• Photonics Research
  • Vol. 5, Issue 5, 450 (2017)
Jian Liu1、2 and Ka-Di Zhu1、2、*
Author Affiliations
  • 1Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), 800 DongChuan Road, Shanghai 200240, China
  • 2School of Physics and Astronomy, Shanghai Jiao Tong University, 800 DongChuan Road, Shanghai 200240, China
  • show less
    DOI: 10.1364/PRJ.5.000450 Cite this Article Set citation alerts
    Jian Liu, Ka-Di Zhu. Coupled quantum molecular cavity optomechanics with surface plasmon enhancement[J]. Photonics Research, 2017, 5(5): 450 Copy Citation Text show less

    Abstract

    Cavity optomechanics is applied to study the coupling behavior of interacting molecules in surface plasmon systems driven by two-color laser beams. Different from the traditional force–distance measurement, due to a resonant frequency shift or a peak splitting on the probe spectrum, we have proposed a convenient method to measure the van der Waals force strength and interaction energy via nonlinear spectroscopy. The minimum force value can reach approximately 10?15 N, which is 3 to 4 orders of magnitude smaller than the widely applied atomic force microscope (AFM). It is also shown that two adjacent molecules with similar chemical structures and nearly equal vibrational frequencies can be easily distinguished by the splitting of the transparency peak. Based on this coupled optomechanical system, we also conceptually design a tunable optical switch by van der Waals interaction. Our results will provide new approaches for understanding the complex and dynamic interactions in molecule–plasmon systems.
    gn=αnQnωcε0Vc2ωn.(1)

    View in Article

    Vint=14πϵ0(e2R+e2R+x1x2e2R+x1e2Rx2).(2)

    View in Article

    Vint2e24πϵ0R3x1x2.(3)

    View in Article

    Hint=Vintλ(a1+a2+a1a2+)(4)

    View in Article

    λ=e24πϵ0R3m1m2ω1ω2,(5)

    View in Article

    H=Δpuc+c+Σn=1,2ωnan+anΣn=1,2gnc+c(an++an)λ(a1+a2+a1a2+)iΩpu(cc+)iΩpr(ceiδtc+eiδt),(6)

    View in Article

    dcdt=(iΔpu+κ)c+(ig1Q1+ig2Q2)c+Ωpu+Ωpreiδt+κexa^in+κ0f^in,(7)

    View in Article

    d2Q1dt2+γ1dQ1dt+(ω12+λ2)Q1λ(ω1+ω2)Q2=2(g1ω1g2λ)c+c+ξ^1,(8)

    View in Article

    d2Q2dt2+γ2dQ2dt+(ω22+λ2)Q2λ(ω1+ω2)Q1=2(g2ω2g1λ)c+c+ξ^2,(9)

    View in Article

    ξ^n+(t)ξ^n(t)=κωndω2πωeiω(tt)[1+coth(ω2κBT)].(10)

    View in Article

    c¯=Ωpui(ΔpuΣn=1,2gnQn)+κ,(11)

    View in Article

    Q1¯=[R1(ω22+λ2)+WR2]|c|2(ω12+λ2)(ω22+λ2)W2,(12)

    View in Article

    Q2¯=[R2(ω12+λ2)+WR1]|c|2(ω12+λ2)(ω22+λ2)W2.(13)

    View in Article

    c=c0+δc,Q1(t)=Q10+δQ1,Q2(t)=Q20+δQ2.(14)

    View in Article

    δc.=κδc+ig1(Q10δc+c0δQ1)+ig2(Q20δc+c0δQ2)+Ωpu+Ωpreiδt,(15)

    View in Article

    δQ¨1+γ1δQ.1+(ω12+λ2)δQ1λ(ω1+ω2)δQ2=2(g1ω1g2λ)c02,(16)

    View in Article

    δQ¨2+γ2δQ.2+(ω22+λ2)δQ2λ(ω1+ω2)δQ1=2(g2ω2g1λ)c02.(17)

    View in Article

    δc=c+eiδt+ceiδt,(18)

    View in Article

    δQ1=Q1+eiδt+Q1eiδt,(19)

    View in Article

    δQ2=Q2+eiδt+Q2eiδt.(20)

    View in Article

    c0=ΩpuiΔpu+κiδig1Q10ig2Q20,(21)

    View in Article

    c+=Ωpr+ic0(g1Q1++g2Q2+)iΔpu+κiδig1Q10ig2Q20,(22)

    View in Article

    c=ic0(g1Q1+g2Q2)iΔpu+κ+iδig1Q10ig2Q20,(23)

    View in Article

    (ω12+λ2)Q10λ(ω1+ω2)Q20=2(g1ω1g2λ)c02,(24)

    View in Article

    Q1+=λ(ω1+ω2)Q2++2(g1ω1g2λ)(c0*c++c0c*)δ2iγ1δ+ω12+λ2,(25)

    View in Article

    Q1=λ(ω1+ω2)Q2+2(g1ω1g2λ)(c0*c+c0c+*)δ2+iγ1δ+ω12+λ2,(26)

    View in Article

    (ω22+λ2)Q20λ(ω1+ω2)Q10=2(g2ω2g1λ)c02,(27)

    View in Article

    Q2+=λ(ω1+ω2)Q1++2(g2ω2g1λ)(c0*c++c0c*)δ2iγ2δ+ω22+λ2,(28)

    View in Article

    Q2=λ(ω1+ω2)Q1+2(g2ω2g1λ)(c0*c+c0c+*)δ2+iγ2δ+ω22+λ2.(29)

    View in Article

    c+=Ωpr[(A1A2W2)(TP)+Zω0](A1A2W2)(T2P2)+2PZω0,(30)

    View in Article

    Ωpu2=[κ2+(Δpug1Q10g2Q20)2]ω0(31)

    View in Article

    t(ωpr)=Ωpr/2κ2κc+Ωpr/2κ=12κc+/Ωpr.(32)

    View in Article

    Jian Liu, Ka-Di Zhu. Coupled quantum molecular cavity optomechanics with surface plasmon enhancement[J]. Photonics Research, 2017, 5(5): 450
    Download Citation