Abstract

Optically levitated nano-objects in vacuum are among the highest quality mechanical oscillators, and thus of great interest for force sensing, cavity quantum optomechanics, and nanothermodynamic studies. These precision applications require exquisite control. Here, we present full control over the rotational and translational dynamics of an optically levitated silicon nanorod. We trap its center-of-mass and align it along the linear polarization of the laser field. The rod can be set into rotation at a predefined frequency by exploiting the radiation pressure exerted by elliptically polarized light. The rotational motion of the rod dynamically modifies the optical potential, which allows tuning of the rotational frequency over hundreds of kilohertz. Through nanofabrication, we can tailor all of the trapping frequencies and the optical torque, achieving reproducible dynamics that are stable over months, and analytically predict the motion with great accuracy. This first demonstration of full ro-translational control of nanoparticles in vacuum opens up the fields of rotational optomechanics, rotational ground state cooling, and the study of rotational thermodynamics in the underdamped regime.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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2016 (10)

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530, 313–316 (2016).
[Crossref]

P. Z. G. Fonseca, E. B. Aranas, J. Millen, T. S. Monteiro, and P. F. Barker, “Nonlinear dynamics and millikelvin cavity-cooling of levitated nanoparticles,” Phys. Rev. Lett. 117, 173602 (2016).
[Crossref]

G. Ranjit, M. Cunningham, K. Casey, and A. A. Geraci, “Zeptonewton force sensing with nanospheres in an optical lattice,” Phys. Rev. A 93, 053801 (2016).
[Crossref]

A. T. M. A. Rahman, A. C. Frangeskou, M. S. Kim, S. Bose, G. W. Morley, and P. F. Barker, “Burning and graphitization of optically levitated nanodiamonds in vacuum,” Sci. Rep. 6, 21633 (2016).
[Crossref]

T. M. Hoang, Y. Ma, J. Ahn, J. Bang, F. Robicheaux, Z.-Q. Yin, and T. Li, “Torsional optomechanics of a levitated nonspherical nanoparticle,” Phys. Rev. Lett. 117, 123604 (2016).
[Crossref]

B. A. Stickler, S. Nimmrichter, L. Martinetz, S. Kuhn, M. Arndt, and K. Hornberger, “Rotranslational cavity cooling of dielectric rods and disks,” Phys. Rev. A 94, 033818 (2016).
[Crossref]

J. Millen, S. Kuhn, F. Patolsky, A. Kosloff, and M. Arndt, “Cooling and manipulation of nanoparticles in high vacuum,” Proc. SPIE 9922, 99220C (2016).
[Crossref]

B. A. Stickler, B. Papendell, and K. Hornberger, “Spatio-orientational decoherence of nanoparticles,” Phys. Rev. A 94, 033828 (2016).
[Crossref]

C. Zhong and F. Robicheaux, “Decoherence of rotational degrees of freedom,” Phys. Rev. A 94, 052109 (2016).
[Crossref]

S. H. Simpson, L. Chvátal, and P. Zemánek, “Synchronization of colloidal rotors through angular optical binding,” Phys. Rev. A 93, 023842 (2016).
[Crossref]

2015 (7)

B. W. Shore, P. Dömötör, E. Sadurní, G. Süssmann, and W. P. Schleich, “Scattering of a particle with internal structure from a single slit,” New J. Phys. 17, 013046 (2015).
[Crossref]

B. A. Stickler and K. Hornberger, “Molecular rotations in matter-wave interferometry,” Phys. Rev. A 92, 023619 (2015).
[Crossref]

M. Bhattacharya, “Rotational cavity optomechanics,” J. Opt. Soc. Am. B 32, B55 (2015).
[Crossref]

H. Shi and M. Bhattacharya, “Optomechanics based on angular momentum exchange between light and matter,” J. Phys. B 49, 153001 (2015).
[Crossref]

L. Shao, Z.-J. Yang, D. Andrén, P. Johansson, and M. Käll, “Gold nanorod rotary motors driven by resonant light scattering,” ACS Nano 9, 12542–12551 (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]

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

2014 (4)

J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, “Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state,” Nat. Nanotech. 9, 358–364 (2014).
[Crossref]

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

M. Arndt and K. Hornberger, “Insight review: testing the limits of quantum mechanical superpositions,” Nat. Phys. 10, 271–277 (2014).
[Crossref]

J. Bateman, S. Nimmrichter, K. Hornberger, and H. Ulbricht, “Near-field interferometry of a free-falling nanoparticle from a point-like source,” Nat. Commun. 5, 4788 (2014).
[Crossref]

2013 (5)

J. Bochmann, A. Vainsencher, D. D. Awschalom, and A. N. Cleland, “Nanomechanical coupling between microwave and optical photons,” Nat. Phys. 9, 712–716 (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]

N. Kiesel, F. Blaser, U. Delic, D. Grass, R. Kaltenbaek, and M. Aspelmeyer, “Cavity cooling of an optically levitated nanoparticle,” Proc. Natl. Acad. Sci. USA 110, 14180–14185 (2013).
[Crossref]

P. Asenbaum, S. Kuhn, S. Nimmrichter, U. Sezer, and M. Arndt, “Cavity cooling of free silicon nanoparticles in high-vacuum,” Nat. Commun. 4, 2743 (2013).
[Crossref]

A. Lehmuskero, R. Ogier, T. Gschneidtner, P. Johansson, and M. Käll, “Ultrafast spinning of gold nanoparticles in water using circularly polarized light,” Nano Lett. 13, 3129–3134 (2013).
[Crossref]

2012 (2)

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. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, “A high-resolution microchip optomechanical accelerometer,” Nat. Photonics 6, 768–772 (2012).
[Crossref]

2011 (4)

J. Chan, T. P. Mayer 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]

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref]

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

J. T. Rubin and L. I. Deych, “Optical forces due to spherical microresonators and their manifestation in optically induced orbital motion of nanoparticles,” Phys. Rev. A 84, 023844 (2011).
[Crossref]

2010 (5)

L. Tong, V. D. Miljkovic, and M. Kall, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano Lett. 10, 268–273 (2010).
[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]

B. Kane, “Levitated spinning graphene flakes in an electric quadrupole ion trap,” Phys. Rev. B 82, 115441 (2010).
[Crossref]

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]

O. Romero-Isart, M. Juan, R. Quidant, and J. Cirac, “Toward quantum superposition of living organisms,” New J. Phys. 12, 033015 (2010).
[Crossref]

2009 (1)

P. H. Jones, F. Palmisano, F. Bonaccorso, P. G. Gucciardi, G. Calogero, A. C. Ferrari, and O. M. Marago, “Rotation detection in light-driven nanorotors,” ACS Nano 3, 3077–3084 (2009).
[Crossref]

2008 (1)

F. Borghese, P. Denti, R. Saija, M. Iatì, and O. Maragò, “Radiation torque and force on optically trapped linear nanostructures,” Phys. Rev. Lett. 100, 163903 (2008).
[Crossref]

2007 (1)

M. Bhattacharya and P. Meystre, “Using a Laguerre-Gaussian beam to trap and cool the rotational motion of a mirror,” Phys. Rev. Lett. 99, 153603 (2007).
[Crossref]

2006 (1)

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. MacKowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref]

2001 (1)

N. Schlosser, G. Reymond, I. Protsenko, and P. Grangier, “Sub-Poissonian loading of single atoms in a microscopic dipole trap,” Nature 411, 1024–1027 (2001).
[Crossref]

1998 (2)

W. D. Phillips, “Nobel Lecture: laser cooling and trapping of neutral atoms,” Rev. Mod. Phys. 70, 721–741 (1998).
[Crossref]

M. E. J. Friese, T. A. Nieminen, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical alignment and spinning of laser-trapped microscopic particles,” Nature 394, 348–350 (1998).
[Crossref]

1996 (1)

R. Penrose, “On gravity’s role in quantum state reduction,” Gen. Relativity Gravitation 28, 581–600 (1996).
[Crossref]

1993 (1)

A. J. P. Van Haasteren, H. J. Frankena, J. J. G. M. Vandertol, and M. O. van Deventer, “Modeling and characterization of an electrooptic polarization controller on LiNbO3,” J. Lightwave Technol. 11, 1151–1157 (1993).
[Crossref]

1990 (2)

G. C. Ghirardi, R. Grassi, and A. Rimini, “Continuous-spontaneous-reduction model involving gravity,” Phys. Rev. A 42, 1057–1064 (1990).
[Crossref]

G. C. Ghirardi, P. Pearle, and A. Rimini, “Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles,” Phys. Rev. A 42, 78–89 (1990).
[Crossref]

1987 (2)

L. Diósi, “A universal master equation for the gravitational violation of quantum mechanics,” Phys. Lett. A 120, 377–381 (1987).
[Crossref]

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

1981 (1)

A. D. Eisner and I. Gallily, “On the stochastic nature of the motion of nonspherical aerosol particles: III. The rotational diffusion diadic and applications,” J. Colloid Interface Sci. 81, 214–233 (1981).
[Crossref]

Ahn, J.

T. M. Hoang, Y. Ma, J. Ahn, J. Bang, F. Robicheaux, Z.-Q. Yin, and T. Li, “Torsional optomechanics of a levitated nonspherical nanoparticle,” Phys. Rev. Lett. 117, 123604 (2016).
[Crossref]

Allman, M. S.

J. D. Teufel, T. Donner, D. Li, J. W. Harlow, M. S. Allman, K. Cicak, A. J. Sirois, J. D. Whittaker, K. W. Lehnert, and R. W. Simmonds, “Sideband cooling of micromechanical motion to the quantum ground state,” Nature 475, 359–363 (2011).
[Crossref]

Anant, V.

R. Riedinger, S. Hong, R. A. Norte, J. A. Slater, J. Shang, A. G. Krause, V. Anant, M. Aspelmeyer, and S. Gröblacher, “Non-classical correlations between single photons and phonons from a mechanical oscillator,” Nature 530, 313–316 (2016).
[Crossref]

Anders, J.

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

Andrén, D.

L. Shao, Z.-J. Yang, D. Andrén, P. Johansson, and M. Käll, “Gold nanorod rotary motors driven by resonant light scattering,” ACS Nano 9, 12542–12551 (2015).
[Crossref]

Aranas, E. B.

P. Z. G. Fonseca, E. B. Aranas, J. Millen, T. S. Monteiro, and P. F. Barker, “Nonlinear dynamics and millikelvin cavity-cooling of levitated nanoparticles,” Phys. Rev. Lett. 117, 173602 (2016).
[Crossref]

Arcizet, O.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. MacKowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97, 133601 (2006).
[Crossref]

Arita, Y.

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

Arndt, M.

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Supplementary Material (1)

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» Supplement 1: PDF (889 KB)      Supplement 1

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Figures (4)

Fig. 1.
Fig. 1.

(a) Nanofabricated silicon nanorods of length (725±15)  nm and diameter d(130±13)  nm are optically levitated in a standing laser wave at low pressures. The light they scatter is collected by a multimode optical fiber placed close to the trap waist. (b) The rods have five degrees of freedom that can be controlled: three translational (x,y,z) and two rotational (α,β). (c) By monitoring the scattered light, trapping of all five degrees of freedom can be observed in the PSD when the trap light is linearly polarized. These data were acquired at a pressure of 4 mbar. The appearance of the various harmonics can be explained by slight misalignment of the trap as discussed in Supplement 1.

Fig. 2.
Fig. 2.

(a) Experimental setup. Light at λ=1550  nm is produced by a fiber laser (Keysight 81663A), and then goes through an electro-optical in-fiber polarization controller (EOSPACE), allowing us to realize arbitrary wave-plate operations. The light is amplified in a fiber amplifier (Hangzhou Huatai Optic HA5435B-1) and split equally to make the two arms of the trap. Stress-induced birefringence in the fibers can be accounted for with polarization controlling paddles (PCPs). The system is completely fiber-based until out-coupled to the aspheric trapping lenses (f=20  mm). The inset shows a scanning electron microscopy micrograph of a rod that was launched and captured on a sample plate. The scattered light signal reveals the nanorod dynamics in case of (b) co-linear polarization, and (c) the strongly driven rotation of the rod for circularly polarized trapping light.

Fig. 3.
Fig. 3.

Comparing the dynamics when the nanorod is (a) trapped in all degrees of freedom by linearly polarized light and (b) driven to rotate in the α direction by circularly polarized light. (c) The PSD for circularly (red) and linearly (blue) polarized light. For circular polarization, the trapping frequency fα vanishes, and the rotational frequency fα,rot appears. The peak at fβ vanishes since the motion in β is stabilized when the rod is spinning. Markers indicate predicted trapping frequencies. The rotational frequency scales (d) linearly with power, and (e) decreases with increasing pressure, as predicted by Eq. (5). Markers represent the mean value of fα,rot, the shaded areas represent the full range of fα,rot, and solid lines are the theoretically expected maximal value of fα,rot. The broad frequency distribution of fα,rot is due to coupling between the motion in α and x, y (radial). (f) Perturbations from the equilibrium position (lower panel) are reflected in instantaneous frequency fluctuations (top panel). (g) The correlation between the radial position and fα,rot.

Fig. 4.
Fig. 4.

Effect of performing a QWP operation on the trapping light at 5 mbar, either increasing from 0° (crosses) or decreasing from 90° (circles). At 0° and 90° the trap is linearly polarized along the y axis. At 45° the polarization is circular. (a) Shift of the trapping frequencies for different QWP settings. For small deviations from linear polarization the trapping frequencies decrease due to a lower trapping potential. At 30° from the starting linear polarization, the light is circularly polarized enough to drive fα,rot, at which point fα,β vanish, and fz drops. At 85° from the starting linear polarization, the motion becomes trapped again. (b) Because of this hysteresis the driven rotational frequency fα,rot can be tuned over several hundred kilohertz via the ellipticity of the trapping field. The markers indicate the mean value of fα,rot, and the shaded region represents the range of measured frequencies.

Equations (5)

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fx,y=12π8Ptotχπϱcw04,fz=12π4Ptotχk2πϱcw02,fβ=12π48Ptotχπϱcw022(Δχχ+(k)212),fα=12π48PtotΔχπϱcw022,
Nα=PtotΔχ2d4k348cw02[Δχη1(k)+χη2(k)],
η1(k)=3411dξ(1ξ2)sinc2(kξ2),η2(k)=3811dξ(13ξ2)sinc2(kξ2).
Γ=dpg2M2πmgkBT(32+π4),
fα,max=Nα2πIΓ,

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