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 1015  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.

© 2017 Chinese Laser Press

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References

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2016 (9)

R. Chikkaraddy, B. Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
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S. Gwo, C. Y. Wang, H. Y. Chen, M. H. Lin, L. Sun, X. Li, W. L. Chen, Y. M. Chang, and H. Ahn, “Plasmonic metasurfaces for nonlinear optics and quantitative SERS,” ACS Photon. 3, 1371–1384 (2016).
[Crossref]

J. Prinz, C. Heck, L. Ellerik, V. Merk, and I. Bald, “DNA origami based Au-Ag-core-shell nanoparticle dimers with single-molecule SERS sensitivity,” Nanoscale 8, 5612–5620 (2016).
[Crossref]

P. Roelli, C. Galland, N. Piro, and T. J. Kippenberg, “Molecular cavity optomechanics as a theory of plasmon-enhanced Raman scattering,” Nat. Nanotechnol. 11, 164–169 (2016).
[Crossref]

M. K. Schmidt and J. Aizpurua, “Nanocavities: optomechanics goes molecular,” Nat. Nanotechnol. 11, 114–115 (2016).
[Crossref]

S. Kawai, A. S. Foster, T. Björkman, S. Nowakowska, J. Björk, F. F. Canova, L. H. Gade, T. A. Jung, and E. Meyer, “Van der Waals interactions and the limits of isolated atom models at interfaces,” Nat. Commun. 7, 11559 (2016).
[Crossref]

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 93, 053801 (2016).
[Crossref]

Y. Zhang, Y. Luo, Y. Zhang, Y. J. Yu, Y. M. Kuang, L. Zhang, Q. S. Meng, Y. Luo, J. L. Yang, Z. C. Dong, and J. G. Hou, “Visualizing coherent intermolecular dipole-dipole coupling in real space,” Nature 531, 623–627 (2016).
[Crossref]

C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. M. Sliwa, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “A Schrödinger cat living in two boxes,” Science 352, 1087–1091 (2016).
[Crossref]

2015 (2)

S. Jiang, Y. Zhang, R. Zhang, C. Hu, M. Liao, Y. Lou, J. Yang, Z. Dong, and J. G. Hou, “Distinguishing adjacent molecules on a surface using plasmon-enhanced Raman scattering,” Nat. Nanotechnol. 10, 865–869 (2015).
[Crossref]

S. P. Jarvis, M. A. Rashid, A. Sweetman, J. Leaf, S. Taylor, P. Moriarty, and J. Dunn, “Intermolecular artifacts in probe microscope images of C60 assemblies,” Phys. Rev. B 92, 241405 (2015).
[Crossref]

2014 (2)

P. C. Ma, J. Q. Zhang, Y. Xiao, M. Feng, and Z. M. Zhang, “Tunable double optomechanically induced transparency in an optomechanical system,” Phys. Rev. A 90, 043825 (2014).
[Crossref]

W. Zhu and K. B. Crozier, “Quantum mechanical limit to plasmonic enhancement as observed by surface-enhanced Raman scattering,” Nat. Commun. 5, 5228–5236 (2014).
[Crossref]

2013 (3)

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, “Directional Raman scattering from single molecules in the feed gaps of optical antennas,” Nano Lett. 13, 2194–2198 (2013).
[Crossref]

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Lou, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[Crossref]

L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, “Direct measurement of the van der Waals interaction between two Rydberg atoms,” Phys. Rev. Lett. 110, 263201 (2013).
[Crossref]

2012 (5)

J. A. Scholl, A. L. Koh, and J. A. Dionne, “Quantum plasmon resonances of individual metallic nanoparticles,” Nature 483, 421–427 (2012).
[Crossref]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

C. Humbert, O. Pluchery, E. Lacaze, A. Tadjeddine, and B. Busson, “A multiscale description of molecular adsorption on gold nanoparticles by nonlinear optical spectroscopy,” Phys. Chem. Chem. Phys. 14, 280–289 (2012).
[Crossref]

M. D. Sonntag, J. M. Klingsporn, L. K. Garibay, J. M. Roberts, J. A. Dieringer, T. Seideman, K. A. Scheidt, L. Jensen, G. C. Schatz, and R. P. Van Duyne, “Single-molecule tip-enhanced Raman spectroscopy,” J. Phys. Chem. C 116, 478–483 (2012).
[Crossref]

E. M. van Schrojenstein Lantman, T. Deckert-Gaudig, A. J. G. Mank, V. Deckert, and B. M. Weckhuysen, “Catalytic processes monitored at the nanoscale with tip-enhanced Raman spectroscopy,” Nat. Nanotechnol. 7, 583–586 (2012).
[Crossref]

2011 (2)

R. Treffer, X. Lin, E. Bailo, T. D. Gaudig, and V. Deckert, “Distinction of nucleobases-a tip-enhanced Raman approach,” Beilstein J. Nanotechnol. 2, 628–637 (2011).
[Crossref]

K. R. Brown, C. Ospelkaus, Y. Colombe, A. C. Wilson, D. Leibfried, and D. J. Wineland, “Coupled quantized mechanical oscillators,” Nature 471, 196–199 (2011).
[Crossref]

2010 (2)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

D. R. Ward, F. Hüer, F. Pauly, J. C. Cuevas, and D. Natelson, “Optical rectification and field enhancement in a plasmonic nanogap,” Nat. Nanotechnol. 5, 732–736 (2010).
[Crossref]

2009 (1)

S. Berweger, C. C. Neacsu, Y. Mao, H. Zhou, S. S. Wong, and M. B. Raschke, “Optical nanocrystallography with tip-enhanced phonon Raman spectroscopy,” Nat. Nanotechnol. 4, 496–499 (2009).
[Crossref]

2008 (4)

J. P. Camden, J. A. Dieringer, Y. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130, 12616–12617 (2008).
[Crossref]

J. Steidtner and B. Pettinger, “Tip-enhanced Raman spectroscopy and microscopy on single dye molecules with 15  nm resolution,” Phys. Rev. Lett. 100, 236101 (2008).
[Crossref]

X. M. Qian and S. M. Nie, “Single-molecule and single-nanoparticle SERS: from fundamental mechanisms to biomedical applications,” Chem. Soc. Rev. 37, 912–920 (2008).
[Crossref]

C. Gourier, A. Jegou, J. Husson, and F. Pincet, “A nanospring named erythrocyte. The biomembrane force probe,” Cell. Mol. Bioeng. 1, 263–275 (2008).
[Crossref]

2005 (1)

P. Mülschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[Crossref]

2001 (2)

T. Hugel and M. Seitz, “The study of molecular interactions by AFM force spectroscopy,” Macromol. Rapid Commun. 22, 989–1016 (2001).
[Crossref]

V. Giovannetti and D. Vitali, “Phase-noise measurement in a cavity with a movable mirror undergoing quantum Brownian motion,” Phys. Rev. A 63, 023812 (2001).
[Crossref]

1997 (1)

S. Nie and S. R. Emory, “Probing single molecules and single nanoparticles by surface-enhanced Raman scattering,” Science 275, 1102–1106 (1997).
[Crossref]

1992 (1)

S. B. Smith, L. Finzi, and C. Bustamante, “Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads,” Science 258, 1122–1126 (1992).
[Crossref]

Ahn, H.

S. Gwo, C. Y. Wang, H. Y. Chen, M. H. Lin, L. Sun, X. Li, W. L. Chen, Y. M. Chang, and H. Ahn, “Plasmonic metasurfaces for nonlinear optics and quantitative SERS,” ACS Photon. 3, 1371–1384 (2016).
[Crossref]

Aizpurua, J.

M. K. Schmidt and J. Aizpurua, “Nanocavities: optomechanics goes molecular,” Nat. Nanotechnol. 11, 114–115 (2016).
[Crossref]

R. Zhang, Y. Zhang, Z. C. Dong, S. Jiang, C. Zhang, L. G. Chen, L. Zhang, Y. Liao, J. Aizpurua, Y. Lou, J. L. Yang, and J. G. Hou, “Chemical mapping of a single molecule by plasmon-enhanced Raman scattering,” Nature 498, 82–86 (2013).
[Crossref]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

Arcizet, O.

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

Axline, C.

C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. M. Sliwa, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “A Schrödinger cat living in two boxes,” Science 352, 1087–1091 (2016).
[Crossref]

Bailo, E.

R. Treffer, X. Lin, E. Bailo, T. D. Gaudig, and V. Deckert, “Distinction of nucleobases-a tip-enhanced Raman approach,” Beilstein J. Nanotechnol. 2, 628–637 (2011).
[Crossref]

Bald, I.

J. Prinz, C. Heck, L. Ellerik, V. Merk, and I. Bald, “DNA origami based Au-Ag-core-shell nanoparticle dimers with single-molecule SERS sensitivity,” Nanoscale 8, 5612–5620 (2016).
[Crossref]

Barrow, S. J.

R. Chikkaraddy, B. Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
[Crossref]

Baumberg, J. J.

R. Chikkaraddy, B. Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
[Crossref]

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

Béguin, L.

L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, “Direct measurement of the van der Waals interaction between two Rydberg atoms,” Phys. Rev. Lett. 110, 263201 (2013).
[Crossref]

Benz, F.

R. Chikkaraddy, B. Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, “Single-molecule strong coupling at room temperature in plasmonic nanocavities,” Nature 535, 127–130 (2016).
[Crossref]

Berweger, S.

S. Berweger, C. C. Neacsu, Y. Mao, H. Zhou, S. S. Wong, and M. B. Raschke, “Optical nanocrystallography with tip-enhanced phonon Raman spectroscopy,” Nat. Nanotechnol. 4, 496–499 (2009).
[Crossref]

Best, M. D.

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, “Directional Raman scattering from single molecules in the feed gaps of optical antennas,” Nano Lett. 13, 2194–2198 (2013).
[Crossref]

Björk, J.

S. Kawai, A. S. Foster, T. Björkman, S. Nowakowska, J. Björk, F. F. Canova, L. H. Gade, T. A. Jung, and E. Meyer, “Van der Waals interactions and the limits of isolated atom models at interfaces,” Nat. Commun. 7, 11559 (2016).
[Crossref]

Björkman, T.

S. Kawai, A. S. Foster, T. Björkman, S. Nowakowska, J. Björk, F. F. Canova, L. H. Gade, T. A. Jung, and E. Meyer, “Van der Waals interactions and the limits of isolated atom models at interfaces,” Nat. Commun. 7, 11559 (2016).
[Crossref]

Blumoff, J.

C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. M. Sliwa, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “A Schrödinger cat living in two boxes,” Science 352, 1087–1091 (2016).
[Crossref]

Borisov, A. G.

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491, 574–577 (2012).
[Crossref]

Browaeys, A.

L. Béguin, A. Vernier, R. Chicireanu, T. Lahaye, and A. Browaeys, “Direct measurement of the van der Waals interaction between two Rydberg atoms,” Phys. Rev. Lett. 110, 263201 (2013).
[Crossref]

Brown, K. R.

K. R. Brown, C. Ospelkaus, Y. Colombe, A. C. Wilson, D. Leibfried, and D. J. Wineland, “Coupled quantized mechanical oscillators,” Nature 471, 196–199 (2011).
[Crossref]

Busson, B.

C. Humbert, O. Pluchery, E. Lacaze, A. Tadjeddine, and B. Busson, “A multiscale description of molecular adsorption on gold nanoparticles by nonlinear optical spectroscopy,” Phys. Chem. Chem. Phys. 14, 280–289 (2012).
[Crossref]

Bustamante, C.

S. B. Smith, L. Finzi, and C. Bustamante, “Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads,” Science 258, 1122–1126 (1992).
[Crossref]

Camden, J. P.

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, “Directional Raman scattering from single molecules in the feed gaps of optical antennas,” Nano Lett. 13, 2194–2198 (2013).
[Crossref]

J. P. Camden, J. A. Dieringer, Y. Wang, D. J. Masiello, L. D. Marks, G. C. Schatz, and R. P. Van Duyne, “Probing the structure of single-molecule surface-enhanced Raman scattering hot spots,” J. Am. Chem. Soc. 130, 12616–12617 (2008).
[Crossref]

Canova, F. F.

S. Kawai, A. S. Foster, T. Björkman, S. Nowakowska, J. Björk, F. F. Canova, L. H. Gade, T. A. Jung, and E. Meyer, “Van der Waals interactions and the limits of isolated atom models at interfaces,” Nat. Commun. 7, 11559 (2016).
[Crossref]

Casey, K.

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 93, 053801 (2016).
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J. Am. Chem. Soc. (1)

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Figures (4)

Fig. 1.
Fig. 1.

(a) Diagram of surface plasmon cavity optomechanical system driven by a strong pump laser and probed by a weak signal laser. The double molecules reside on the substrate. (b) Molecules of thiophenol and GBT in their lowest energy conformations. (c) Interacting molecules with R the intermolecular distance, and x1 and x2 the distances between different charges for the instantaneous dipoles.

Fig. 2.
Fig. 2.

(a) Transmission spectrum of the probe beam as a function of the probe–pump detuning with different van der Waals coupling rates for the same molecules (GBT). We choose λ=0,0.2,and0.4  THz; and Δp=0. The other parameters are Ωpu2=0.22  eV2, ω1=ω2=32.2  THz, g1=g2=70  GHz, κ/(2π)=33  THz, and γ1,2/(2π)=0.06  THz. (b) Energy levels of the coupled system corresponding to the transmission peak shift. (c) Linear relationship between frequency shift and coupling rate.

Fig. 3.
Fig. 3.

(a) Transmission spectrum of the probe beam as a function of the probe–pump detuning with various van der Waals coupling rates for different two molecules (thiophenol and GBT). We choose λ=0,0.1,and0.4  THz; Δp=0; Ωpu2=0.22  eV2; and ω1=32.1  THz, ω2=32.2  THz, g1=4.7  GHz, g2=70  GHz, κ/(2π)=33  THz, γ1,2/(2π)=0.06  THz. (b) Energy levels of the coupled system corresponding to the enhanced peak splitting. (c) Linear relationship between split distance D and coupling rate λ.

Fig. 4.
Fig. 4.

Transmission and reflection spectrum of a signal beam with different range between molecules (thiophenol and GBT) in the case of Ωpu2=0.09  eV2. Other parameters are same with Fig. 2.

Equations (32)

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gn=αnQnωcε0Vc2ωn.
Vint=14πϵ0(e2R+e2R+x1x2e2R+x1e2Rx2).
Vint2e24πϵ0R3x1x2.
Hint=Vintλ(a1+a2+a1a2+)
λ=e24πϵ0R3m1m2ω1ω2,
H=Δpuc+c+Σn=1,2ωnan+anΣn=1,2gnc+c(an++an)λ(a1+a2+a1a2+)iΩpu(cc+)iΩpr(ceiδtc+eiδt),
dcdt=(iΔpu+κ)c+(ig1Q1+ig2Q2)c+Ωpu+Ωpreiδt+κexa^in+κ0f^in,
d2Q1dt2+γ1dQ1dt+(ω12+λ2)Q1λ(ω1+ω2)Q2=2(g1ω1g2λ)c+c+ξ^1,
d2Q2dt2+γ2dQ2dt+(ω22+λ2)Q2λ(ω1+ω2)Q1=2(g2ω2g1λ)c+c+ξ^2,
ξ^n+(t)ξ^n(t)=κωndω2πωeiω(tt)[1+coth(ω2κBT)].
c¯=Ωpui(ΔpuΣn=1,2gnQn)+κ,
Q1¯=[R1(ω22+λ2)+WR2]|c|2(ω12+λ2)(ω22+λ2)W2,
Q2¯=[R2(ω12+λ2)+WR1]|c|2(ω12+λ2)(ω22+λ2)W2.
c=c0+δc,Q1(t)=Q10+δQ1,Q2(t)=Q20+δQ2.
δc.=κδc+ig1(Q10δc+c0δQ1)+ig2(Q20δc+c0δQ2)+Ωpu+Ωpreiδt,
δQ¨1+γ1δQ.1+(ω12+λ2)δQ1λ(ω1+ω2)δQ2=2(g1ω1g2λ)c02,
δQ¨2+γ2δQ.2+(ω22+λ2)δQ2λ(ω1+ω2)δQ1=2(g2ω2g1λ)c02.
δc=c+eiδt+ceiδt,
δQ1=Q1+eiδt+Q1eiδt,
δQ2=Q2+eiδt+Q2eiδt.
c0=ΩpuiΔpu+κiδig1Q10ig2Q20,
c+=Ωpr+ic0(g1Q1++g2Q2+)iΔpu+κiδig1Q10ig2Q20,
c=ic0(g1Q1+g2Q2)iΔpu+κ+iδig1Q10ig2Q20,
(ω12+λ2)Q10λ(ω1+ω2)Q20=2(g1ω1g2λ)c02,
Q1+=λ(ω1+ω2)Q2++2(g1ω1g2λ)(c0*c++c0c*)δ2iγ1δ+ω12+λ2,
Q1=λ(ω1+ω2)Q2+2(g1ω1g2λ)(c0*c+c0c+*)δ2+iγ1δ+ω12+λ2,
(ω22+λ2)Q20λ(ω1+ω2)Q10=2(g2ω2g1λ)c02,
Q2+=λ(ω1+ω2)Q1++2(g2ω2g1λ)(c0*c++c0c*)δ2iγ2δ+ω22+λ2,
Q2=λ(ω1+ω2)Q1+2(g2ω2g1λ)(c0*c+c0c+*)δ2+iγ2δ+ω22+λ2.
c+=Ωpr[(A1A2W2)(TP)+Zω0](A1A2W2)(T2P2)+2PZω0,
Ωpu2=[κ2+(Δpug1Q10g2Q20)2]ω0
t(ωpr)=Ωpr/2κ2κc+Ωpr/2κ=12κc+/Ωpr.

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