Abstract

We introduce a new optical technique where a train of short optical pulses is utilized to disturb a trapped microscopic particle. Using fast (250 kHz) and accurate (nm) detection of the position of the particle, accurately synchronized to the repetition rate of the laser pulses, we can coherently superimpose the displacement caused by each individual laser pulse. Thereby we are able to both bypass the influence from the Brownian motion of the trapped particle and to simultaneously increase the ability to localize its average trajectory by n, where n is the number of repetitive pulses. In the results presented here we utilize a train of 1200 pulses to kick a 5 μm polystyrene sphere and obtain a spatial resolution corresponding to 0.09 nm and a time resolution of 4 μs. The magnitude of the optical force pushing the particle corresponds to 104g and enables an investigation of both the hydrodynamical drag and the inertial effects caused by the particle and the surrounding liquid. Our results enables a more accurate testing of the existing extended models for the hydrodynamic drag and we discuss the observed agreement between experiments and theory.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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2014 (1)

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref] [PubMed]

2013 (5)

D. S. Grebenkov, M. Vahabi, E. Bertseva, L. Forró, and S. Jeney, “Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium,” Phys. Rev. E 88, 040701 (2013).
[Crossref]

J. Duplat, S. Kheifets, T. Li, M. Raizen, and E. Villermaux, “Superdiffusive trajectories in Brownian motion,” Phys. Rev. E 87, 020105 (2013).
[Crossref]

T. Li and M. G. Raizen, “Brownian motion at short time scales,” Ann. Phys. (Berlin) 525, 281–295 (2013).
[Crossref]

T. B. Lindballe, M. V. G. Kristensen, K. Berg-Sørensen, S. R. Keiding, and H. Stapelfeldt, “Pulsed laser manipulation of an optically trapped bead: averaging thermal noise and measuring the pulsed force amplitude,” Opt. Express 21, 1986–1996 (2013).
[Crossref] [PubMed]

S. A. Ellingsen, “Theory of microdroplet and microbubble deformation by Gaussian laser beam,” J. Opt. Soc. Am. B 30, 1694 (2013).
[Crossref]

2012 (1)

M. Grimm, T. Franosch, and S. Jeney, “High-resolution detection of Brownian motion for quantitative optical tweezers experiments,” Phys. Rev. E 86, 021912 (2012).
[Crossref]

2011 (4)

D. Preece, R. Warren, R.M.L. Evans, G.M. Gibson, M.J. Padgett, J.M. Cooper, and M. Tassieri, “Optical tweezers: wideband microrheology,” J. Opt. 13, 044022 (2011)
[Crossref]

R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nature Phys. 7, 576–580 (2011).
[Crossref]

T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foffi, L. Forró, and S. Jeney, “Resonances arising from hydrodynamic memory in Brownian motion,” Nature 478, 85–88 (2011).
[Crossref] [PubMed]

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

2010 (2)

2007 (2)

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

B. Lukić, S. Jeney, v. Sviben, A. Kulik, E.-L. Florin, and L. Forró, “Motion of a colloidal particle in an optical trap,” Phys. Rev. E 76, 011112 (2007).
[Crossref]

2006 (1)

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

2005 (1)

B. Lukić, S. Jeney, C. Tischer, a. J. Kulik, L. Forró, and E.-L. L. E.-L. Florin, “Direct Observation of Nondiffusive Motion of a Brownian Particle,” Phys. Rev. Lett. 95, 160601 (2005).
[Crossref]

2004 (1)

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594 (2004).
[Crossref]

1998 (1)

M. W. Allersma, F. Gittes, M. J. DeCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

1992 (1)

H. Clercx and P. Schram, “Brownian particles in shear flow and harmonic potentials: A study of long-time tails,” Phys. Rev. A 46, 1942–1950 (1992).
[Crossref] [PubMed]

1970 (1)

A. Askin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

1957 (1)

I. Proudman and J. Pearson, “Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder,” J. Fluid Mech. 2, 237–262 (1957).
[Crossref]

1906 (1)

A. Einstein, “Zur Theorie der Brownschen Bewegung,” Ann. Phys. (Berlin) 324,371–381 (1906).
[Crossref]

1905 (1)

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. (Berlin) 322, 549–560 (1905).
[Crossref]

1828 (1)

R. Brown, “XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies,” Philosophical Magazine Series 2 4, 161–173 (1828).
[Crossref]

Allersma, M. W.

M. W. Allersma, F. Gittes, M. J. DeCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Askin, A.

A. Askin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

Badii, L.

F. Oberhettinger and L. Badii, Tables of Laplace transforms (Springer Berlin Heidelberg, 1973).
[Crossref]

Belushkin, M.

T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foffi, L. Forró, and S. Jeney, “Resonances arising from hydrodynamic memory in Brownian motion,” Nature 478, 85–88 (2011).
[Crossref] [PubMed]

Berg-Sørensen, K.

Bertseva, E.

D. S. Grebenkov, M. Vahabi, E. Bertseva, L. Forró, and S. Jeney, “Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium,” Phys. Rev. E 88, 040701 (2013).
[Crossref]

Betzig, E.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

Bonifacino, J.S.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

Boyce, M.C.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Brau, P.R.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Brown, R.

R. Brown, “XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies,” Philosophical Magazine Series 2 4, 161–173 (1828).
[Crossref]

Castro, C.E.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Chavez, I.

R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nature Phys. 7, 576–580 (2011).
[Crossref]

Clercx, H.

H. Clercx and P. Schram, “Brownian particles in shear flow and harmonic potentials: A study of long-time tails,” Phys. Rev. A 46, 1942–1950 (1992).
[Crossref] [PubMed]

Cooper, J.M.

D. Preece, R. Warren, R.M.L. Evans, G.M. Gibson, M.J. Padgett, J.M. Cooper, and M. Tassieri, “Optical tweezers: wideband microrheology,” J. Opt. 13, 044022 (2011)
[Crossref]

Davidson, M.W.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

DeCastro, M. J.

M. W. Allersma, F. Gittes, M. J. DeCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Duplat, J.

J. Duplat, S. Kheifets, T. Li, M. Raizen, and E. Villermaux, “Superdiffusive trajectories in Brownian motion,” Phys. Rev. E 87, 020105 (2013).
[Crossref]

Einstein, A.

A. Einstein, “Zur Theorie der Brownschen Bewegung,” Ann. Phys. (Berlin) 324,371–381 (1906).
[Crossref]

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. (Berlin) 322, 549–560 (1905).
[Crossref]

Ellingsen, S. A.

Evans, R.M.L.

D. Preece, R. Warren, R.M.L. Evans, G.M. Gibson, M.J. Padgett, J.M. Cooper, and M. Tassieri, “Optical tweezers: wideband microrheology,” J. Opt. 13, 044022 (2011)
[Crossref]

Ferrer, J. M.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Florin, E.-L.

R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nature Phys. 7, 576–580 (2011).
[Crossref]

B. Lukić, S. Jeney, v. Sviben, A. Kulik, E.-L. Florin, and L. Forró, “Motion of a colloidal particle in an optical trap,” Phys. Rev. E 76, 011112 (2007).
[Crossref]

Florin, E.-L. L. E.-L.

B. Lukić, S. Jeney, C. Tischer, a. J. Kulik, L. Forró, and E.-L. L. E.-L. Florin, “Direct Observation of Nondiffusive Motion of a Brownian Particle,” Phys. Rev. Lett. 95, 160601 (2005).
[Crossref]

Flyvbjerg, H.

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594 (2004).
[Crossref]

Foffi, G.

T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foffi, L. Forró, and S. Jeney, “Resonances arising from hydrodynamic memory in Brownian motion,” Nature 478, 85–88 (2011).
[Crossref] [PubMed]

Forde, N. R.

Forró, L.

D. S. Grebenkov, M. Vahabi, E. Bertseva, L. Forró, and S. Jeney, “Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium,” Phys. Rev. E 88, 040701 (2013).
[Crossref]

T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foffi, L. Forró, and S. Jeney, “Resonances arising from hydrodynamic memory in Brownian motion,” Nature 478, 85–88 (2011).
[Crossref] [PubMed]

B. Lukić, S. Jeney, v. Sviben, A. Kulik, E.-L. Florin, and L. Forró, “Motion of a colloidal particle in an optical trap,” Phys. Rev. E 76, 011112 (2007).
[Crossref]

B. Lukić, S. Jeney, C. Tischer, a. J. Kulik, L. Forró, and E.-L. L. E.-L. Florin, “Direct Observation of Nondiffusive Motion of a Brownian Particle,” Phys. Rev. Lett. 95, 160601 (2005).
[Crossref]

Franosch, T.

M. Grimm, T. Franosch, and S. Jeney, “High-resolution detection of Brownian motion for quantitative optical tweezers experiments,” Phys. Rev. E 86, 021912 (2012).
[Crossref]

T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foffi, L. Forró, and S. Jeney, “Resonances arising from hydrodynamic memory in Brownian motion,” Nature 478, 85–88 (2011).
[Crossref] [PubMed]

Gibson, G.M.

D. Preece, R. Warren, R.M.L. Evans, G.M. Gibson, M.J. Padgett, J.M. Cooper, and M. Tassieri, “Optical tweezers: wideband microrheology,” J. Opt. 13, 044022 (2011)
[Crossref]

Gittes, F.

M. W. Allersma, F. Gittes, M. J. DeCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Glueckstad, J.

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

Glüuckstad, J.

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

Grebenkov, D. S.

D. S. Grebenkov, M. Vahabi, E. Bertseva, L. Forró, and S. Jeney, “Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium,” Phys. Rev. E 88, 040701 (2013).
[Crossref]

Grimm, M.

M. Grimm, T. Franosch, and S. Jeney, “High-resolution detection of Brownian motion for quantitative optical tweezers experiments,” Phys. Rev. E 86, 021912 (2012).
[Crossref]

T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foffi, L. Forró, and S. Jeney, “Resonances arising from hydrodynamic memory in Brownian motion,” Nature 478, 85–88 (2011).
[Crossref] [PubMed]

Hashitsume, N.

M. Toda, R. Kubo, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Berlin Heidelberg, 1985).

Hess, H.F.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

Huang, R.

R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nature Phys. 7, 576–580 (2011).
[Crossref]

Jeney, S.

D. S. Grebenkov, M. Vahabi, E. Bertseva, L. Forró, and S. Jeney, “Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium,” Phys. Rev. E 88, 040701 (2013).
[Crossref]

M. Grimm, T. Franosch, and S. Jeney, “High-resolution detection of Brownian motion for quantitative optical tweezers experiments,” Phys. Rev. E 86, 021912 (2012).
[Crossref]

R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nature Phys. 7, 576–580 (2011).
[Crossref]

T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foffi, L. Forró, and S. Jeney, “Resonances arising from hydrodynamic memory in Brownian motion,” Nature 478, 85–88 (2011).
[Crossref] [PubMed]

B. Lukić, S. Jeney, v. Sviben, A. Kulik, E.-L. Florin, and L. Forró, “Motion of a colloidal particle in an optical trap,” Phys. Rev. E 76, 011112 (2007).
[Crossref]

B. Lukić, S. Jeney, C. Tischer, a. J. Kulik, L. Forró, and E.-L. L. E.-L. Florin, “Direct Observation of Nondiffusive Motion of a Brownian Particle,” Phys. Rev. Lett. 95, 160601 (2005).
[Crossref]

Kamm, R.D.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Keiding, S. R.

T. B. Lindballe, M. V. G. Kristensen, K. Berg-Sørensen, S. R. Keiding, and H. Stapelfeldt, “Pulsed laser manipulation of an optically trapped bead: averaging thermal noise and measuring the pulsed force amplitude,” Opt. Express 21, 1986–1996 (2013).
[Crossref] [PubMed]

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

Kheifets, S.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref] [PubMed]

J. Duplat, S. Kheifets, T. Li, M. Raizen, and E. Villermaux, “Superdiffusive trajectories in Brownian motion,” Phys. Rev. E 87, 020105 (2013).
[Crossref]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref] [PubMed]

Kristensen, M. V.

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

Kristensen, M. V. G.

Kubo, R.

M. Toda, R. Kubo, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Berlin Heidelberg, 1985).

Kulik, A.

B. Lukić, S. Jeney, v. Sviben, A. Kulik, E.-L. Florin, and L. Forró, “Motion of a colloidal particle in an optical trap,” Phys. Rev. E 76, 011112 (2007).
[Crossref]

Kulik, a. J.

B. Lukić, S. Jeney, C. Tischer, a. J. Kulik, L. Forró, and E.-L. L. E.-L. Florin, “Direct Observation of Nondiffusive Motion of a Brownian Particle,” Phys. Rev. Lett. 95, 160601 (2005).
[Crossref]

Kylling, A. P.

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

Landau, L.

L. Landau and E. Lifshitz, Fluid Mechanics (Pergamon, 1959).

Lang, M.J.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Lee, H.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Li, T.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref] [PubMed]

J. Duplat, S. Kheifets, T. Li, M. Raizen, and E. Villermaux, “Superdiffusive trajectories in Brownian motion,” Phys. Rev. E 87, 020105 (2013).
[Crossref]

T. Li and M. G. Raizen, “Brownian motion at short time scales,” Ann. Phys. (Berlin) 525, 281–295 (2013).
[Crossref]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref] [PubMed]

Lifshitz, E.

L. Landau and E. Lifshitz, Fluid Mechanics (Pergamon, 1959).

Lindballe, T. B.

T. B. Lindballe, M. V. G. Kristensen, K. Berg-Sørensen, S. R. Keiding, and H. Stapelfeldt, “Pulsed laser manipulation of an optically trapped bead: averaging thermal noise and measuring the pulsed force amplitude,” Opt. Express 21, 1986–1996 (2013).
[Crossref] [PubMed]

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

Lindwasser, O.W.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

Lukic, B.

R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nature Phys. 7, 576–580 (2011).
[Crossref]

B. Lukić, S. Jeney, v. Sviben, A. Kulik, E.-L. Florin, and L. Forró, “Motion of a colloidal particle in an optical trap,” Phys. Rev. E 76, 011112 (2007).
[Crossref]

B. Lukić, S. Jeney, C. Tischer, a. J. Kulik, L. Forró, and E.-L. L. E.-L. Florin, “Direct Observation of Nondiffusive Motion of a Brownian Particle,” Phys. Rev. Lett. 95, 160601 (2005).
[Crossref]

Matsudaira, P.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Medellin, D.

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref] [PubMed]

Melin, K.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref] [PubMed]

Mor, F. M.

T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foffi, L. Forró, and S. Jeney, “Resonances arising from hydrodynamic memory in Brownian motion,” Nature 478, 85–88 (2011).
[Crossref] [PubMed]

Oberhettinger, F.

F. Oberhettinger and L. Badii, Tables of Laplace transforms (Springer Berlin Heidelberg, 1973).
[Crossref]

Olenych, S.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

Padgett, M.J.

D. Preece, R. Warren, R.M.L. Evans, G.M. Gibson, M.J. Padgett, J.M. Cooper, and M. Tassieri, “Optical tweezers: wideband microrheology,” J. Opt. 13, 044022 (2011)
[Crossref]

Palima, D. Z.

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

Patterson, G.H.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

Pearson, J.

I. Proudman and J. Pearson, “Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder,” J. Fluid Mech. 2, 237–262 (1957).
[Crossref]

Preece, D.

D. Preece, R. Warren, R.M.L. Evans, G.M. Gibson, M.J. Padgett, J.M. Cooper, and M. Tassieri, “Optical tweezers: wideband microrheology,” J. Opt. 13, 044022 (2011)
[Crossref]

Proudman, I.

I. Proudman and J. Pearson, “Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder,” J. Fluid Mech. 2, 237–262 (1957).
[Crossref]

Raizen, M.

J. Duplat, S. Kheifets, T. Li, M. Raizen, and E. Villermaux, “Superdiffusive trajectories in Brownian motion,” Phys. Rev. E 87, 020105 (2013).
[Crossref]

Raizen, M. G.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref] [PubMed]

T. Li and M. G. Raizen, “Brownian motion at short time scales,” Ann. Phys. (Berlin) 525, 281–295 (2013).
[Crossref]

R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nature Phys. 7, 576–580 (2011).
[Crossref]

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref] [PubMed]

Schmidt, C. F.

M. W. Allersma, F. Gittes, M. J. DeCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Schram, P.

H. Clercx and P. Schram, “Brownian particles in shear flow and harmonic potentials: A study of long-time tails,” Phys. Rev. A 46, 1942–1950 (1992).
[Crossref] [PubMed]

Simha, A.

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref] [PubMed]

Sougrat, R.

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

Stapelfeldt, H.

T. B. Lindballe, M. V. G. Kristensen, K. Berg-Sørensen, S. R. Keiding, and H. Stapelfeldt, “Pulsed laser manipulation of an optically trapped bead: averaging thermal noise and measuring the pulsed force amplitude,” Opt. Express 21, 1986–1996 (2013).
[Crossref] [PubMed]

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

Stewart, R. J.

M. W. Allersma, F. Gittes, M. J. DeCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

Sviben, v.

B. Lukić, S. Jeney, v. Sviben, A. Kulik, E.-L. Florin, and L. Forró, “Motion of a colloidal particle in an optical trap,” Phys. Rev. E 76, 011112 (2007).
[Crossref]

Tam, B.K.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Tarsa, P.B.

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

Tassieri, M.

D. Preece, R. Warren, R.M.L. Evans, G.M. Gibson, M.J. Padgett, J.M. Cooper, and M. Tassieri, “Optical tweezers: wideband microrheology,” J. Opt. 13, 044022 (2011)
[Crossref]

Taute, K. M.

R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nature Phys. 7, 576–580 (2011).
[Crossref]

Tischer, C.

B. Lukić, S. Jeney, C. Tischer, a. J. Kulik, L. Forró, and E.-L. L. E.-L. Florin, “Direct Observation of Nondiffusive Motion of a Brownian Particle,” Phys. Rev. Lett. 95, 160601 (2005).
[Crossref]

Toda, M.

M. Toda, R. Kubo, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Berlin Heidelberg, 1985).

Vahabi, M.

D. S. Grebenkov, M. Vahabi, E. Bertseva, L. Forró, and S. Jeney, “Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium,” Phys. Rev. E 88, 040701 (2013).
[Crossref]

van der Horst, A.

Villermaux, E.

J. Duplat, S. Kheifets, T. Li, M. Raizen, and E. Villermaux, “Superdiffusive trajectories in Brownian motion,” Phys. Rev. E 87, 020105 (2013).
[Crossref]

Warren, R.

D. Preece, R. Warren, R.M.L. Evans, G.M. Gibson, M.J. Padgett, J.M. Cooper, and M. Tassieri, “Optical tweezers: wideband microrheology,” J. Opt. 13, 044022 (2011)
[Crossref]

Ann. Phys. (Berlin) (3)

A. Einstein, “Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen,” Ann. Phys. (Berlin) 322, 549–560 (1905).
[Crossref]

A. Einstein, “Zur Theorie der Brownschen Bewegung,” Ann. Phys. (Berlin) 324,371–381 (1906).
[Crossref]

T. Li and M. G. Raizen, “Brownian motion at short time scales,” Ann. Phys. (Berlin) 525, 281–295 (2013).
[Crossref]

Biophys. J. (1)

M. W. Allersma, F. Gittes, M. J. DeCastro, R. J. Stewart, and C. F. Schmidt, “Two-dimensional tracking of ncd motility by back focal plane interferometry,” Biophys. J. 74, 1074–1085 (1998).
[Crossref] [PubMed]

J. Eur. Opt. Soc-Rapid (1)

T. B. Lindballe, M. V. Kristensen, A. P. Kylling, D. Z. Palima, J. Glueckstad, S. R. Keiding, H. Stapelfeldt, and J. Glüuckstad, “Three-dimensional imaging and force characterization of multiple trapped particles in low NA counterpropagating optical traps,” J. Eur. Opt. Soc-Rapid 6, 11057 (2011).
[Crossref]

J. Fluid Mech. (1)

I. Proudman and J. Pearson, “Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder,” J. Fluid Mech. 2, 237–262 (1957).
[Crossref]

J. Opt. (1)

D. Preece, R. Warren, R.M.L. Evans, G.M. Gibson, M.J. Padgett, J.M. Cooper, and M. Tassieri, “Optical tweezers: wideband microrheology,” J. Opt. 13, 044022 (2011)
[Crossref]

J. Opt. A (1)

P.R. Brau, J. M. Ferrer, H. Lee, C.E. Castro, B.K. Tam, P.B. Tarsa, P. Matsudaira, M.C. Boyce, R.D. Kamm, and M.J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. A 9, 103 (2007)
[Crossref]

J. Opt. Soc. Am. B (1)

Nature (1)

T. Franosch, M. Grimm, M. Belushkin, F. M. Mor, G. Foffi, L. Forró, and S. Jeney, “Resonances arising from hydrodynamic memory in Brownian motion,” Nature 478, 85–88 (2011).
[Crossref] [PubMed]

Nature Phys. (1)

R. Huang, I. Chavez, K. M. Taute, B. Lukić, S. Jeney, M. G. Raizen, and E.-L. Florin, “Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid,” Nature Phys. 7, 576–580 (2011).
[Crossref]

Opt. Express (2)

Philosophical Magazine Series 2 (1)

R. Brown, “XXVII. A brief account of microscopical observations made in the months of June, July and August 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies,” Philosophical Magazine Series 2 4, 161–173 (1828).
[Crossref]

Phys. Rev. A (1)

H. Clercx and P. Schram, “Brownian particles in shear flow and harmonic potentials: A study of long-time tails,” Phys. Rev. A 46, 1942–1950 (1992).
[Crossref] [PubMed]

Phys. Rev. E (4)

D. S. Grebenkov, M. Vahabi, E. Bertseva, L. Forró, and S. Jeney, “Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium,” Phys. Rev. E 88, 040701 (2013).
[Crossref]

J. Duplat, S. Kheifets, T. Li, M. Raizen, and E. Villermaux, “Superdiffusive trajectories in Brownian motion,” Phys. Rev. E 87, 020105 (2013).
[Crossref]

B. Lukić, S. Jeney, v. Sviben, A. Kulik, E.-L. Florin, and L. Forró, “Motion of a colloidal particle in an optical trap,” Phys. Rev. E 76, 011112 (2007).
[Crossref]

M. Grimm, T. Franosch, and S. Jeney, “High-resolution detection of Brownian motion for quantitative optical tweezers experiments,” Phys. Rev. E 86, 021912 (2012).
[Crossref]

Phys. Rev. Lett. (2)

B. Lukić, S. Jeney, C. Tischer, a. J. Kulik, L. Forró, and E.-L. L. E.-L. Florin, “Direct Observation of Nondiffusive Motion of a Brownian Particle,” Phys. Rev. Lett. 95, 160601 (2005).
[Crossref]

A. Askin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156 (1970).
[Crossref]

Rev. Sci. Instrum. (1)

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75, 594 (2004).
[Crossref]

Science (3)

T. Li, S. Kheifets, D. Medellin, and M. G. Raizen, “Measurement of the instantaneous velocity of a Brownian particle,” Science 328, 1673–1675 (2010).
[Crossref] [PubMed]

S. Kheifets, A. Simha, K. Melin, T. Li, and M. G. Raizen, “Observation of Brownian motion in liquids at short times: instantaneous velocity and memory loss,” Science 343, 1493–1496 (2014).
[Crossref] [PubMed]

E. Betzig, G.H. Patterson, R. Sougrat, O.W. Lindwasser, S. Olenych, J.S. Bonifacino, M.W. Davidson, J. Lippincott-Schwartz, and H.F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642 (2006)
[Crossref] [PubMed]

Other (3)

M. Toda, R. Kubo, and N. Hashitsume, Statistical Physics II: Nonequilibrium Statistical Mechanics (Springer Berlin Heidelberg, 1985).

F. Oberhettinger and L. Badii, Tables of Laplace transforms (Springer Berlin Heidelberg, 1973).
[Crossref]

L. Landau and E. Lifshitz, Fluid Mechanics (Pergamon, 1959).

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Figures (5)

Fig. 1
Fig. 1 The counter propagating optical trap geometry, with the two 1065 nm trapping beams; the 635 nm detection beam; and the 532 nm kicking beam. O1, O2 and OA are objectives.
Fig. 2
Fig. 2 (a) shows the power spectrum, S(f), of the measured data (•) and the measured data substracted the noise floor () of a R = 5μm bead and the associated fits with the Stokes (- - -) and the Stokes-Boussinesq friction (—), respectively. A few noise peaks were excluded before the measured power spectrum were averaged in logarithmic blocks and fitted taking both blur and anti aliasing into account [25]. (b) shows the measured response function (•) of the detection system at 637 nm. It rises instantaneously and falls of as: F respons = A 1 exp ( t 2 / ( 2 t 1 2 ) ) + A 2 exp ( t / t 2 ), where A1 = 0.77, A2 = 0.22, t1 = 8.3μs, and t2 = 25.9μs.
Fig. 3
Fig. 3 Particle trace (R = 5μm particle) in the direction of kicking, with y = 0 at the center of the trap. (a) shows the trace of the trapped particle without kicking. The particle fluctuates around the center of the trap with a standard deviation of σy = 54nm. (b) show three examples of traces when the particle is kicked by a laser pulse at t = 0 marked with short black lines. (c) shows the average trace corresponding to 1200 kick pulses. The fluctuations caused by Brownian motion are averaged out and the dynamics of the kicked particle is clearly visible. The standard deviation of the averaged trace is reduced by approximately n, where n corresponds to the 1200 events and is equal to σ y avg = 1.5 nm.
Fig. 4
Fig. 4 (a) is a zoom of the first 0.5 ms of Fig. 3(c) (•) with the scaled Stokes (- - -) and Stokes-Boussinesq (—) averaged position. The calculated positions have been convolved with the time response function of the detector. (b) is the experimental traces (normalized to equal amplitude) at 0.56(○), 0.78(∇), 1(+), and times the maximal kicking power. The error bars in both (a) and (b) are based on the averaged position standard deviation, σ y avg = 1.5 nm.
Fig. 5
Fig. 5 (a) shows the size dependent rise of the particles for radii of: 2.5 μm (∇), 5 μm (○), and 10 μm (Δ), respectively (b) shows the maximal displacement for a R = 5μm at different kick pulse intensities. The line is a linear fits given as a guide to the eye. The error bars in (a) and (b) corresponds to the appertaining position standard deviations of the traces

Equations (9)

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

F res ( t ) = F fric ( t ) + F th ( t ) + F ext ( t )
F ext ( t ) = κ y ( t ) + I ( t )
F fric = γ y ˙ ( t ) , γ = 6 π η R
F fric = γ ( y ˙ ( t ) + R ρ η 1 π 0 t d t y ¨ ( t ) t t ) 1 2 4 3 π ρ R 3 y ¨ ( t ) .
( τ p + 1 9 τ f ) y ¨ ( t ) = y ˙ ( t ) τ f 1 π 0 t d t y ¨ ( t ) t t 1 τ κ y ( t ) + 2 A ¯ δ ( t ) + ξ th ( t )
y ˜ ( s ) = G ˜ ( s ) ( A ¯ + ζ t h ) G ˜ ( s ) = ( ( τ p + 1 9 τ f ) s 2 + τ f s 3 + s 2 + τ κ 1 ) 1
y ( t ) = A ¯ τ p + 1 9 τ f ( r 1 e r 1 2 t erfc ( r 1 t ) ( r 1 r 2 ) ( r 1 r 3 ) ( r 1 r 4 ) + r 2 e r 2 2 t erfc ( r 2 t ) ( r 2 r 1 ) ( r 2 r 3 ) ( r 2 r 4 ) + r 3 e r 3 2 t erfc ( r 3 t ) ( r 3 r 1 ) ( r 3 r 2 ) ( r 3 r 4 ) + r 4 e r 4 2 t erfc ( r 4 t ) ( r 4 r 1 ) ( r 4 r 2 ) ( r 4 r 3 ) )
y ( t ) = A ¯ ϑ ( e ( ϑ 1 ) t 2 τ p e ( ϑ + 1 ) t 2 τ p )
A ¯ e t τ κ for τ κ τ p

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