Spin-momentum-mixing interactions with cavity-mediated supersolid in spinor condensates

Jingjun You; Su Yi; Yuangang Deng

doi:10.1364/PRJ.544164

Journals >Photonics Research >Volume 13 >Issue 4 >Page 987 > Article

Photonics Research
Vol. 13, Issue 4, 987 (2025)

Spin-momentum-mixing interactions with cavity-mediated supersolid in spinor condensates

Jingjun You¹, Su Yi^2,3,4,*, and Yuangang Deng^1,5,*

Author Affiliations

¹Guangdong Provincial Key Laboratory of Quantum Metrology and Sensing & School of Physics and Astronomy, Sun Yat-sen University (Zhuhai Campus), Zhuhai 519082, China

²Institute of Fundamental Physics and Quantum Technology & School of Physics, Ningbo University, Ningbo 315211, China

³Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China

⁴e-mail: yisu@nbu.edu.cn

⁵e-mail: dengyg3@mail.sysu.edu.cn

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DOI: 10.1364/PRJ.544164 Cite this Article Set citation alerts

Jingjun You, Su Yi, Yuangang Deng, "Spin-momentum-mixing interactions with cavity-mediated supersolid in spinor condensates," Photonics Res. 13, 987 (2025) Copy Citation Text

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Abstract

Ultracold atoms with cavity-mediated long-range interactions offer a promising platform for exploring emergent quantum phenomena. Building on recent experimental progress, we propose a novel scheme to create supersolid square and plane wave phases in spin-1/2 condensates. We demonstrate that the self-ordered supersolid phase supports an undamped gapless Goldstone mode across a broad parameter regime. This proposal is comprehensively described by the two-component Tavis–Cummings model with hosting a

U (1)

symmetry. By exploiting the superradiant photon-exchange process, our approach also constructs the cavity-mediated spin-momentum-mixing interactions between highly correlated spin and momentum modes, which may open avenues for exploring spin-momentum squeezing and spatially distributed multipartite entanglement.

{\hat{H}}_{0} = ℏ Δ_{c} {\hat{a}}^{†} \hat{a} + \sum_{σ σ^{'}} \int d r {\hat{ψ}}_{σ}^{†} (r) [{\hat{h}}_{σ σ^{'}} + V_{b} (r) δ_{σ σ^{'}}] {\hat{ψ}}_{σ^{'}} (r) + \frac{1}{2} \sum_{σ σ^{'}} \frac{4 π ℏ^{2} a_{σ σ^{'}}}{m} \int d r {\hat{ψ}}_{σ}^{†} (r) {\hat{ψ}}_{σ^{'}}^{†} (r) {\hat{ψ}}_{σ^{'}} (r) {\hat{ψ}}_{σ} (r),

(1)

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{\hat{H}}_{1} = {\tilde{Δ}}_{c} {\hat{a}}^{†} \hat{a} + ω_{0} {\hat{J}}_{z} + \frac{g_{1}}{\sqrt{2}} (\hat{a} {\hat{J}}_{-}^{(1)} + \frac{g_{2}}{g_{1}} {\hat{a}}^{†} {\hat{J}}_{-}^{(2)} + H.c.),

(2)

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{\hat{H}}_{2} = \frac{1}{2} \int d r d r^{'} U_{eff} (r, r^{'}) {V_{1} {\hat{S}}_{-} (r) {\hat{S}}_{+} (r^{'}) + V_{2} {\hat{S}}_{+} (r) {\hat{S}}_{-} (r^{'}) + V_{3} [{\hat{S}}_{+} (r) {\hat{S}}_{+} (r^{'}) + H.c.]},

(3)

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{\hat{H}}_{3} = \sum_{j = 1,2} \frac{V_{j}}{2} {\hat{b}}_{↑, 0}^{†} {\hat{b}}_{↓, j}^{†} {\hat{b}}_{↑, 0} {\hat{b}}_{↓, j} + \frac{V_{3}}{2} ({\hat{b}}_{↑, 0}^{†} {\hat{b}}_{↑, 0}^{†} {\hat{b}}_{↓, 1} {\hat{b}}_{↓, 2} + H.c.) .

(4)

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{\hat{H}}_{4} = ω_{1} {\hat{b}}_{↓,1}^{†} {\hat{b}}_{↓, 1} + ω_{2} {\hat{b}}_{↓, 2}^{†} {\hat{b}}_{↓, 2} + \frac{N V_{3}}{2} ({\hat{b}}_{↓, 1} {\hat{b}}_{↓, 2} + H.c.),

(5)

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| ψ_{S} ⟩ = \exp [r ({\hat{b}}_{↓,1} {\hat{b}}_{↓,1} - {\hat{b}}_{↓,1}^{†} {\hat{b}}_{↓,1}^{†})] | 0,0 ⟩ = \frac{1}{\cosh r} \sum_{n = 0}^{\infty} {(- \tanh r)}^{n} | n, n ⟩,

(6)

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Jingjun You, Su Yi, Yuangang Deng, "Spin-momentum-mixing interactions with cavity-mediated supersolid in spinor condensates," Photonics Res. 13, 987 (2025)

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