Three-Component Ultracold Fermi Gases with Spin-Orbit Coupling

Lihong Zhou, Xiaoling Cui, and Wei Yi

Phys. Rev. Lett. 112, 195301 – Published 12 May 2014

Abstract

We investigate the pairing physics in a three-component Fermi-Fermi mixture, where a few fermionic impurities are immersed in a noninteracting two-component Fermi gas with synthetic spin-orbit coupling (SOC), and interact attractively with one spin species in the Fermi gas. Because of the interplay of SOC and the spin-selective interaction, the molecular state intrinsically acquires a nonzero center-of-mass momentum, which results in a new type of Fulde-Ferrell (FF) pairing in spin-orbit coupled Fermi systems. The existence of the Fermi sea can also lead to the competition between FF-like molecular states with different center-of-mass momenta, which corresponds to a first-order transition between FF phases in the thermodynamic limit. As the interaction strength is tuned, a polaron-molecule transition occurs in the highly imbalanced system, where the boundary varies nonmonotonically with SOC parameters and gives rise to the reentrance of polaron states. The rich physics in this system can be probed using existing experimental techniques.

Received 8 April 2014

DOI:https://doi.org/10.1103/PhysRevLett.112.195301

Authors & Affiliations

Lihong Zhou¹, Xiaoling Cui^1,*, and Wei Yi^2,3,†

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Key Laboratory of Quantum Information, University of Science and Technology of China, CAS, Hefei, Anhui 230026, People’s Republic of China
³Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China

^*xlcui@iphy.ac.cn
^†wyiz@ustc.edu.cn

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Vol. 112, Iss. 19 — 16 May 2014

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Figure 1
Schematics of the three-component Fermi-Fermi mixture. The impurity atoms interact spin-selectively with a spin-orbit coupled two-component Fermi gas. The spin superpositions in both helicity branches are momentum dependent, as characterized by $θ_{k}$ (see text). The pairing states naturally acquire a nonzero c.m. momentum in the system.
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Figure 2
(a) Two-body bound state energies as functions of interaction strength for $η = 1$ , with $h / E_{0} = 0.2$ (solid line), $h / E_{0} = 0.4$ (dashed line), $h / E_{0} = 1$ (dash-dotted line), and $h / E_{0} = 2$ (dotted line). (b) Center-of-mass momentum of bound states in (a). (c) Two-body bound state threshold for varying $h$ and a fixed $α k_{0} / E_{0} = 1$ , with the mass ratio $η = 1$ (solid line), $η = 6 / 40$ (dashed line), and $η = 40 / 6$ (dash-dotted line). (d) Typical probability distribution of the two-body wave function in the lower helicity branch, $| φ_{k, -} |^{2}$ , in the $k_{z} = 0$ plane, with $α k_{0} / E_{0} = 1$ , $h / E_{0} = 0.2$ , $(k_{0} a_{s})^{- 1} = 0.5$ , and $η = 1$ . The threshold energy $E_{th}$ and the unit of energy $E_{0}$ are defined in the text.
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Figure 3
(a) Molecular energies relative to the Fermi surface $E_{h}$ as functions of the center-of-mass momentum $Q_{x}$ for $(k_{F} a_{s})^{- 1} = 0.5$ , with $h / E_{F} = 1.2$ (solid line), $h / E_{F} = 1$ (dashed line), and $h / E_{F} = 0.8$ (dash-dotted line). (b) Normalized molecular energies as functions of $Q_{x}$ for $h / E_{F} = 1$ , with $(k_{F} a_{s})^{- 1} = 0.57$ (solid line), $(k_{F} a_{s})^{- 1} = 0.6$ (dashed line), and $(k_{F} a_{s})^{- 1} = 0.7$ (dash-dotted line). The normalization in (b) is with respect to the molecular energies $E_{M 0}$ at $Q_{x} / k_{F} = - 1.5$ . For both figures, $α k_{F} / E_{F} = 0.5$ , and the mass ratio $η = 40 / 6$ corresponds to the case of a Li-K-K mixture.
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Figure 4
(a) Comparison of molecular and polaron energies for a fixed $α k_{F} / E_{F} = 0.5$ , and different $(k_{F} a_{s})^{- 1}$ , where $(k_{F} a_{s})^{- 1} = 0.8$ (solid line), $(k_{F} a_{s})^{- 1} = 0.9$ (dashed line), and $(k_{F} a_{s})^{- 1} = 1$ (dash-dotted line). The thin red curves represent polaron energy $E_{p} / E_{F}$ , while the thick blue curves represent the molecular energy relative to the Fermi surface $(E_{M} - E_{h}) / E_{F}$ . The vertical dotted line marks the boundary between parameter regions with one Fermi surface (1FS) and with two Fermi surfaces (2FS). (b) Boundary of polaron-molecule transition, with $α k_{F} / E_{F} = 0.2$ (solid line), $α k_{F} / E_{F} = 0.5$ (dashed line), $α k_{F} / E_{F} = 1$ (dash-dotted line). In all cases, the mass ratio $η = 1$ .
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Figure 5
(a) Ground state c.m. momentum $Q_{x}$ (solid, left $y$ axis) and pairing gap $Δ_{Q}$ (dashed, right $y$ axis) as functions of $1 / (k_{0} a_{s})$ . Here we choose $(h, μ_{a}, μ_{b}) = (0.5, 0.75, 1) E_{0}$ . (b) Phase diagram in the [ $μ_{b} / E_{0}, (k_{0} a_{s})^{- 1}$ ] plane. The red (blue) curve shows the N-FF1 (FF1-FF2) transition boundary, where both boundaries are of first order. $h$ and $μ_{a}$ are the same as in (a) and (b). In all cases, the mass ratio $η = 40 / 6$ .
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