Abstract

Coupling between mesoscopic particles levitated in vacuum is a prerequisite for the realization of a large-scale array of particles in an underdamped environment as well as potential studies at the classical–quantum interface. Here, we demonstrate for the first time, to the best of our knowledge, optical binding between two rotating microparticles mediated by light scattering in vacuum. We investigate autocorrelations between the two normal modes of oscillation determined by the center-of-mass and the relative positions of the two-particle system. The inter-particle coupling, as a consequence of optical binding, removes the degeneracy of the normal mode frequencies, which is in good agreement with theory. We further demonstrate that the optically bound array of rotating microparticles retains their optical coupling during gyroscopic cooling, and exhibits cooperative motion whose center-of-mass is stabilized.

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References

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    [Crossref]
  2. A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
    [Crossref]
  3. J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
    [Crossref]
  4. T. C. Li, S. Kheifets, and M. G. Raizen, “Millikelvin cooling of an optically trapped microsphere in vacuum,” Nat. Phys. 7, 527–530 (2011).
    [Crossref]
  5. J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
    [Crossref]
  6. G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 10593, 053801 (2016).
    [Crossref]
  7. J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
    [Crossref]
  8. Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4, 2374 (2013).
    [Crossref]
  9. S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
    [Crossref]
  10. S. Kuhn, A. Kosloff, B. A. Stickler, F. Patolsky, K. Hornberger, M. Arndt, and J. Millen, “Full rotational control of levitated silicon nanorods,” Optica 4, 356–360 (2017).
    [Crossref]
  11. A. Manjavacas and F. J. G. de Abajo, “Vacuum friction in rotating particles,” Phys. Rev. Lett. 105, 113601 (2010).
    [Crossref]
  12. R. K. Zhao, A. Manjavacas, F. J. G. de Abajo, and J. B. Pendry, “Rotational quantum friction,” Phys. Rev. Lett. 109, 123604 (2012).
    [Crossref]
  13. Y. Arita, M. Mazilu, T. Vettenburg, E. M. Wright, and K. Dholakia, “Rotation of two trapped microparticles in vacuum: observation of optically mediated parametric resonances,” Opt. Lett. 40, 4751–4754 (2015).
    [Crossref]
  14. K. Dholakia and P. Zemanek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
    [Crossref]
  15. M. Guillon and B. Stout, “Optical trapping and binding in air: imaging and spectroscopic analysis,” Phys. Rev. A 77, 023806 (2008).
    [Crossref]
  16. S. Maayani, L. L. Martin, and T. Carmon, “Optical binding in white light,” Opt. Lett. 40, 1818–1821 (2015).
    [Crossref]
  17. O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
    [Crossref]
  18. J. Millen, T. Deesuwan, P. F. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
    [Crossref]
  19. Y. L. Li, J. Millen, and P. F. Barker, “Simultaneous cooling of coupled mechanical oscillators using whispering gallery mode resonances,” Opt. Express 24, 1392–1401 (2016).
    [Crossref]
  20. R. Madugani, Y. Yang, J. M. Ward, V. H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
    [Crossref]
  21. Y. Arita, A. W. McKinley, M. Mazilu, H. Rubinsztein-Dunlop, and K. Dholakia, “Picoliter rheology of gaseous media using a rotating optically trapped birefringent microparticle,” Anal. Chem. 83, 8855–8858 (2011).
    [Crossref]
  22. Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
    [Crossref]
  23. J. C. Meiners and S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
    [Crossref]
  24. P. Bartlett, S. I. Henderson, and S. J. Mitchell, “Measurement of the hydrodynamic forces between two polymer-coated spheres,” Philos. Trans. R. Soc. London A 359, 883–895 (2001).
    [Crossref]
  25. N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
    [Crossref]
  26. M. Mazilu, A. Rudhall, E. M. Wright, and K. Dholakia, “An interacting dipole model to explore broadband transverse optical binding,” J. Phys. 24, 464117 (2012).
    [Crossref]
  27. M.-T. Wei, J. Ng, C. T. Chan, and H. D. Ou-Yang, “Lateral optical binding between two colloidal particles,” Sci. Rep. 6, 38883 (2016).
    [Crossref]
  28. Y. Arita, M. Chen, E. M. Wright, and K. Dholakia, “Dynamics of a levitated microparticle in vacuum trapped by a perfect vortex beam: three-dimensional motion around a complex optical potential,” J. Opt. Soc. Am. B 34, C14–C19 (2017).
    [Crossref]
  29. F. Monteiro, S. Ghosh, E. C. van Assendelft, and D. C. Moore, “Optical rotation of levitated spheres in high vacuum,” Phys. Rev. A 97, 051802 (2018).
    [Crossref]
  30. J. Millen, P. Z. Fonseca, T. Mavrogordatos, T. S. Monteiro, and P. F. Barker, “Cavity cooling a single charged levitated nanosphere,” Phys. Rev. Lett. 114, 123602 (2015).
    [Crossref]

2018 (1)

F. Monteiro, S. Ghosh, E. C. van Assendelft, and D. C. Moore, “Optical rotation of levitated spheres in high vacuum,” Phys. Rev. A 97, 051802 (2018).
[Crossref]

2017 (2)

2016 (4)

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 10593, 053801 (2016).
[Crossref]

Y. L. Li, J. Millen, and P. F. Barker, “Simultaneous cooling of coupled mechanical oscillators using whispering gallery mode resonances,” Opt. Express 24, 1392–1401 (2016).
[Crossref]

Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
[Crossref]

M.-T. Wei, J. Ng, C. T. Chan, and H. D. Ou-Yang, “Lateral optical binding between two colloidal particles,” Sci. Rep. 6, 38883 (2016).
[Crossref]

2015 (5)

R. Madugani, Y. Yang, J. M. Ward, V. H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

J. Millen, P. Z. Fonseca, T. Mavrogordatos, T. S. Monteiro, and P. F. Barker, “Cavity cooling a single charged levitated nanosphere,” Phys. Rev. Lett. 114, 123602 (2015).
[Crossref]

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Y. Arita, M. Mazilu, T. Vettenburg, E. M. Wright, and K. Dholakia, “Rotation of two trapped microparticles in vacuum: observation of optically mediated parametric resonances,” Opt. Lett. 40, 4751–4754 (2015).
[Crossref]

S. Maayani, L. L. Martin, and T. Carmon, “Optical binding in white light,” Opt. Lett. 40, 1818–1821 (2015).
[Crossref]

2014 (1)

J. Millen, T. Deesuwan, P. F. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

2013 (2)

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
[Crossref]

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4, 2374 (2013).
[Crossref]

2012 (3)

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

R. K. Zhao, A. Manjavacas, F. J. G. de Abajo, and J. B. Pendry, “Rotational quantum friction,” Phys. Rev. Lett. 109, 123604 (2012).
[Crossref]

M. Mazilu, A. Rudhall, E. M. Wright, and K. Dholakia, “An interacting dipole model to explore broadband transverse optical binding,” J. Phys. 24, 464117 (2012).
[Crossref]

2011 (3)

Y. Arita, A. W. McKinley, M. Mazilu, H. Rubinsztein-Dunlop, and K. Dholakia, “Picoliter rheology of gaseous media using a rotating optically trapped birefringent microparticle,” Anal. Chem. 83, 8855–8858 (2011).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

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

2010 (5)

P. F. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[Crossref]

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
[Crossref]

K. Dholakia and P. Zemanek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[Crossref]

A. Manjavacas and F. J. G. de Abajo, “Vacuum friction in rotating particles,” Phys. Rev. Lett. 105, 113601 (2010).
[Crossref]

2008 (1)

M. Guillon and B. Stout, “Optical trapping and binding in air: imaging and spectroscopic analysis,” Phys. Rev. A 77, 023806 (2008).
[Crossref]

2007 (1)

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[Crossref]

2001 (1)

P. Bartlett, S. I. Henderson, and S. J. Mitchell, “Measurement of the hydrodynamic forces between two polymer-coated spheres,” Philos. Trans. R. Soc. London A 359, 883–895 (2001).
[Crossref]

1999 (1)

J. C. Meiners and S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[Crossref]

Alegre, T. P. M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Anders, J.

J. Millen, T. Deesuwan, P. F. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Ansmann, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Arita, Y.

Y. Arita, M. Chen, E. M. Wright, and K. Dholakia, “Dynamics of a levitated microparticle in vacuum trapped by a perfect vortex beam: three-dimensional motion around a complex optical potential,” J. Opt. Soc. Am. B 34, C14–C19 (2017).
[Crossref]

Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
[Crossref]

Y. Arita, M. Mazilu, T. Vettenburg, E. M. Wright, and K. Dholakia, “Rotation of two trapped microparticles in vacuum: observation of optically mediated parametric resonances,” Opt. Lett. 40, 4751–4754 (2015).
[Crossref]

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4, 2374 (2013).
[Crossref]

Y. Arita, A. W. McKinley, M. Mazilu, H. Rubinsztein-Dunlop, and K. Dholakia, “Picoliter rheology of gaseous media using a rotating optically trapped birefringent microparticle,” Anal. Chem. 83, 8855–8858 (2011).
[Crossref]

Arndt, M.

S. Kuhn, A. Kosloff, B. A. Stickler, F. Patolsky, K. Hornberger, M. Arndt, and J. Millen, “Full rotational control of levitated silicon nanorods,” Optica 4, 356–360 (2017).
[Crossref]

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Asenbaum, P.

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Aspelmeyer, M.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Barker, P. F.

Y. L. Li, J. Millen, and P. F. Barker, “Simultaneous cooling of coupled mechanical oscillators using whispering gallery mode resonances,” Opt. Express 24, 1392–1401 (2016).
[Crossref]

J. Millen, P. Z. Fonseca, T. Mavrogordatos, T. S. Monteiro, and P. F. Barker, “Cavity cooling a single charged levitated nanosphere,” Phys. Rev. Lett. 114, 123602 (2015).
[Crossref]

J. Millen, T. Deesuwan, P. F. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

P. F. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[Crossref]

Bartlett, P.

P. Bartlett, S. I. Henderson, and S. J. Mitchell, “Measurement of the hydrodynamic forces between two polymer-coated spheres,” Philos. Trans. R. Soc. London A 359, 883–895 (2001).
[Crossref]

Bialczak, R. C.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Brzobohatý, O.

Carmon, T.

Casey, K.

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 10593, 053801 (2016).
[Crossref]

Chan, C. T.

M.-T. Wei, J. Ng, C. T. Chan, and H. D. Ou-Yang, “Lateral optical binding between two colloidal particles,” Sci. Rep. 6, 38883 (2016).
[Crossref]

Chan, J.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Chen, M.

Cheshnovsky, O.

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Cižmár, T.

Cleland, A. N.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Craig, D.

Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
[Crossref]

Cunningham, M.

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 10593, 053801 (2016).
[Crossref]

de Abajo, F. J. G.

R. K. Zhao, A. Manjavacas, F. J. G. de Abajo, and J. B. Pendry, “Rotational quantum friction,” Phys. Rev. Lett. 109, 123604 (2012).
[Crossref]

A. Manjavacas and F. J. G. de Abajo, “Vacuum friction in rotating particles,” Phys. Rev. Lett. 105, 113601 (2010).
[Crossref]

Deesuwan, T.

J. Millen, T. Deesuwan, P. F. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Deutsch, B.

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

Dholakia, K.

Y. Arita, M. Chen, E. M. Wright, and K. Dholakia, “Dynamics of a levitated microparticle in vacuum trapped by a perfect vortex beam: three-dimensional motion around a complex optical potential,” J. Opt. Soc. Am. B 34, C14–C19 (2017).
[Crossref]

Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
[Crossref]

Y. Arita, M. Mazilu, T. Vettenburg, E. M. Wright, and K. Dholakia, “Rotation of two trapped microparticles in vacuum: observation of optically mediated parametric resonances,” Opt. Lett. 40, 4751–4754 (2015).
[Crossref]

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4, 2374 (2013).
[Crossref]

M. Mazilu, A. Rudhall, E. M. Wright, and K. Dholakia, “An interacting dipole model to explore broadband transverse optical binding,” J. Phys. 24, 464117 (2012).
[Crossref]

Y. Arita, A. W. McKinley, M. Mazilu, H. Rubinsztein-Dunlop, and K. Dholakia, “Picoliter rheology of gaseous media using a rotating optically trapped birefringent microparticle,” Anal. Chem. 83, 8855–8858 (2011).
[Crossref]

K. Dholakia and P. Zemanek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[Crossref]

O. Brzobohatý, T. Čižmár, V. Karásek, M. Šiler, K. Dholakia, and P. Zemánek, “Experimental and theoretical determination of optical binding forces,” Opt. Express 18, 25389–25402 (2010).
[Crossref]

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[Crossref]

Fonseca, P. Z.

J. Millen, P. Z. Fonseca, T. Mavrogordatos, T. S. Monteiro, and P. F. Barker, “Cavity cooling a single charged levitated nanosphere,” Phys. Rev. Lett. 114, 123602 (2015).
[Crossref]

Geraci, A. A.

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 10593, 053801 (2016).
[Crossref]

Ghosh, S.

F. Monteiro, S. Ghosh, E. C. van Assendelft, and D. C. Moore, “Optical rotation of levitated spheres in high vacuum,” Phys. Rev. A 97, 051802 (2018).
[Crossref]

Gieseler, J.

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
[Crossref]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

Gröblacher, S.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Guillon, M.

M. Guillon and B. Stout, “Optical trapping and binding in air: imaging and spectroscopic analysis,” Phys. Rev. A 77, 023806 (2008).
[Crossref]

Henderson, S. I.

P. Bartlett, S. I. Henderson, and S. J. Mitchell, “Measurement of the hydrodynamic forces between two polymer-coated spheres,” Philos. Trans. R. Soc. London A 359, 883–895 (2001).
[Crossref]

Hill, J. T.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Hofheinz, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Hornberger, K.

S. Kuhn, A. Kosloff, B. A. Stickler, F. Patolsky, K. Hornberger, M. Arndt, and J. Millen, “Full rotational control of levitated silicon nanorods,” Optica 4, 356–360 (2017).
[Crossref]

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Karásek, V.

Kheifets, S.

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

Kosloff, A.

S. Kuhn, A. Kosloff, B. A. Stickler, F. Patolsky, K. Hornberger, M. Arndt, and J. Millen, “Full rotational control of levitated silicon nanorods,” Optica 4, 356–360 (2017).
[Crossref]

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Krause, A.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Kuhn, S.

S. Kuhn, A. Kosloff, B. A. Stickler, F. Patolsky, K. Hornberger, M. Arndt, and J. Millen, “Full rotational control of levitated silicon nanorods,” Optica 4, 356–360 (2017).
[Crossref]

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Le, V. H.

R. Madugani, Y. Yang, J. M. Ward, V. H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

Lenander, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Li, T. C.

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

Li, Y. L.

Lucero, E.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Maayani, S.

Madugani, R.

R. Madugani, Y. Yang, J. M. Ward, V. H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

Manjavacas, A.

R. K. Zhao, A. Manjavacas, F. J. G. de Abajo, and J. B. Pendry, “Rotational quantum friction,” Phys. Rev. Lett. 109, 123604 (2012).
[Crossref]

A. Manjavacas and F. J. G. de Abajo, “Vacuum friction in rotating particles,” Phys. Rev. Lett. 105, 113601 (2010).
[Crossref]

Marchington, R. F.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[Crossref]

Martin, L. L.

Martinis, J. M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Mavrogordatos, T.

J. Millen, P. Z. Fonseca, T. Mavrogordatos, T. S. Monteiro, and P. F. Barker, “Cavity cooling a single charged levitated nanosphere,” Phys. Rev. Lett. 114, 123602 (2015).
[Crossref]

Mazilu, M.

Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
[Crossref]

Y. Arita, M. Mazilu, T. Vettenburg, E. M. Wright, and K. Dholakia, “Rotation of two trapped microparticles in vacuum: observation of optically mediated parametric resonances,” Opt. Lett. 40, 4751–4754 (2015).
[Crossref]

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4, 2374 (2013).
[Crossref]

M. Mazilu, A. Rudhall, E. M. Wright, and K. Dholakia, “An interacting dipole model to explore broadband transverse optical binding,” J. Phys. 24, 464117 (2012).
[Crossref]

Y. Arita, A. W. McKinley, M. Mazilu, H. Rubinsztein-Dunlop, and K. Dholakia, “Picoliter rheology of gaseous media using a rotating optically trapped birefringent microparticle,” Anal. Chem. 83, 8855–8858 (2011).
[Crossref]

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[Crossref]

McKinley, A. W.

Y. Arita, A. W. McKinley, M. Mazilu, H. Rubinsztein-Dunlop, and K. Dholakia, “Picoliter rheology of gaseous media using a rotating optically trapped birefringent microparticle,” Anal. Chem. 83, 8855–8858 (2011).
[Crossref]

Meiners, J. C.

J. C. Meiners and S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[Crossref]

Metzger, N. K.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[Crossref]

Millen, J.

S. Kuhn, A. Kosloff, B. A. Stickler, F. Patolsky, K. Hornberger, M. Arndt, and J. Millen, “Full rotational control of levitated silicon nanorods,” Optica 4, 356–360 (2017).
[Crossref]

Y. L. Li, J. Millen, and P. F. Barker, “Simultaneous cooling of coupled mechanical oscillators using whispering gallery mode resonances,” Opt. Express 24, 1392–1401 (2016).
[Crossref]

J. Millen, P. Z. Fonseca, T. Mavrogordatos, T. S. Monteiro, and P. F. Barker, “Cavity cooling a single charged levitated nanosphere,” Phys. Rev. Lett. 114, 123602 (2015).
[Crossref]

J. Millen, T. Deesuwan, P. F. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Mitchell, S. J.

P. Bartlett, S. I. Henderson, and S. J. Mitchell, “Measurement of the hydrodynamic forces between two polymer-coated spheres,” Philos. Trans. R. Soc. London A 359, 883–895 (2001).
[Crossref]

Monteiro, F.

F. Monteiro, S. Ghosh, E. C. van Assendelft, and D. C. Moore, “Optical rotation of levitated spheres in high vacuum,” Phys. Rev. A 97, 051802 (2018).
[Crossref]

Monteiro, T. S.

J. Millen, P. Z. Fonseca, T. Mavrogordatos, T. S. Monteiro, and P. F. Barker, “Cavity cooling a single charged levitated nanosphere,” Phys. Rev. Lett. 114, 123602 (2015).
[Crossref]

Moore, D. C.

F. Monteiro, S. Ghosh, E. C. van Assendelft, and D. C. Moore, “Optical rotation of levitated spheres in high vacuum,” Phys. Rev. A 97, 051802 (2018).
[Crossref]

Neeley, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Ng, J.

M.-T. Wei, J. Ng, C. T. Chan, and H. D. Ou-Yang, “Lateral optical binding between two colloidal particles,” Sci. Rep. 6, 38883 (2016).
[Crossref]

Nic Chormaic, S.

R. Madugani, Y. Yang, J. M. Ward, V. H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

Nimmrichter, S.

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Novotny, L.

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
[Crossref]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

O’Connell, A. D.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Ou-Yang, H. D.

M.-T. Wei, J. Ng, C. T. Chan, and H. D. Ou-Yang, “Lateral optical binding between two colloidal particles,” Sci. Rep. 6, 38883 (2016).
[Crossref]

Painter, O.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Patolsky, F.

S. Kuhn, A. Kosloff, B. A. Stickler, F. Patolsky, K. Hornberger, M. Arndt, and J. Millen, “Full rotational control of levitated silicon nanorods,” Optica 4, 356–360 (2017).
[Crossref]

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Pendry, J. B.

R. K. Zhao, A. Manjavacas, F. J. G. de Abajo, and J. B. Pendry, “Rotational quantum friction,” Phys. Rev. Lett. 109, 123604 (2012).
[Crossref]

Quake, S. R.

J. C. Meiners and S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[Crossref]

Quidant, R.

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
[Crossref]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

Raizen, M. G.

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

Ranjit, G.

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 10593, 053801 (2016).
[Crossref]

Richards, J. M.

Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
[Crossref]

Rubinsztein-Dunlop, H.

Y. Arita, A. W. McKinley, M. Mazilu, H. Rubinsztein-Dunlop, and K. Dholakia, “Picoliter rheology of gaseous media using a rotating optically trapped birefringent microparticle,” Anal. Chem. 83, 8855–8858 (2011).
[Crossref]

Rudhall, A.

M. Mazilu, A. Rudhall, E. M. Wright, and K. Dholakia, “An interacting dipole model to explore broadband transverse optical binding,” J. Phys. 24, 464117 (2012).
[Crossref]

Safavi-Naeini, A. H.

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Sank, D.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Sclafani, M.

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Šiler, M.

Smith, R. L.

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[Crossref]

Spalding, G. C.

Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
[Crossref]

Spesyvtseva, S. E. S.

Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
[Crossref]

Stickler, B. A.

S. Kuhn, A. Kosloff, B. A. Stickler, F. Patolsky, K. Hornberger, M. Arndt, and J. Millen, “Full rotational control of levitated silicon nanorods,” Optica 4, 356–360 (2017).
[Crossref]

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Stout, B.

M. Guillon and B. Stout, “Optical trapping and binding in air: imaging and spectroscopic analysis,” Phys. Rev. A 77, 023806 (2008).
[Crossref]

van Assendelft, E. C.

F. Monteiro, S. Ghosh, E. C. van Assendelft, and D. C. Moore, “Optical rotation of levitated spheres in high vacuum,” Phys. Rev. A 97, 051802 (2018).
[Crossref]

Vettenburg, T.

Wang, H.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Ward, J. M.

R. Madugani, Y. Yang, J. M. Ward, V. H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

Wei, M.-T.

M.-T. Wei, J. Ng, C. T. Chan, and H. D. Ou-Yang, “Lateral optical binding between two colloidal particles,” Sci. Rep. 6, 38883 (2016).
[Crossref]

Weides, M.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Wenner, J.

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

Wright, E. M.

Y. Arita, M. Chen, E. M. Wright, and K. Dholakia, “Dynamics of a levitated microparticle in vacuum trapped by a perfect vortex beam: three-dimensional motion around a complex optical potential,” J. Opt. Soc. Am. B 34, C14–C19 (2017).
[Crossref]

Y. Arita, M. Mazilu, T. Vettenburg, E. M. Wright, and K. Dholakia, “Rotation of two trapped microparticles in vacuum: observation of optically mediated parametric resonances,” Opt. Lett. 40, 4751–4754 (2015).
[Crossref]

M. Mazilu, A. Rudhall, E. M. Wright, and K. Dholakia, “An interacting dipole model to explore broadband transverse optical binding,” J. Phys. 24, 464117 (2012).
[Crossref]

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[Crossref]

Yang, Y.

R. Madugani, Y. Yang, J. M. Ward, V. H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

Zemanek, P.

K. Dholakia and P. Zemanek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[Crossref]

Zemánek, P.

Zhao, R. K.

R. K. Zhao, A. Manjavacas, F. J. G. de Abajo, and J. B. Pendry, “Rotational quantum friction,” Phys. Rev. Lett. 109, 123604 (2012).
[Crossref]

ACS Nano (1)

Y. Arita, J. M. Richards, M. Mazilu, G. C. Spalding, S. E. S. Spesyvtseva, D. Craig, and K. Dholakia, “Rotational dynamics and heating of trapped nanovaterite particles,” ACS Nano 10, 11505–11510 (2016).
[Crossref]

Anal. Chem. (1)

Y. Arita, A. W. McKinley, M. Mazilu, H. Rubinsztein-Dunlop, and K. Dholakia, “Picoliter rheology of gaseous media using a rotating optically trapped birefringent microparticle,” Anal. Chem. 83, 8855–8858 (2011).
[Crossref]

Appl. Phys. Lett. (1)

R. Madugani, Y. Yang, J. M. Ward, V. H. Le, and S. Nic Chormaic, “Optomechanical transduction and characterization of a silica microsphere pendulum via evanescent light,” Appl. Phys. Lett. 106, 241101 (2015).
[Crossref]

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

J. Phys. (1)

M. Mazilu, A. Rudhall, E. M. Wright, and K. Dholakia, “An interacting dipole model to explore broadband transverse optical binding,” J. Phys. 24, 464117 (2012).
[Crossref]

Nano Lett. (1)

S. Kuhn, P. Asenbaum, A. Kosloff, M. Sclafani, B. A. Stickler, S. Nimmrichter, K. Hornberger, O. Cheshnovsky, F. Patolsky, and M. Arndt, “Cavity-assisted manipulation of freely rotating silicon nanorods in high vacuum,” Nano Lett. 15, 5604–5608 (2015).
[Crossref]

Nat. Commun. (1)

Y. Arita, M. Mazilu, and K. Dholakia, “Laser-induced rotation and cooling of a trapped microgyroscope in vacuum,” Nat. Commun. 4, 2374 (2013).
[Crossref]

Nat. Nanotechnol. (1)

J. Millen, T. Deesuwan, P. F. Barker, and J. Anders, “Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere,” Nat. Nanotechnol. 9, 425–429 (2014).
[Crossref]

Nat. Phys. (2)

J. Gieseler, L. Novotny, and R. Quidant, “Thermal nonlinearities in a nanomechanical oscillator,” Nat. Phys. 9, 806–810 (2013).
[Crossref]

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

Nature (2)

A. D. O’Connell, M. Hofheinz, M. Ansmann, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, D. Sank, H. Wang, M. Weides, J. Wenner, J. M. Martinis, and A. N. Cleland, “Quantum ground state and single-phonon control of a mechanical resonator,” Nature 464, 697–703 (2010).
[Crossref]

J. Chan, T. P. M. Alegre, A. H. Safavi-Naeini, J. T. Hill, A. Krause, S. Gröblacher, M. Aspelmeyer, and O. Painter, “Laser cooling of a nanomechanical oscillator into its quantum ground state,” Nature 478, 89–92 (2011).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Optica (1)

Philos. Trans. R. Soc. London A (1)

P. Bartlett, S. I. Henderson, and S. J. Mitchell, “Measurement of the hydrodynamic forces between two polymer-coated spheres,” Philos. Trans. R. Soc. London A 359, 883–895 (2001).
[Crossref]

Phys. Rev. A (3)

F. Monteiro, S. Ghosh, E. C. van Assendelft, and D. C. Moore, “Optical rotation of levitated spheres in high vacuum,” Phys. Rev. A 97, 051802 (2018).
[Crossref]

M. Guillon and B. Stout, “Optical trapping and binding in air: imaging and spectroscopic analysis,” Phys. Rev. A 77, 023806 (2008).
[Crossref]

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 10593, 053801 (2016).
[Crossref]

Phys. Rev. Lett. (7)

P. F. Barker, “Doppler cooling a microsphere,” Phys. Rev. Lett. 105, 073002 (2010).
[Crossref]

J. Gieseler, B. Deutsch, R. Quidant, and L. Novotny, “Subkelvin parametric feedback cooling of a laser-trapped nanoparticle,” Phys. Rev. Lett. 109, 103603 (2012).
[Crossref]

A. Manjavacas and F. J. G. de Abajo, “Vacuum friction in rotating particles,” Phys. Rev. Lett. 105, 113601 (2010).
[Crossref]

R. K. Zhao, A. Manjavacas, F. J. G. de Abajo, and J. B. Pendry, “Rotational quantum friction,” Phys. Rev. Lett. 109, 123604 (2012).
[Crossref]

J. Millen, P. Z. Fonseca, T. Mavrogordatos, T. S. Monteiro, and P. F. Barker, “Cavity cooling a single charged levitated nanosphere,” Phys. Rev. Lett. 114, 123602 (2015).
[Crossref]

N. K. Metzger, R. F. Marchington, M. Mazilu, R. L. Smith, K. Dholakia, and E. M. Wright, “Measurement of the restoring forces acting on two optically bound particles from normal mode correlations,” Phys. Rev. Lett. 98, 068102 (2007).
[Crossref]

J. C. Meiners and S. R. Quake, “Direct measurement of hydrodynamic cross correlations between two particles in an external potential,” Phys. Rev. Lett. 82, 2211–2214 (1999).
[Crossref]

Rev. Mod. Phys. (1)

K. Dholakia and P. Zemanek, “Colloquium: gripped by light: optical binding,” Rev. Mod. Phys. 82, 1767–1791 (2010).
[Crossref]

Sci. Rep. (1)

M.-T. Wei, J. Ng, C. T. Chan, and H. D. Ou-Yang, “Lateral optical binding between two colloidal particles,” Sci. Rep. 6, 38883 (2016).
[Crossref]

Supplementary Material (4)

NameDescription
» Supplement 1       supplemental document
» Visualization 1       v001 Supplementary video
» Visualization 2       v002 Supplementary video
» Visualization 3       v003 Supplementary video

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Figures (5)

Fig. 1.
Fig. 1. Schematic showing the two normal modes of the bound array. (a) Stroboscopic image of two vaterite microparticles optically levitated and rotated in vacuum. The scale bar shows 5 μm. (b) The two normal modes of the bound array are depicted in the graphic, where R is the equilibrium particle separation of the particle centers, and x 1 , 2 indicate small displacements from the equilibrium position of the two particles along the x axis. The dashed line represents the potential related to the CoM motion of the two-particle system. The spring between the two spheres indicates the optical cross-interaction between the particles, the relative motion of them within the system. (c) The array is formed by the two foci of the trapping laser beams of 1070 nm propagating along the z axis within a range of the inter-particle separation ( 8    μm R 11    μm ).
Fig. 2.
Fig. 2. Two normal modes of the bound array and each autocorrelation function. (a) Position fluctuations for the CoM normal mode X 1 = ( 1 / 2 ) ( x 1 + x 2 ) , and the relative normal mode X 2 = ( 1 / 2 ) ( x 1 x 2 ) . (b) Normalized autocorrelation functions for X 1 (green) and X 2 (red). (c) An expanded view of (b) in the range of 0    s t 0.04    s . (d) Power spectral densities of X 1 and X 2 around their normal mode frequencies.
Fig. 3.
Fig. 3. Rotational and translational dynamics and ξ / κ of two rotating particles with a = 2.2    μm and with R = 9.8    μm at P = 0.081    mBar . (a) Power spectrum of the two rotating particles exhibiting their translational and rotational mode frequencies. (b) An expanded view in the frequency range of 10    kHz 100    kHz showing the two rotational frequencies of f r 1 , f r 2 and their second harmonics 2 f r 1 , 2 f r 2 together with their DFG signal 2 | f r 1 f r 2 | . (c) Rotational mode frequencies of the two particles for different damping coefficients Γ . (d) Normalized DFG signal 2 | f r 1 f r 2 | / f ^ r and ξ / κ . The dashed lines in (c) and (d) mark the parametric resonances between the rotational and translational motion of the particles.
Fig. 4.
Fig. 4. Particle displacement and rotational frequency shift induced by optical binding. (a)  ξ / κ and particle displacement Δ d as a function of R at P = 0.037    mBar . Inset images show the particle displacement Δ d induced by the presence of the other particle with R = 9.8    μm . (b) Rotational frequencies of the two rotating particles at different residual gas pressures. The frequency shift is induced at 1 / P = 26.9    mBar 1 (dashed line) by removing one of the particles. Inset images indicate the regimes of two-particle and single-particle systems.
Fig. 5.
Fig. 5. Rotation-induced cooling of the two-particle system. (a) A series of power spectra of the two rotating microparticles showing different CoM motion temperature T . Each line color corresponds to a different T as indicated in (b), where T is calibrated at NTP. (b) CoM motion T as a function of the mean rotation rate f ^ r and the corresponding residual gas pressure P . The dashed line marks the parametric resonances.

Equations (9)

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m A 11 d 2 d t 2 ( x 1 x 2 ) + d d t ( x 1 x 2 ) = ( A 11 A 12 A 12 A 11 ) ( f 1 ( t ) κ x 1 + ξ x 2 f 2 ( t ) κ x 2 + ξ x 1 ) ,
f j ( t ) = 0 ,
f i ( τ 1 ) f j ( τ 2 ) = 2 δ i j λ j k B T δ ( τ 1 τ 2 ) ,
d 2 X j d t 2 + Γ d X j d t + ω j 2 X j = ( F j m A 11 ) , j = 1 , 2 ,
ω 1 2 = ω 0 2 [ 1 ( ξ κ ) ] ( 1 + ε ) ,
ω 2 2 = ω 0 2 [ 1 + ( ξ κ ) ] ( 1 ε ) ,
X j ( t 1 ) X j ( t 2 ) = λ j k B T m 2 A 11 2 Ω j 2 Γ cos ( Ω j | t 1 t 2 | ) e Γ | t 1 t 2 | ,
ξ κ = [ ( 1 + ε ) / ( 1 ε ) Ω 1 2 / Ω 2 2 ] [ ( 1 + ε ) / ( 1 ε ) + Ω 1 2 / Ω 2 2 ] .
S ( f ) d f = σ 2 = k B T κ .

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