Abstract

We explore the laser spot position (LSP) dependence of photothermal mode cooling in a microcantilever-based Fabry–Perot cavity. Experiments on photothermal cooling demonstrate that the direction of photothermal backaction on the first two cantilever modes is LSP dependent, which can be either parallel or antiparallel. A theoretical analysis of this LSP-dependent effect identifies the parallel and the antiparallel coupling regions along the lever. Simulation results are in quantitative agreement with our experimental observations. We conclude that the cooling limit imposed by photothermal mode coupling can be surmounted by operating in the parallel coupling region.

© 2012 Optical Society of America

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  1. S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
    [CrossRef]
  2. T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
    [CrossRef]
  3. J. Restrepo, J. Gabelli, C. Ciuti, and I. Favero, “Classical and quantum theory of photothermal cavity cooling of a mechanical oscillator,” http://arxiv.org/abs/1011.3911 .
  4. S. Kuehn, S. A. Hickman, and J. A. Marohn, J. Chem. Phys. 128, 052208 (2008).
    [CrossRef]
  5. R. García and R. Pérez, Surf. Sci. Rep. 47, 197 (2002).
    [CrossRef]
  6. F. Marquardt and S. M. Girvin, Physics 2, 40 (2009).
    [CrossRef]
  7. J. H. Chow, B. S. Sheard, D. E. McClelland, and M. B. Gray, Opt. Lett. 30, 708 (2005).
    [CrossRef]
  8. C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
    [CrossRef]
  9. S. D. Liberato, N. Lambert, and F. Nori, Phys. Rev. A 83, 033809 (2011).
    [CrossRef]
  10. H. Fu, Y. Liu, J. Chen, and G. Cao, Sens. Actuators A 163, 533 (2010).
    [CrossRef]
  11. C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, Phys. Rev. B 78, 035309 (2008).
    [CrossRef]
  12. G. Jourdan, F. Comin, and J. Chevrier, Phys. Rev. Lett. 101, 133904 (2008).
    [CrossRef]
  13. K. J. Bruland, J. L. Garbini, W. M. Dougherty, S. H. Chao, S. E. Jensen, and J. A. Sidles, Rev. Sci. Instrum. 70, 3542 (1999).
    [CrossRef]
  14. C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
    [CrossRef]
  15. J. R. Serrano, L. M. Phinney, and J. W. Rogers, Int. J. Heat Mass Transfer 52, 2255 (2009).
    [CrossRef]
  16. G. C. Ratcliff, D. A. Erie, and R. Superfine, Appl. Phys. Lett. 72, 1911 (1998).
    [CrossRef]

2011 (1)

S. D. Liberato, N. Lambert, and F. Nori, Phys. Rev. A 83, 033809 (2011).
[CrossRef]

2010 (1)

H. Fu, Y. Liu, J. Chen, and G. Cao, Sens. Actuators A 163, 533 (2010).
[CrossRef]

2009 (3)

J. R. Serrano, L. M. Phinney, and J. W. Rogers, Int. J. Heat Mass Transfer 52, 2255 (2009).
[CrossRef]

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
[CrossRef]

F. Marquardt and S. M. Girvin, Physics 2, 40 (2009).
[CrossRef]

2008 (5)

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef]

S. Kuehn, S. A. Hickman, and J. A. Marohn, J. Chem. Phys. 128, 052208 (2008).
[CrossRef]

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
[CrossRef]

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, Phys. Rev. B 78, 035309 (2008).
[CrossRef]

G. Jourdan, F. Comin, and J. Chevrier, Phys. Rev. Lett. 101, 133904 (2008).
[CrossRef]

2005 (1)

2004 (1)

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef]

2002 (1)

R. García and R. Pérez, Surf. Sci. Rep. 47, 197 (2002).
[CrossRef]

1999 (1)

K. J. Bruland, J. L. Garbini, W. M. Dougherty, S. H. Chao, S. E. Jensen, and J. A. Sidles, Rev. Sci. Instrum. 70, 3542 (1999).
[CrossRef]

1998 (1)

G. C. Ratcliff, D. A. Erie, and R. Superfine, Appl. Phys. Lett. 72, 1911 (1998).
[CrossRef]

Aspelmeyer, M.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
[CrossRef]

Bruland, K. J.

K. J. Bruland, J. L. Garbini, W. M. Dougherty, S. H. Chao, S. E. Jensen, and J. A. Sidles, Rev. Sci. Instrum. 70, 3542 (1999).
[CrossRef]

Cao, G.

H. Fu, Y. Liu, J. Chen, and G. Cao, Sens. Actuators A 163, 533 (2010).
[CrossRef]

Chao, S. H.

K. J. Bruland, J. L. Garbini, W. M. Dougherty, S. H. Chao, S. E. Jensen, and J. A. Sidles, Rev. Sci. Instrum. 70, 3542 (1999).
[CrossRef]

Chen, J.

H. Fu, Y. Liu, J. Chen, and G. Cao, Sens. Actuators A 163, 533 (2010).
[CrossRef]

Chevrier, J.

G. Jourdan, F. Comin, and J. Chevrier, Phys. Rev. Lett. 101, 133904 (2008).
[CrossRef]

Chow, J. H.

Cole, G. D.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
[CrossRef]

Comin, F.

G. Jourdan, F. Comin, and J. Chevrier, Phys. Rev. Lett. 101, 133904 (2008).
[CrossRef]

Dougherty, W. M.

K. J. Bruland, J. L. Garbini, W. M. Dougherty, S. H. Chao, S. E. Jensen, and J. A. Sidles, Rev. Sci. Instrum. 70, 3542 (1999).
[CrossRef]

Erie, D. A.

G. C. Ratcliff, D. A. Erie, and R. Superfine, Appl. Phys. Lett. 72, 1911 (1998).
[CrossRef]

Favero, I.

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
[CrossRef]

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, Phys. Rev. B 78, 035309 (2008).
[CrossRef]

Fu, H.

H. Fu, Y. Liu, J. Chen, and G. Cao, Sens. Actuators A 163, 533 (2010).
[CrossRef]

Garbini, J. L.

K. J. Bruland, J. L. Garbini, W. M. Dougherty, S. H. Chao, S. E. Jensen, and J. A. Sidles, Rev. Sci. Instrum. 70, 3542 (1999).
[CrossRef]

García, R.

R. García and R. Pérez, Surf. Sci. Rep. 47, 197 (2002).
[CrossRef]

Gigan, S.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
[CrossRef]

Girvin, S. M.

F. Marquardt and S. M. Girvin, Physics 2, 40 (2009).
[CrossRef]

Gray, M. B.

Gröblacher, S.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
[CrossRef]

Hertzberg, J. B.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
[CrossRef]

Hickman, S. A.

S. Kuehn, S. A. Hickman, and J. A. Marohn, J. Chem. Phys. 128, 052208 (2008).
[CrossRef]

Jensen, S. E.

K. J. Bruland, J. L. Garbini, W. M. Dougherty, S. H. Chao, S. E. Jensen, and J. A. Sidles, Rev. Sci. Instrum. 70, 3542 (1999).
[CrossRef]

Jourdan, G.

G. Jourdan, F. Comin, and J. Chevrier, Phys. Rev. Lett. 101, 133904 (2008).
[CrossRef]

Karrai, K.

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, Phys. Rev. B 78, 035309 (2008).
[CrossRef]

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
[CrossRef]

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef]

Kuehn, S.

S. Kuehn, S. A. Hickman, and J. A. Marohn, J. Chem. Phys. 128, 052208 (2008).
[CrossRef]

Lambert, N.

S. D. Liberato, N. Lambert, and F. Nori, Phys. Rev. A 83, 033809 (2011).
[CrossRef]

Liberato, S. D.

S. D. Liberato, N. Lambert, and F. Nori, Phys. Rev. A 83, 033809 (2011).
[CrossRef]

Liu, Y.

H. Fu, Y. Liu, J. Chen, and G. Cao, Sens. Actuators A 163, 533 (2010).
[CrossRef]

Ludwig, M.

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
[CrossRef]

Marohn, J. A.

S. Kuehn, S. A. Hickman, and J. A. Marohn, J. Chem. Phys. 128, 052208 (2008).
[CrossRef]

Marquardt, F.

F. Marquardt and S. M. Girvin, Physics 2, 40 (2009).
[CrossRef]

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
[CrossRef]

McClelland, D. E.

Metzger, C.

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
[CrossRef]

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, Phys. Rev. B 78, 035309 (2008).
[CrossRef]

Metzger, C. H.

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef]

Neuenhahn, C.

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
[CrossRef]

Nori, F.

S. D. Liberato, N. Lambert, and F. Nori, Phys. Rev. A 83, 033809 (2011).
[CrossRef]

Ortlieb, A.

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
[CrossRef]

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, Phys. Rev. B 78, 035309 (2008).
[CrossRef]

Pérez, R.

R. García and R. Pérez, Surf. Sci. Rep. 47, 197 (2002).
[CrossRef]

Phinney, L. M.

J. R. Serrano, L. M. Phinney, and J. W. Rogers, Int. J. Heat Mass Transfer 52, 2255 (2009).
[CrossRef]

Ratcliff, G. C.

G. C. Ratcliff, D. A. Erie, and R. Superfine, Appl. Phys. Lett. 72, 1911 (1998).
[CrossRef]

Rogers, J. W.

J. R. Serrano, L. M. Phinney, and J. W. Rogers, Int. J. Heat Mass Transfer 52, 2255 (2009).
[CrossRef]

Schwab, K. C.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
[CrossRef]

Serrano, J. R.

J. R. Serrano, L. M. Phinney, and J. W. Rogers, Int. J. Heat Mass Transfer 52, 2255 (2009).
[CrossRef]

Sheard, B. S.

Sidles, J. A.

K. J. Bruland, J. L. Garbini, W. M. Dougherty, S. H. Chao, S. E. Jensen, and J. A. Sidles, Rev. Sci. Instrum. 70, 3542 (1999).
[CrossRef]

Superfine, R.

G. C. Ratcliff, D. A. Erie, and R. Superfine, Appl. Phys. Lett. 72, 1911 (1998).
[CrossRef]

Vahala, K. J.

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef]

Vanner, M. R.

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

G. C. Ratcliff, D. A. Erie, and R. Superfine, Appl. Phys. Lett. 72, 1911 (1998).
[CrossRef]

Int. J. Heat Mass Transfer (1)

J. R. Serrano, L. M. Phinney, and J. W. Rogers, Int. J. Heat Mass Transfer 52, 2255 (2009).
[CrossRef]

J. Chem. Phys. (1)

S. Kuehn, S. A. Hickman, and J. A. Marohn, J. Chem. Phys. 128, 052208 (2008).
[CrossRef]

Nat. Phys. (1)

S. Gröblacher, J. B. Hertzberg, M. R. Vanner, G. D. Cole, S. Gigan, K. C. Schwab, and M. Aspelmeyer, Nat. Phys. 5, 485 (2009).
[CrossRef]

Nature (1)

C. H. Metzger and K. Karrai, Nature 432, 1002 (2004).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

S. D. Liberato, N. Lambert, and F. Nori, Phys. Rev. A 83, 033809 (2011).
[CrossRef]

Phys. Rev. B (1)

C. Metzger, I. Favero, A. Ortlieb, and K. Karrai, Phys. Rev. B 78, 035309 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

G. Jourdan, F. Comin, and J. Chevrier, Phys. Rev. Lett. 101, 133904 (2008).
[CrossRef]

C. Metzger, M. Ludwig, C. Neuenhahn, A. Ortlieb, I. Favero, K. Karrai, and F. Marquardt, Phys. Rev. Lett. 101, 133903 (2008).
[CrossRef]

Physics (1)

F. Marquardt and S. M. Girvin, Physics 2, 40 (2009).
[CrossRef]

Rev. Sci. Instrum. (1)

K. J. Bruland, J. L. Garbini, W. M. Dougherty, S. H. Chao, S. E. Jensen, and J. A. Sidles, Rev. Sci. Instrum. 70, 3542 (1999).
[CrossRef]

Science (1)

T. J. Kippenberg and K. J. Vahala, Science 321, 1172 (2008).
[CrossRef]

Sens. Actuators A (1)

H. Fu, Y. Liu, J. Chen, and G. Cao, Sens. Actuators A 163, 533 (2010).
[CrossRef]

Surf. Sci. Rep. (1)

R. García and R. Pérez, Surf. Sci. Rep. 47, 197 (2002).
[CrossRef]

Other (1)

J. Restrepo, J. Gabelli, C. Ciuti, and I. Favero, “Classical and quantum theory of photothermal cavity cooling of a mechanical oscillator,” http://arxiv.org/abs/1011.3911 .

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematics of the experimental setup. (Inset) Reflectivity of the cavity changes periodically with the cavity length. Points b and r are the working points with maximum interferential detection sensitivity at blue and red detuning condition, respectively [13].(b) Shapes of mode 0 and mode 1. The photothermal coupling to the first two mechanical modes of microlever are investigated at five LSPs denoted by P1 to P5.

Fig. 2.
Fig. 2.

Thermal noise amplitude of (a) mode 0 and (b) mode 1 detected at P3 for the different laser powers. Insets in graphs (a) and (b): effective damping factors Γeff at working points b (dashed line) and r (solid line) as a function of laser power.

Fig. 3.
Fig. 3.

Photothermal coupling to mode 0 (solid line) and mode 1 (dashed line) at positions (a) P1, (b) P2, (c) P4, and (d) P5.

Fig. 4.
Fig. 4.

(a) Photothermal damping ratio of mode 1 measured experimentally (squares) and calculated theoretically (solid line). Thermal noise amplitude of (b) mode 0 and (c) mode 1 at position P1. The first two mechanical modes are enhanced at working point r (dashed line) and suppressed at point b (solid line) simultaneously.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ma¨n+mΓna˙n+Knan=Fth+Fbol,
ΔTl(x,t)=A0tDl(x)I(u)u|u0[1exp(ttτ)]u˙(t)dt,
[ω02ω2+iωΓ0+γG0(l)ϕ0(l)m(1+iωτ)γG0(l)ϕ1(l)m(1+iωτ)γG1(l)ϕ0(l)m(1+iωτ)ω12ω2+iωΓ1+γG1(l)ϕ1(l)m(1+iωτ)]aω=Fth,ωm,
βn=dΔΓeff,ndΔΓeff,0=Gn(l)ϕn(l)(1+ω02τ2)G0(l)ϕ0(l)(1+ωn2τ2).

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