Abstract

We demonstrate a lock-in particle tracking scheme in optical tweezers based on stroboscopic modulation of an illuminating optical field. This scheme is found to evade low frequency noise sources while otherwise producing an equivalent position measurement to continuous measurement. This was demonstrated to yield up to 20 dB of noise suppression at both low frequencies (< 1 kHz), where low frequency electronic noise was significant, and around 630 kHz where laser relaxation oscillations introduced laser noise. The setup is simple, and compatible with any trapping optics.

© 2013 Optical Society of America

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References

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  1. A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
    [Crossref] [PubMed]
  2. M. A. Taylor, J. Knittel, and W. P. Bowen, “Fundamental constraints on particle tracking with optical tweezers,” New J. Phys. 15, 023018 (2013).
    [Crossref]
  3. F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
    [Crossref]
  4. I. Chavez, R. Huang, K. Henderson, E.-L. Florin, and M. G. Raizen, “Development of a fast position-sensitive laser beam detector,” Rev. Sci. Instrum. 79, 105104 (2008).
    [Crossref] [PubMed]
  5. J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
    [Crossref]
  6. J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
    [Crossref] [PubMed]
  7. A. Jannasch, A. F. Demirörs, P. D. J. van Oostrum, A. van Blaaderen, and E. Schäffer, “Nanonewton optical force trap employing anti-reflection coated, high-refractive-index titania microspheres,” Nature Photon. 6, 469–473 (2012).
    [Crossref]
  8. K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, 1993 “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
    [Crossref] [PubMed]
  9. C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73, 705–748 (2004).
    [Crossref]
  10. C. Bustamante, “Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics,” Q. Rev. Biophys. 38, 291–301 (2005).
    [Crossref]
  11. W. J. Greenleaf and S. M. Block, “Single-molecule, motion-based DNA sequencing using RNA polymerase,” Science 313, 801 (2006).
    [Crossref] [PubMed]
  12. P. Kukura, H. Ewers, C. Müller, A. Renn, A. Helenius, and V. Sandoghdar, “High-speed nanoscopic tracking of the position and orientation of a single virus,” Nat. Methods 6, 923–929 (2009).
    [Crossref] [PubMed]
  13. M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nature Photon. (2013).
    [Crossref]
  14. S. Yamada, D. Wirtz, and S. C. Kuo, “Mechanics of living cells measured by laser tracking microrheology,” Biophys. J. 78, 1736–1747 (2000).
    [Crossref] [PubMed]
  15. E. N. Senning and A. H. Marcus, “Actin polymerization driven mitochondrial transport in mating S. cerevisiae,” Proc. Natl. Acad. Sci. USA 107, 721–725 (2010).
    [Crossref] [PubMed]
  16. I. M. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, “Anomalous diffusion in living yeast cells,” Phys. Rev. Lett. 93, 078102 (2004).
    [Crossref]
  17. 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]
  18. R. Huang, I. Chavez I, 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]
  19. D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
    [Crossref] [PubMed]
  20. T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nature Phys. 7, 527–530 (2011).
    [Crossref]
  21. M. A. Taylor, J. Knittel, M. T. L. Hsu, H.-A. Bachor, and W. P. Bowen, “Sagnac interferometer-enhanced particle tracking in optical tweezers,” J. Opt. 13, 044014 (2011).
    [Crossref]
  22. J. W. Tay, M. T. L. Hsu, and W. P. Bowen, “Quantum limited particle sensing in optical tweezers,” Phys. Rev. A 80063806 (2009).
    [Crossref]
  23. P. Kwee and B. Willke, “Automatic laser beam characterization of monolithic Nd:YAG nonplanar ring lasers,” Appl. Opt. 476022–6032 (2008)
    [Crossref] [PubMed]

2013 (1)

M. A. Taylor, J. Knittel, and W. P. Bowen, “Fundamental constraints on particle tracking with optical tweezers,” New J. Phys. 15, 023018 (2013).
[Crossref]

2012 (1)

A. Jannasch, A. F. Demirörs, P. D. J. van Oostrum, A. van Blaaderen, and E. Schäffer, “Nanonewton optical force trap employing anti-reflection coated, high-refractive-index titania microspheres,” Nature Photon. 6, 469–473 (2012).
[Crossref]

2011 (4)

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]

R. Huang, I. Chavez I, 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, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nature Phys. 7, 527–530 (2011).
[Crossref]

M. A. Taylor, J. Knittel, M. T. L. Hsu, H.-A. Bachor, and W. P. Bowen, “Sagnac interferometer-enhanced particle tracking in optical tweezers,” J. Opt. 13, 044014 (2011).
[Crossref]

2010 (2)

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

E. N. Senning and A. H. Marcus, “Actin polymerization driven mitochondrial transport in mating S. cerevisiae,” Proc. Natl. Acad. Sci. USA 107, 721–725 (2010).
[Crossref] [PubMed]

2009 (2)

P. Kukura, H. Ewers, C. Müller, A. Renn, A. Helenius, and V. Sandoghdar, “High-speed nanoscopic tracking of the position and orientation of a single virus,” Nat. Methods 6, 923–929 (2009).
[Crossref] [PubMed]

J. W. Tay, M. T. L. Hsu, and W. P. Bowen, “Quantum limited particle sensing in optical tweezers,” Phys. Rev. A 80063806 (2009).
[Crossref]

2008 (3)

P. Kwee and B. Willke, “Automatic laser beam characterization of monolithic Nd:YAG nonplanar ring lasers,” Appl. Opt. 476022–6032 (2008)
[Crossref] [PubMed]

I. Chavez, R. Huang, K. Henderson, E.-L. Florin, and M. G. Raizen, “Development of a fast position-sensitive laser beam detector,” Rev. Sci. Instrum. 79, 105104 (2008).
[Crossref] [PubMed]

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

2006 (1)

W. J. Greenleaf and S. M. Block, “Single-molecule, motion-based DNA sequencing using RNA polymerase,” Science 313, 801 (2006).
[Crossref] [PubMed]

2005 (1)

C. Bustamante, “Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics,” Q. Rev. Biophys. 38, 291–301 (2005).
[Crossref]

2004 (2)

I. M. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, “Anomalous diffusion in living yeast cells,” Phys. Rev. Lett. 93, 078102 (2004).
[Crossref]

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73, 705–748 (2004).
[Crossref]

2000 (1)

S. Yamada, D. Wirtz, and S. C. Kuo, “Mechanics of living cells measured by laser tracking microrheology,” Biophys. J. 78, 1736–1747 (2000).
[Crossref] [PubMed]

1998 (1)

1994 (1)

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[Crossref] [PubMed]

1993 (1)

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, 1993 “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

1987 (1)

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[Crossref] [PubMed]

Ashkin, A.

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[Crossref] [PubMed]

Bachor, H.-A.

M. A. Taylor, J. Knittel, M. T. L. Hsu, H.-A. Bachor, and W. P. Bowen, “Sagnac interferometer-enhanced particle tracking in optical tweezers,” J. Opt. 13, 044014 (2011).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nature Photon. (2013).
[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.

I. M. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, “Anomalous diffusion in living yeast cells,” Phys. Rev. Lett. 93, 078102 (2004).
[Crossref]

Block, S. M.

W. J. Greenleaf and S. M. Block, “Single-molecule, motion-based DNA sequencing using RNA polymerase,” Science 313, 801 (2006).
[Crossref] [PubMed]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, 1993 “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

Bowen, W. P.

M. A. Taylor, J. Knittel, and W. P. Bowen, “Fundamental constraints on particle tracking with optical tweezers,” New J. Phys. 15, 023018 (2013).
[Crossref]

M. A. Taylor, J. Knittel, M. T. L. Hsu, H.-A. Bachor, and W. P. Bowen, “Sagnac interferometer-enhanced particle tracking in optical tweezers,” J. Opt. 13, 044014 (2011).
[Crossref]

J. W. Tay, M. T. L. Hsu, and W. P. Bowen, “Quantum limited particle sensing in optical tweezers,” Phys. Rev. A 80063806 (2009).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nature Photon. (2013).
[Crossref]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

C. Bustamante, “Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics,” Q. Rev. Biophys. 38, 291–301 (2005).
[Crossref]

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73, 705–748 (2004).
[Crossref]

Chang, D. E.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

Chavez, I.

I. Chavez, R. Huang, K. Henderson, E.-L. Florin, and M. G. Raizen, “Development of a fast position-sensitive laser beam detector,” Rev. Sci. Instrum. 79, 105104 (2008).
[Crossref] [PubMed]

Chavez I, I.

R. Huang, I. Chavez I, 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]

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73, 705–748 (2004).
[Crossref]

Daria, V.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nature Photon. (2013).
[Crossref]

Demirörs, A. F.

A. Jannasch, A. F. Demirörs, P. D. J. van Oostrum, A. van Blaaderen, and E. Schäffer, “Nanonewton optical force trap employing anti-reflection coated, high-refractive-index titania microspheres,” Nature Photon. 6, 469–473 (2012).
[Crossref]

Dziedzic, J.

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[Crossref] [PubMed]

Ewers, H.

P. Kukura, H. Ewers, C. Müller, A. Renn, A. Helenius, and V. Sandoghdar, “High-speed nanoscopic tracking of the position and orientation of a single virus,” Nat. Methods 6, 923–929 (2009).
[Crossref] [PubMed]

Finer, J. T.

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[Crossref] [PubMed]

Florin, E.-L.

R. Huang, I. Chavez I, 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]

I. Chavez, R. Huang, K. Henderson, E.-L. Florin, and M. G. Raizen, “Development of a fast position-sensitive laser beam detector,” Rev. Sci. Instrum. 79, 105104 (2008).
[Crossref] [PubMed]

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.

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73, 705–748 (2004).
[Crossref]

Forró, L.

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]

Franosch, T.

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]

Gittes, F.

Greenleaf, W. J.

W. J. Greenleaf and S. M. Block, “Single-molecule, motion-based DNA sequencing using RNA polymerase,” Science 313, 801 (2006).
[Crossref] [PubMed]

Grimm, 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]

Hage, B.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nature Photon. (2013).
[Crossref]

Helenius, A.

P. Kukura, H. Ewers, C. Müller, A. Renn, A. Helenius, and V. Sandoghdar, “High-speed nanoscopic tracking of the position and orientation of a single virus,” Nat. Methods 6, 923–929 (2009).
[Crossref] [PubMed]

Henderson, K.

I. Chavez, R. Huang, K. Henderson, E.-L. Florin, and M. G. Raizen, “Development of a fast position-sensitive laser beam detector,” Rev. Sci. Instrum. 79, 105104 (2008).
[Crossref] [PubMed]

Hsu, M. T. L.

M. A. Taylor, J. Knittel, M. T. L. Hsu, H.-A. Bachor, and W. P. Bowen, “Sagnac interferometer-enhanced particle tracking in optical tweezers,” J. Opt. 13, 044014 (2011).
[Crossref]

J. W. Tay, M. T. L. Hsu, and W. P. Bowen, “Quantum limited particle sensing in optical tweezers,” Phys. Rev. A 80063806 (2009).
[Crossref]

Huang, R.

R. Huang, I. Chavez I, 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]

I. Chavez, R. Huang, K. Henderson, E.-L. Florin, and M. G. Raizen, “Development of a fast position-sensitive laser beam detector,” Rev. Sci. Instrum. 79, 105104 (2008).
[Crossref] [PubMed]

Izhaky, D.

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73, 705–748 (2004).
[Crossref]

Jannasch, A.

A. Jannasch, A. F. Demirörs, P. D. J. van Oostrum, A. van Blaaderen, and E. Schäffer, “Nanonewton optical force trap employing anti-reflection coated, high-refractive-index titania microspheres,” Nature Photon. 6, 469–473 (2012).
[Crossref]

Janousek, J.

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nature Photon. (2013).
[Crossref]

Jeney, S.

R. Huang, I. Chavez I, 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]

Kheifets, S.

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nature Phys. 7, 527–530 (2011).
[Crossref]

Kimble, H. J.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

Knittel, J.

M. A. Taylor, J. Knittel, and W. P. Bowen, “Fundamental constraints on particle tracking with optical tweezers,” New J. Phys. 15, 023018 (2013).
[Crossref]

M. A. Taylor, J. Knittel, M. T. L. Hsu, H.-A. Bachor, and W. P. Bowen, “Sagnac interferometer-enhanced particle tracking in optical tweezers,” J. Opt. 13, 044014 (2011).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nature Photon. (2013).
[Crossref]

Kukura, P.

P. Kukura, H. Ewers, C. Müller, A. Renn, A. Helenius, and V. Sandoghdar, “High-speed nanoscopic tracking of the position and orientation of a single virus,” Nat. Methods 6, 923–929 (2009).
[Crossref] [PubMed]

Kuo, S. C.

S. Yamada, D. Wirtz, and S. C. Kuo, “Mechanics of living cells measured by laser tracking microrheology,” Biophys. J. 78, 1736–1747 (2000).
[Crossref] [PubMed]

Kwee, P.

Li, T.

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nature Phys. 7, 527–530 (2011).
[Crossref]

Lukic, B.

R. Huang, I. Chavez I, 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]

Marcus, A. H.

E. N. Senning and A. H. Marcus, “Actin polymerization driven mitochondrial transport in mating S. cerevisiae,” Proc. Natl. Acad. Sci. USA 107, 721–725 (2010).
[Crossref] [PubMed]

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

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]

Müller, C.

P. Kukura, H. Ewers, C. Müller, A. Renn, A. Helenius, and V. Sandoghdar, “High-speed nanoscopic tracking of the position and orientation of a single virus,” Nat. Methods 6, 923–929 (2009).
[Crossref] [PubMed]

Munteanu, E.-L.

I. M. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, “Anomalous diffusion in living yeast cells,” Phys. Rev. Lett. 93, 078102 (2004).
[Crossref]

Oddershede, L.

I. M. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, “Anomalous diffusion in living yeast cells,” Phys. Rev. Lett. 93, 078102 (2004).
[Crossref]

Painter, O.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

Papp, S. B.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

Raizen, M. G.

T. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nature Phys. 7, 527–530 (2011).
[Crossref]

R. Huang, I. Chavez I, 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]

I. Chavez, R. Huang, K. Henderson, E.-L. Florin, and M. G. Raizen, “Development of a fast position-sensitive laser beam detector,” Rev. Sci. Instrum. 79, 105104 (2008).
[Crossref] [PubMed]

Regal, C. A.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

Renn, A.

P. Kukura, H. Ewers, C. Müller, A. Renn, A. Helenius, and V. Sandoghdar, “High-speed nanoscopic tracking of the position and orientation of a single virus,” Nat. Methods 6, 923–929 (2009).
[Crossref] [PubMed]

Sandoghdar, V.

P. Kukura, H. Ewers, C. Müller, A. Renn, A. Helenius, and V. Sandoghdar, “High-speed nanoscopic tracking of the position and orientation of a single virus,” Nat. Methods 6, 923–929 (2009).
[Crossref] [PubMed]

Schäffer, E.

A. Jannasch, A. F. Demirörs, P. D. J. van Oostrum, A. van Blaaderen, and E. Schäffer, “Nanonewton optical force trap employing anti-reflection coated, high-refractive-index titania microspheres,” Nature Photon. 6, 469–473 (2012).
[Crossref]

Schmidt, C. F.

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23, 7–9 (1998).
[Crossref]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, 1993 “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

Schnapp, B. J.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, 1993 “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

Senning, E. N.

E. N. Senning and A. H. Marcus, “Actin polymerization driven mitochondrial transport in mating S. cerevisiae,” Proc. Natl. Acad. Sci. USA 107, 721–725 (2010).
[Crossref] [PubMed]

Simmons, R. M.

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[Crossref] [PubMed]

Smith, S. B.

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

Spudich, J. A.

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[Crossref] [PubMed]

Svoboda, K.

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, 1993 “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

Taute, K. M.

R. Huang, I. Chavez I, 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]

Tay, J. W.

J. W. Tay, M. T. L. Hsu, and W. P. Bowen, “Quantum limited particle sensing in optical tweezers,” Phys. Rev. A 80063806 (2009).
[Crossref]

Taylor, M. A.

M. A. Taylor, J. Knittel, and W. P. Bowen, “Fundamental constraints on particle tracking with optical tweezers,” New J. Phys. 15, 023018 (2013).
[Crossref]

M. A. Taylor, J. Knittel, M. T. L. Hsu, H.-A. Bachor, and W. P. Bowen, “Sagnac interferometer-enhanced particle tracking in optical tweezers,” J. Opt. 13, 044014 (2011).
[Crossref]

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nature Photon. (2013).
[Crossref]

Thon, G.

I. M. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, “Anomalous diffusion in living yeast cells,” Phys. Rev. Lett. 93, 078102 (2004).
[Crossref]

Tolic-Nørrelykke, I. M.

I. M. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, “Anomalous diffusion in living yeast cells,” Phys. Rev. Lett. 93, 078102 (2004).
[Crossref]

van Blaaderen, A.

A. Jannasch, A. F. Demirörs, P. D. J. van Oostrum, A. van Blaaderen, and E. Schäffer, “Nanonewton optical force trap employing anti-reflection coated, high-refractive-index titania microspheres,” Nature Photon. 6, 469–473 (2012).
[Crossref]

van Oostrum, P. D. J.

A. Jannasch, A. F. Demirörs, P. D. J. van Oostrum, A. van Blaaderen, and E. Schäffer, “Nanonewton optical force trap employing anti-reflection coated, high-refractive-index titania microspheres,” Nature Photon. 6, 469–473 (2012).
[Crossref]

Willke, B.

Wilson, D. J.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

Wirtz, D.

S. Yamada, D. Wirtz, and S. C. Kuo, “Mechanics of living cells measured by laser tracking microrheology,” Biophys. J. 78, 1736–1747 (2000).
[Crossref] [PubMed]

Yamada, S.

S. Yamada, D. Wirtz, and S. C. Kuo, “Mechanics of living cells measured by laser tracking microrheology,” Biophys. J. 78, 1736–1747 (2000).
[Crossref] [PubMed]

Ye, J.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

Zoller, P.

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

Annu. Rev. Biochem. (2)

J. R. Moffitt, Y. R. Chemla, S. B. Smith, and C. Bustamante, “Recent advances in optical tweezers,” Annu. Rev. Biochem. 77, 205–228 (2008).
[Crossref]

C. Bustamante, Y. R. Chemla, N. R. Forde, and D. Izhaky, “Mechanical processes in biochemistry,” Annu. Rev. Biochem. 73, 705–748 (2004).
[Crossref]

Appl. Opt. (1)

Biophys. J. (1)

S. Yamada, D. Wirtz, and S. C. Kuo, “Mechanics of living cells measured by laser tracking microrheology,” Biophys. J. 78, 1736–1747 (2000).
[Crossref] [PubMed]

J. Opt. (1)

M. A. Taylor, J. Knittel, M. T. L. Hsu, H.-A. Bachor, and W. P. Bowen, “Sagnac interferometer-enhanced particle tracking in optical tweezers,” J. Opt. 13, 044014 (2011).
[Crossref]

Nat. Methods (1)

P. Kukura, H. Ewers, C. Müller, A. Renn, A. Helenius, and V. Sandoghdar, “High-speed nanoscopic tracking of the position and orientation of a single virus,” Nat. Methods 6, 923–929 (2009).
[Crossref] [PubMed]

Nature (3)

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]

K. Svoboda, C. F. Schmidt, B. J. Schnapp, and S. M. Block, 1993 “Direct observation of kinesin stepping by optical trapping interferometry,” Nature 365, 721–727 (1993).
[Crossref] [PubMed]

J. T. Finer, R. M. Simmons, and J. A. Spudich, “Single myosin molecule mechanics: piconewton forces and nanometre steps,” Nature 368, 113–119 (1994).
[Crossref] [PubMed]

Nature Photon. (1)

A. Jannasch, A. F. Demirörs, P. D. J. van Oostrum, A. van Blaaderen, and E. Schäffer, “Nanonewton optical force trap employing anti-reflection coated, high-refractive-index titania microspheres,” Nature Photon. 6, 469–473 (2012).
[Crossref]

Nature Phys. (2)

R. Huang, I. Chavez I, 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, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nature Phys. 7, 527–530 (2011).
[Crossref]

New J. Phys. (1)

M. A. Taylor, J. Knittel, and W. P. Bowen, “Fundamental constraints on particle tracking with optical tweezers,” New J. Phys. 15, 023018 (2013).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (1)

J. W. Tay, M. T. L. Hsu, and W. P. Bowen, “Quantum limited particle sensing in optical tweezers,” Phys. Rev. A 80063806 (2009).
[Crossref]

Phys. Rev. Lett. (1)

I. M. Tolić-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, “Anomalous diffusion in living yeast cells,” Phys. Rev. Lett. 93, 078102 (2004).
[Crossref]

Proc. Natl. Acad. Sci. USA (2)

D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble, and P. Zoller, “Cavity opto-mechanics using an optically levitated nanosphere,” Proc. Natl. Acad. Sci. USA 107, 1005–1010 (2010).
[Crossref] [PubMed]

E. N. Senning and A. H. Marcus, “Actin polymerization driven mitochondrial transport in mating S. cerevisiae,” Proc. Natl. Acad. Sci. USA 107, 721–725 (2010).
[Crossref] [PubMed]

Q. Rev. Biophys. (1)

C. Bustamante, “Unfolding single RNA molecules: bridging the gap between equilibrium and non-equilibrium statistical thermodynamics,” Q. Rev. Biophys. 38, 291–301 (2005).
[Crossref]

Rev. Sci. Instrum. (1)

I. Chavez, R. Huang, K. Henderson, E.-L. Florin, and M. G. Raizen, “Development of a fast position-sensitive laser beam detector,” Rev. Sci. Instrum. 79, 105104 (2008).
[Crossref] [PubMed]

Science (2)

W. J. Greenleaf and S. M. Block, “Single-molecule, motion-based DNA sequencing using RNA polymerase,” Science 313, 801 (2006).
[Crossref] [PubMed]

A. Ashkin and J. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[Crossref] [PubMed]

Other (1)

M. A. Taylor, J. Janousek, V. Daria, J. Knittel, B. Hage, H.-A. Bachor, and W. P. Bowen, “Biological measurement beyond the quantum limit,” Nature Photon. (2013).
[Crossref]

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Figures (3)
Fig. 1
Fig. 1 An illumination optical field is modulated by its interaction with the particle (red). In order to measure this, it is mixed with another bright local oscillator field (dark blue). However, the local oscillator also has some low-frequency noise present. If the illumination field frequency matches the local oscillator frequency, as shown on the left, then the low-frequency noise competes with the low-frequency particle motion signal. However, if it is in amplitude modulated side-bands, as shown on the right, then the low-frequency particle motion can be isolated from the low-frequency noise, thereby improving the measurement sensitivity.

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Fig. 2
Fig. 2 Layout of the optical lock-in tracking scheme used here. PBS: polarizing beam-splitter, DM: dichroic mirror, λ/4: quarter waveplate. Particles are trapped with a 30 mW trapping field which has been amplitude modulated at 2.5 MHz in a fiber Mach-Zehnder modulator (dark red). Back-scattered light from this trapping field is combined with a 3 mW local oscillator field (light red). Since the back-scattered light passes through the quarter waveplate twice, its polarization is rotated and it passes straight through the polarizing beamsplitter. The interference between the scattered field and the local oscillator is measured on a split detector to track the particles. A separate green field is used to image the particles in the trap.

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Fig. 3
Fig. 3 Particle tracking spectra are shown from simultaneous continuous (a) and lock-in (b) measurements. The gold trace shows the noise floor present in the absence of a trapped particle which corresponds to the measurement imprecision, and the blue shows the measured signal with a 0.5 μm polystyrene bead held in the trap. For clarity, the traces are smoothed with a logarithmic width filter, and this broadens the sharp electrical noise features. The prominent spectral peak around 630 kHz in the continuous data is laser noise which arises from the laser diode relaxation oscillations, and this noise feature is barely visible in the lock-in results. Subplot (c) shows the factor by which the noise floor has been lowered for the lock-in results.

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Equations (7)

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

I ( t ) = G ∫ U ( X , Y ) | E ( t ) | 2 d X d Y + N E ( t )
I ( t ) = G ∫ U ( X , Y ) | E LO ( t ) | 2 + 2 U ( X , Y ) Re { E LO ( t ) E s * ( t ) } d X d Y + N E ( t ) .
E s = E s | x = 0 + x ( t ) d E s d x | x = 0 = ( A s ( t ) + ξ ( t ) ) ψ s ( X , Y ) | x = 0 + x ( t ) ( A s ( t ) + ξ ( t ) ) d ψ s ( X , Y ) d x | x = 0 .
I sig = 2 G x ( t ) A s ( t ) ∫ U ( X , Y ) Re { E LO d ψ s * ( X , Y ) d x | x = 0 } d X d Y ,
= g x ( t ) A s ( t )
I ( t ) = N opt ( t ) + N E ( t ) + g A s ( t ) x ( t ) ,
I lock − in = 2 I cos ( ω t ) = 2 ( N opt ( t ) + N E ( t ) ) cos ( ω t ) + g A ¯ s x + g A ¯ s x cos ( 2 ω t ) .

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