Generating Giant Vortex in a Fermi Superfluid via Spin-Orbital-Angular-Momentum Coupling

Ke-Ji Chen, Fan Wu, Shi-Guo Peng, Wei Yi, and Lianyi He

Phys. Rev. Lett. 125, 260407 – Published 31 December 2020

Abstract

Spin-orbital-angular-momentum (SOAM) coupling has been realized in recent experiments of Bose-Einstein condensates [Chen et al., Phys. Rev. Lett. 121, 113204 (2018) and Zhang et al., Phys. Rev. Lett. 122, 110402 (2019)], where the orbital angular momentum imprinted upon bosons leads to quantized vortices. For fermions, such an exotic synthetic gauge field can provide fertile ground for fascinating pairing schemes and rich superfluid phases, which are yet to be explored. Here we demonstrate how SOAM coupling stabilizes vortices in Fermi superfluids through a unique mechanism that can be viewed as the angular analog to that of the spin-orbit-coupling-induced Fulde-Ferrell state under a Fermi surface deformation. Remarkably, the vortex size is comparable with the beam waist of Raman lasers generating the SOAM coupling, which is typically much larger than previously observed vortices in Fermi superfluids. With tunable size and core structure, these giant vortex states provide unprecedented experimental access to topological defects in Fermi superfluids.

Received 30 June 2020
Accepted 10 December 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.260407

Physics Subject Headings (PhySH)

Fermionic condensates Spin-orbit coupling

Ultracold gases

Atomic, Molecular & Optical

Authors & Affiliations

Ke-Ji Chen ^1,*, Fan Wu ^1,*, Shi-Guo Peng ², Wei Yi^3,4,†, and Lianyi He ^1,‡

¹Department of Physics and State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China
²State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
³CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
⁴CAS Center For Excellence in Quantum Information and Quantum Physics, Hefei 230026, China

^*These authors contributed equally to this work.
^†wyiz@ustc.edu.cn
^‡lianyi@mail.tsinghua.edu.cn

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Vol. 125, Iss. 26 — 31 December 2020

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Images

Figure 1
(a) A pair of copropagating Raman beams carrying different orbital angular momenta ( $- l_{1} ℏ$ and $- l_{2} ℏ$ ) induce SOAM coupling in atoms, with a transferred angular momentum $2 l ℏ = (l_{1} - l_{2}) ℏ$ . (b) Schematic illustration of the level scheme. (c),(d) Single-particle energy spectra under SOAM coupling for $δ = 0$ (c), and $δ / E_{F} = 0.4$ (d). Black dashed lines denote potential Fermi surfaces in a many-body setting. The parameters are $l = 3$ , $Ω_{0} / E_{F} = 0.2$ , $k_{F} w = 15$ , and $k_{F} R = 15$ . Here the Fermi wave vector $k_{F}$ is defined through the density $n_{0} = k_{F}^{2} / (2 π)$ of a uniform Fermi gas in the area $S = π R^{2}$ , and $E_{F} = ℏ^{2} k_{F}^{2} / (2 M)$ .
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Figure 2
(a) Phase diagram of a two-dimensional Fermi superfluid with SOAM coupling in the $Ω_{0} − δ$ plane.We fix $l = 3$ , and the interaction strength is chosen as $E_{B} / E_{F} = 0.5$ . The phase diagram includes the usual superfluid state with $κ = 0$ , the normal state with $Δ = 0$ , and two vortex states with $κ = - 1$ : a fully gapped vortex state ( $V 1$ ) and a gapless vortex state ( $V 2$ ). (b),(c) Free energies $F$ of the superfluid ( $κ = 0$ ; red dashed), vortex ( $κ = - 1$ ; blue solid) and normal (black dotted) states as functions of $δ$ , with $Ω_{0} / E_{F} = 2$ (b) and $Ω_{0} / E_{F} = 0.5$ (c). The parameters $k_{F} w$ and $k_{F} R$ are the same as those in Fig. 1.
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Figure 3
Energy spectra and vortex-core structures for the SF state with $δ / E_{F} = 0.48$ [(a),(b)], the $V 1$ state with $δ / E_{F} = 0.84$ [(c),(d)], and the $V 2$ state with $δ / E_{F} = 1.05$ [(e),(f)]. In the energy spectra (a),(c),(e), different eigenstates are color coded according to the ratio $\sqrt{⟨ r^{2} ⟩} / R$ , with the root-mean-square of the radius $⟨ r^{2} ⟩ = \sum_{σ} \int d r r^{2} (| u_{σ m n} |^{2} + | v_{σ m n} |^{2})$ . The CdGM states are indicated by black dots in (c). In (b),(d),(f), the blue dash-dotted correspond to the order parameter profile, and red solid (dashed) lines are the radial density profiles of the spin-down (up) atoms, respectively. The radial density is calculated through $n_{σ} (r) = (1 / 2 π) \int d θ n_{σ} (r)$ . Here we take $Ω_{0} / E_{F} = 1.2$ and other parameters are the same as those in Fig. 2.
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Figure 4
Order parameter profiles for $k_{F} w = 5$ (blue solid), $k_{F} w = 10$ (black dashed), and $k_{F} w = 15$ (red dash-dotted). We fix $δ / E_{F} = 0.84$ and $k_{F} R = 15$ , with other parameters the same as those in Fig. 3.
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Figure 5
(a) Densities of the two spin components at the trap center, $n_{σ} (r = 0)$ , as a function of the detuning $δ$ . The blue solid (red dashed) curve denotes the spin-down (spin-up) component. (b),(c) Local densities of state $D_{σ} (r, E)$ for $δ / E_{F} = 0.24$ (b) and $δ / E_{F} = 0.6$ (c). The upper (lower) layer shows the local density of state of the spin-down (spin-up) component. The red circle in (c) indicates the occupied CdGM state responsible for the spin imbalance at $r = 0$ . Here we take $Ω_{0} / E_{F} = 2$ and other parameters are the same as those in Fig. 2.
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