• Photonics Research
  • Vol. 10, Issue 8, 1819 (2022)
Qiancheng Xu1、2, Kaiyu Cui1、2、*, Ning Wu1、2, Xue Feng1、2, Fang Liu1、2, Wei Zhang1、2、3, and Yidong Huang1、2、3
Author Affiliations
  • 1Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
  • 2Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University, Beijing 100084, China
  • 3Beijing Academy of Quantum Information Sciences, Beijing, China
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    DOI: 10.1364/PRJ.447711 Cite this Article Set citation alerts
    Qiancheng Xu, Kaiyu Cui, Ning Wu, Xue Feng, Fang Liu, Wei Zhang, Yidong Huang. Tunable mechanical-mode coupling based on nanobeam-double optomechanical cavities[J]. Photonics Research, 2022, 10(8): 1819 Copy Citation Text show less

    Abstract

    Tunable coupled mechanical resonators with nonequilibrium dynamic phenomena have attracted considerable attention in quantum simulations, quantum computations, and non-Hermitian systems. In this study, we propose tunable mechanical-mode coupling based on nanobeam-double optomechanical cavities. The excited optical mode interacts with both symmetric and antisymmetric mechanical supermodes and mediates coupling at a frequency of approximately 4.96 GHz. The mechanical-mode coupling is tuned through both optical spring and gain effects, and the reduced coupled frequency difference in non-Hermitian parameter space is observed. These results benefit research on the microscopic mechanical parity–time symmetry for topology and on-chip high-sensitivity sensors.
    x¨1+(Γm+Γopt)x˙1+(Ωm+δΩm)2x1+Ωmkx2=F1/meff,x¨2+Γmx˙2+Ωm2x2+Ωmkx1=F2/meff,

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    a˙=(iΔγo2)a+iGx1a+γocsin,x¨1=Ωm2x1Γmx˙1Ωmκx2+G|a|2/meff+F1/meff,x¨2=Ωm2x2Γmx˙2Ωmκx1+F2/meff,(B1)

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    a˙=(iΔ¯γo2)a+iGa¯x1,x¨1=Ωm2x1Γmx˙1Ωmκx2+G(a¯*a+a¯a*)/meff+F1/meff,x¨2=Ωm2x2Γmx˙2Ωmκx1+F2/meff,(B2)

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    a¯=γocsiniΔ¯+γo/2,x¯1=Ga¯2meff(Ωm2κ2),x¯2=κΩmGa¯2meff(Ωm2κ2),(B3)

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    x¨++(Γm+12Γopt)x˙++(Ωm2+Ωmκ+ΩmδΩm)x+=ΩmδΩmx12Γoptx˙+F+/meff,x¨+(Γm+12Γopt)x˙+(Ωm2Ωmκ+ΩmδΩm)x=ΩmδΩmx+12Γoptx˙++F/meff,(B4)

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    δΩm=8g2Ωmγo2+16Ωm2,Γopt=4g2γo16Ωm2γo2+16Ωm2(B5)

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    ϵ1(ω)a(ω)=iGa¯x1(ω),χ11(ω)x1(ω)=Ωmκx2(ω)+F1(ω)/meff,χ21(ω)x2(ω)=Ωmκx1(ω)+F2(ω)/meff,(B6)

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    ϵ1(ω)=i(ω+Δ¯)+γo2,χ11(ω)=Ωm2ω2iωΓmiΣ(ω),χ21(ω)=Ωm2ω2iωΓm,Σ(ω)=G2|a¯|2meff[ϵ(ω)ϵ*(ω)],(B7)

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    x1(ω)=F1/meffΩmκF2/meffχ2χ11Ωm2κ2χ2.(B8)

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    Io=|sinγoc(a¯+a)|2I¯oγoc(din*a+dina*),(B9)

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    din=(1γociΔ+γo/2)sin.(B10)

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    SII(ω)=|H(ω)|2Sxx(ω),(B11)

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    H(ω)=iγocGa¯[din*ϵ(ω)dinϵ*(ω)],(B12)

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    Sxx(ω)=1+Ωm2κ2|χ2(ω)|2|χ11(ω)Ωm2κ2χ2(ω)|2SFF(ω)meff2.(B13)

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    a˙(t)=[iΔ(t)γo2]a(t)+γcain(t),ΔT˙(t)=γthΔT(t)+ηscp,m(γlin+γFCA)|a(t)|2,N˙(t)=γfcN(t)+βfc|a(t)|4,(C1)

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    Δ(t)=ωlωo+ωo[1ndndTΔT(t)+1ndndNN(t)].(C2)

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    Qiancheng Xu, Kaiyu Cui, Ning Wu, Xue Feng, Fang Liu, Wei Zhang, Yidong Huang. Tunable mechanical-mode coupling based on nanobeam-double optomechanical cavities[J]. Photonics Research, 2022, 10(8): 1819
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