Abstract

The high frequency and ultrasmall mass of graphene make it an ideal material for ultrasensitive mass sensing. In this article, based on the all-optical technique, we propose a scheme of an optical mass sensor to weigh the mass of a single atom or molecule via a doubly clamped Z-shaped graphene nanoribbon (GNR). We use the detection of shifts in the resonance frequency of the Z-shaped GNR to determine the mass of an external particle landing on the GNR. The highly sensitive mass sensor proposed here can weigh particles down to the yoctogram and may eventually be enable to realize the mass measurement of nucleons.

© 2013 Optical Society of America

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  30. E. K. Irish, “Generalized rotating-wave approximation for arbitrarily large coupling,” Phys. Rev. Lett. 99, 173601 (2007).
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    [CrossRef]

2013

O. K. Kwon, K. Kim, J. Park, and J. W. Kang, “Molecular dynamics modeling and simulations of graphene-nanoribbon-resonator-based nanobalance as yoctogram resolution detector,” Comput. Mater. Sci. 67, 329–333 (2013).
[CrossRef]

F. Liu and M. Hossein-Zadeh, “Mass sensing with optomechanical oscillation,” IEEE Sens. J. 13, 146–147 (2013).
[CrossRef]

S. Y. Kim, S. Cho, J. W. Kang, and O. K. Kwon, “Molecular dynamics simulation study on mechanical responses of nanoindented monolayer-graphene-nanoribbon,” Phys. E 54, 118–124 (2013).
[CrossRef]

2012

J. W. Kang, J. H. Lee, H. J. Hwang, and K. Kim, “Developing accelerometer based on graphene nanoribbon resonators,” Phys. Lett. A 376, 3248–3255 (2012).
[CrossRef]

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12, 844–849 (2012).
[CrossRef]

K. S. Novoselov, V. I. Falko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[CrossRef]

I. Wilson-Rae, C. Galland, W. Zwerger, and A. Imamoglu, “Exciton-assisted optomechanics with suspended carbon nanotubes,” New J. Phys. 14, 115003 (2012).
[CrossRef]

2011

J. J. Li and K. D. Zhu, “Plasmon-assisted mass sensing in a hybrid nanocrystal coupled to a nanomechanical resonator,” Phys. Rev. B 83, 245421 (2011).
[CrossRef]

C. Jiang, B. Chen, J. J. Li, and K. D. Zhu, “Mass sensing based on a circuit cavity electromechanical system,” J. Appl. Phys. 110, 083107 (2011).
[CrossRef]

D. Prezzi, D. Varsano, A. Ruini, and E. Molinari, “Quantum dot states and optical excitations of edge-modulated graphene nanoribbons,” Phys. Rev. B 84, 041401(R) (2011).
[CrossRef]

S. Roche, “Nanoelectronics: graphene gets a better gap,” Nat. Nanotechnol. 6, 8–9 (2011).
[CrossRef]

Z. Yie, M. A. Zielke, C. B. Burgner, and K. L. Turner, “Comparison of parametric and linear mass detection in the presence of detection noise,” J. Micromech. Microeng. 21, 025027 (2011).
[CrossRef]

2010

M. Sadeghi and R. Naghdabadi, “Nonlinear vibrational analysis of single-layer graphene sheets,” Nanotechnology 21, 105705 (2010).
[CrossRef]

A. M. van der Zande, R. A. Barton, J. S. Alden, C. S. Ruiz-Vargas, W. S. Whitney, P. H. Q. Pham, J. Park, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Large-scale arrays of single-layer graphene resonators,” Nano Lett. 10, 4869–4873 (2010).
[CrossRef]

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]

J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, A. P. Muoth, M. Seitsonen, M. Saleh, X. Feng, K. Muellen, and R. Fasel, “Atomically precise bottom-up fabrication of graphene nanoribbons,” Nature 466, 470–473 (2010).
[CrossRef]

D. Wei and Y. Liu, “Controllable synthesis of graphene and its applications,” Adv. Mater. 22, 3225–3241 (2010).
[CrossRef]

2009

C. Chen, S. Rosenblatt, K. I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. L. Stormer, T. F. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nat. Nanotechnol. 4, 861–867 (2009).
[CrossRef]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

G. P. Guo, Z. R. Lin, T. Tu, G. Cao, X. P. Li, and G. C. Guo, “Quantum computation with graphene nanoribbon,” New J. Phys. 11, 123005 (2009).
[CrossRef]

S. Y. Kim and H. S. Park, “The importance of edge effects on the intrinsic loss mechanisms of graphene nanoresonators,” Nano Lett. 9, 969–974 (2009).
[CrossRef]

2008

A. Sakhaee-Pour, M. T. Ahmadian, and R. Naghdabadi, “Vibrational analysis of single-layered graphene sheets,” Nanotechnology 19, 085702 (2008).
[CrossRef]

H. Y. Chiu, P. Hung, H. W. C. Postma, and M. Bockrath, “Atomic-scale mass sensing using carbon nanotube resoantors,” Nano Lett. 8, 4342–4346 (2008).
[CrossRef]

C. Lee, X. D. Wei, J. W. Kysar, and J. Hone, “Measurement of the elastic property and intrinsic strength of monolayer graphene,” Science 321, 385–388 (2008).
[CrossRef]

2007

Z. F. Wang, Q. W. Shi, Q. Li, X. Wang, J. G. Hou, H. Zheng, Y. Yao, and J. Chen, “Z-shaped graphene nanoribbon quantum dot device,” Appl. Phys. Lett. 91, 053109 (2007).
[CrossRef]

B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, “Spin qubits in graphene quantum dots,” Nat. Phys. 3, 192–196 (2007).
[CrossRef]

P. G. Silvestrov and K. B. Efetov, “Quantum dots in graphene,” Phys. Rev. Lett. 98, 016802 (2007).
[CrossRef]

J. M. Pereira, P. Vasilopoulos, and F. M. Peeters, “Tunable quantum dots in bilayer graphene,” Nano Lett. 7, 946–949 (2007).
[CrossRef]

E. K. Irish, “Generalized rotating-wave approximation for arbitrarily large coupling,” Phys. Rev. Lett. 99, 173601 (2007).
[CrossRef]

2005

E. K. Irish, J. Gea-Banacloche, I. Martin, and K. C. Schwab, “Dynamics of a two-level system strongly coupled to a high-frequency quantum oscillator,” Phys. Rev. B 72, 195410 (2005).
[CrossRef]

K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76, 061101 (2005).
[CrossRef]

2004

M. LaHaye, O. Buu, B. Camarota, and K. Schwab, “Approaching the quantum limit of a nanomechanical resonator,” Science 304, 74–77 (2004).
[CrossRef]

D. Rugar, R. Budakian, H. Mamin, and B. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
[CrossRef]

1991

J. F. Lam, S. R. Forrest, and G. L. Tangonan, “Optical nonlinearities in crystalline organic multiple quantum wells,” Phys. Rev. Lett. 66, 1614–1617 (1991).
[CrossRef]

Ahmadian, M. T.

A. Sakhaee-Pour, M. T. Ahmadian, and R. Naghdabadi, “Vibrational analysis of single-layered graphene sheets,” Nanotechnology 19, 085702 (2008).
[CrossRef]

Ajayan, P. M.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12, 844–849 (2012).
[CrossRef]

Alden, J. S.

A. M. van der Zande, R. A. Barton, J. S. Alden, C. S. Ruiz-Vargas, W. S. Whitney, P. H. Q. Pham, J. Park, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Large-scale arrays of single-layer graphene resonators,” Nano Lett. 10, 4869–4873 (2010).
[CrossRef]

Alemany, L. B.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12, 844–849 (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]

Barton, R. A.

A. M. van der Zande, R. A. Barton, J. S. Alden, C. S. Ruiz-Vargas, W. S. Whitney, P. H. Q. Pham, J. Park, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Large-scale arrays of single-layer graphene resonators,” Nano Lett. 10, 4869–4873 (2010).
[CrossRef]

Bieri, M.

J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, A. P. Muoth, M. Seitsonen, M. Saleh, X. Feng, K. Muellen, and R. Fasel, “Atomically precise bottom-up fabrication of graphene nanoribbons,” Nature 466, 470–473 (2010).
[CrossRef]

Blankenburg, S.

J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, A. P. Muoth, M. Seitsonen, M. Saleh, X. Feng, K. Muellen, and R. Fasel, “Atomically precise bottom-up fabrication of graphene nanoribbons,” Nature 466, 470–473 (2010).
[CrossRef]

Bockrath, M.

H. Y. Chiu, P. Hung, H. W. C. Postma, and M. Bockrath, “Atomic-scale mass sensing using carbon nanotube resoantors,” Nano Lett. 8, 4342–4346 (2008).
[CrossRef]

Bolotin, K. I.

C. Chen, S. Rosenblatt, K. I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. L. Stormer, T. F. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nat. Nanotechnol. 4, 861–867 (2009).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2008).

Braun, T.

J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, A. P. Muoth, M. Seitsonen, M. Saleh, X. Feng, K. Muellen, and R. Fasel, “Atomically precise bottom-up fabrication of graphene nanoribbons,” Nature 466, 470–473 (2010).
[CrossRef]

Budakian, R.

D. Rugar, R. Budakian, H. Mamin, and B. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
[CrossRef]

Bulaev, D. V.

B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, “Spin qubits in graphene quantum dots,” Nat. Phys. 3, 192–196 (2007).
[CrossRef]

Burgner, C. B.

Z. Yie, M. A. Zielke, C. B. Burgner, and K. L. Turner, “Comparison of parametric and linear mass detection in the presence of detection noise,” J. Micromech. Microeng. 21, 025027 (2011).
[CrossRef]

Burkard, G.

B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, “Spin qubits in graphene quantum dots,” Nat. Phys. 3, 192–196 (2007).
[CrossRef]

Buu, O.

M. LaHaye, O. Buu, B. Camarota, and K. Schwab, “Approaching the quantum limit of a nanomechanical resonator,” Science 304, 74–77 (2004).
[CrossRef]

Cai, J.

J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, A. P. Muoth, M. Seitsonen, M. Saleh, X. Feng, K. Muellen, and R. Fasel, “Atomically precise bottom-up fabrication of graphene nanoribbons,” Nature 466, 470–473 (2010).
[CrossRef]

Camarota, B.

M. LaHaye, O. Buu, B. Camarota, and K. Schwab, “Approaching the quantum limit of a nanomechanical resonator,” Science 304, 74–77 (2004).
[CrossRef]

Cao, G.

G. P. Guo, Z. R. Lin, T. Tu, G. Cao, X. P. Li, and G. C. Guo, “Quantum computation with graphene nanoribbon,” New J. Phys. 11, 123005 (2009).
[CrossRef]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109–162 (2009).
[CrossRef]

Chen, B.

C. Jiang, B. Chen, J. J. Li, and K. D. Zhu, “Mass sensing based on a circuit cavity electromechanical system,” J. Appl. Phys. 110, 083107 (2011).
[CrossRef]

Chen, C.

C. Chen, S. Rosenblatt, K. I. Bolotin, W. Kalb, P. Kim, I. Kymissis, H. L. Stormer, T. F. Heinz, and J. Hone, “Performance of monolayer graphene nanomechanical resonators with electrical readout,” Nat. Nanotechnol. 4, 861–867 (2009).
[CrossRef]

Chen, J.

Z. F. Wang, Q. W. Shi, Q. Li, X. Wang, J. G. Hou, H. Zheng, Y. Yao, and J. Chen, “Z-shaped graphene nanoribbon quantum dot device,” Appl. Phys. Lett. 91, 053109 (2007).
[CrossRef]

Chiu, H. Y.

H. Y. Chiu, P. Hung, H. W. C. Postma, and M. Bockrath, “Atomic-scale mass sensing using carbon nanotube resoantors,” Nano Lett. 8, 4342–4346 (2008).
[CrossRef]

Cho, S.

S. Y. Kim, S. Cho, J. W. Kang, and O. K. Kwon, “Molecular dynamics simulation study on mechanical responses of nanoindented monolayer-graphene-nanoribbon,” Phys. E 54, 118–124 (2013).
[CrossRef]

Chui, B.

D. Rugar, R. Budakian, H. Mamin, and B. Chui, “Single spin detection by magnetic resonance force microscopy,” Nature 430, 329–332 (2004).
[CrossRef]

Colombo, L.

K. S. Novoselov, V. I. Falko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[CrossRef]

Craighead, H. G.

A. M. van der Zande, R. A. Barton, J. S. Alden, C. S. Ruiz-Vargas, W. S. Whitney, P. H. Q. Pham, J. Park, J. M. Parpia, H. G. Craighead, and P. L. McEuen, “Large-scale arrays of single-layer graphene resonators,” Nano Lett. 10, 4869–4873 (2010).
[CrossRef]

Deléglise, S.

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]

Efetov, K. B.

P. G. Silvestrov and K. B. Efetov, “Quantum dots in graphene,” Phys. Rev. Lett. 98, 016802 (2007).
[CrossRef]

Ekinci, K. L.

K. L. Ekinci and M. L. Roukes, “Nanoelectromechanical systems,” Rev. Sci. Instrum. 76, 061101 (2005).
[CrossRef]

Falko, V. I.

K. S. Novoselov, V. I. Falko, L. Colombo, P. R. Gellert, M. G. Schwab, and K. Kim, “A roadmap for graphene,” Nature 490, 192–200 (2012).
[CrossRef]

Fasel, R.

J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, A. P. Muoth, M. Seitsonen, M. Saleh, X. Feng, K. Muellen, and R. Fasel, “Atomically precise bottom-up fabrication of graphene nanoribbons,” Nature 466, 470–473 (2010).
[CrossRef]

Feng, X.

J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, A. P. Muoth, M. Seitsonen, M. Saleh, X. Feng, K. Muellen, and R. Fasel, “Atomically precise bottom-up fabrication of graphene nanoribbons,” Nature 466, 470–473 (2010).
[CrossRef]

Forrest, S. R.

J. F. Lam, S. R. Forrest, and G. L. Tangonan, “Optical nonlinearities in crystalline organic multiple quantum wells,” Phys. Rev. Lett. 66, 1614–1617 (1991).
[CrossRef]

Galland, C.

I. Wilson-Rae, C. Galland, W. Zwerger, and A. Imamoglu, “Exciton-assisted optomechanics with suspended carbon nanotubes,” New J. Phys. 14, 115003 (2012).
[CrossRef]

Gao, G.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12, 844–849 (2012).
[CrossRef]

Gao, W.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12, 844–849 (2012).
[CrossRef]

Gavartin, E.

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]

Ge, L.

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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic diagram of mass sensor with a doubly clamped Z-shaped GNR in the presence of a strong pump beam and a weak probe beam. One hydrogen molecule is deposited onto the surface of the Z-shaped GNR resonator in a special evaporator. (b) Atomic structure of Z-shaped GNR. (c) Energy levels of Z-shaped GNR.

Fig. 2.
Fig. 2.

(a) Probe absorption spectrum without landing the external atoms or molecules onto the surface of the Z-shaped GNR resonator. The parameters used are Δpu=0, τn=1.2μs, η=0.086, meff=6.340×1024kg, ωn=7.477GHz, and Ω2=1(GHz)2. (b) Energy levels of the coupled system corresponding to the three peaks in (a).

Fig. 3.
Fig. 3.

Absorption spectrum of the probe field as a function of Δpr before (black solid line) and after (red dashed line) a binding event of one hydrogen molecule. A frequency shift of 0.0164 GHz can be well resolved in the spectrum. Other parameters used are Δpu=0, τn=1.2μs, η=0.086, meff=6.340×1024kg, ωn=7.477GHz, and Ω2=1(GHz)2. The right bottom inset exhibits the relationship between the frequency shift of the GNR and numbers of deposited H2 molecules.

Equations (12)

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H=2Δpuσz+ωnb+b+2ωnη(b++b)σz2(Ωσ++Ω*σ)μ2(σ+Epreiδt+σEpr*eiδt),
σ=σ0+δσ,σz=σ0z+δσz,Z=Z0+δZ.
δσ˙z=Γ1δσz+iΩδ(σ)*iΩ*δσ+iμEpreiδtδ(σ)*iμEpr*eiδtδσ,
δσ˙=(iΔpu+Γ2)δσiωnη(δσZ0+σ0δZ)2iΩδσz2iμEpreiδtδσz,
δ¨Z+1τnδ˙Z+ωn2δZ=ωn2ηδσz,
σ0=2Ωσ0z(Δpu+ωnηZ0)iΓ2,Z0=2ησ0z,
χeff(1)(ωpr)=μσ+ϵ0Epr=μ2ϵ0Γ2χ(ωpr),
(w0+1)[(Δpu0η2ωn0w0)2+1]+2ΩR2w0=0.
ωn=k/meff.
Δm=2meffωn(1(1Δωn/ωn)21).
Δm=meffj(j+1)(Δωnωn)j,j=1,2,3,
ΔmΔm=2meffωnΔωn=R1Δωn,

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