbach resonance in alkaline-earth-like atoms. An impurity of $| e ↑ 〉$ is immersed in a majority Fermi sea of $| g ↓ 〉$ atoms, and can be scattered to the other two atomic states forming the closed channel via interaction. $δ_{g}$ and $δ_{e}$ are the Zeeman shifts of the $| g 〉$ and $| e 〉$ manifolds, respectively.
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Figure 2
(a, b) The eigenenergy shifted by the threshold energy $E_{th}$ , (c) the distribution of wave functions in the open and the closed channels, and (d) the effective mass are plotted for the shallow molecular state. Parameters used here are compatible with a gas of ${}^{173}{Yb}$ atoms with a number density of $n = 2 \times 10^{13} {cm}^{- 3}$ . The resonance takes place at $δ / E_{F} \approx - 5.8$ and the position $δ / E_{F} = 0$ corresponds to $1 / (k_{F} a_{s}) \approx 1.70$ within this parameter set. Notice that the effective mass diverges and changes sign at $δ / E_{F} \approx - 6.6$ , which resides on the BCS side of the resonance with $1 / (k_{F} a_{s}) \approx - 0.18$ .
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Figure 3
(a, b) Energy shifted from the threshold energy, (c) fraction of wave functions within the open-, closed-, and bare-particle-channels, and (d) the effective mass for the shallow polaron state with a fixed momentum $Q = 0$ . The effective mass diverges at $δ / E_{F} \approx - 0.35$ , corresponding to $1 / (k_{F} a_{s}) \approx 1.40$ . Parameters used are the same as in Fig. 2.
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Figure 4
(a) Dispersion of the shallow polaron state for various values of $δ$ . The zero-momentum ${| P 〉}_{Q = 0}$ state is the ground state for large negative $δ$ , which becomes a metastable state by passing through a first-order-like transition around $δ_{p} / E_{F} ≲ - 2.1$ . It eventually becomes unstable by further increasing $δ$ . All dispersion curves are shifted with respect to their corresponding zero-momentum state energy, so that they can be compared in the same plot. (b) The transition between two locally stable polaron states. The polaron state with $| Q | \sim k_{F}$ resembles the zero-center-of-mass-momentum molecular state with increasing $δ$ , as can be seen from (c) the effective mass obtained by fitting the dispersion around the global minimum and (d) the fraction of wave function distribution in the open-, closed-, and bare-particle-channels. In the BEC limit of $δ / E_{F} = 4$ , (e) the closed-channel fraction as a function of $| Q + q |$ suggests that the major contribution to the hole is close to the Fermi surface, while the results of momentum distribution of the $| e ↓ 〉$ state (f) explicitly illustrates the similarity between the finite-momentum polaron and the molecular state. Parameters used are the same as in Fig. 2.
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Figure 5
(a, b) Energies of the molecule (black solid) and the polaron (red dashed) in the shallow branch. A transition in the ground states occurs at around $δ_{c} / E_{F} \approx - 2.3$ or $1 / (k_{F} a_{c}) \approx 0.81$ . Note that this polaron-molecule transition happens before the transition between the zero-momentum and finite-momentum polaron, so that the finite-momentum polaron state is always metastable. The number density used here is $n = 2 \times 10^{13} {cm}^{- 3}$ . (c) The transition point $δ_{c}$ (black dotted) and the corresponding energy $E_{c}$ (blue solid) vary with particle density, highlighting the lack of universality of OFR. (d) The transition point $1 / (k_{F} a_{c})$ shows a nonmonotonic dependence on the effective range $k_{F} | r_{0} |$ .
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Figure 6
(a)–(c) Raman spectra with $δ / E_{F} = - 2.0$ (blue solid), $δ / E_{F} = - 2.2$ (green dotted), $δ / E_{F} = - 2.4$ (red dashed), and $δ / E_{F} = - 2.6$ (black dash-dotted). As the polaron-molecule transition point is at $δ_{c} \approx - 2.3$ , the dashed and solid lines correspond to cases of polaron and molecule, respectively. The momentum recoil of the Raman process is (a) $k_{R} / k_{F} = 0$ , (b) $k_{R} / k_{F} = 2$ , and (c) $k_{R} / k_{F} = 6$ . (d) Peak value of the ground-state Raman spectra with changing $δ$ , with $k_{R} / k_{F} = 0$ (black solid), $k_{R} / k_{F} = 2$ (red dashed), and $k_{R} / k_{F} = 6$ (blue dotted). Other parameters used are the same as in Fig. 2.
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