Precession Motion in Levitated Optomechanics.

We investigate experimentally the dynamics of a nonspherical levitated nanoparticle in a vacuum. In addition to translation and rotation motion, we observe the light torque-induced precession and nutation of the trapped particle. We provide a theoretical model, which we numerically simulate and from which we derive approximate expressions for the motional frequencies. Both the simulation and approximate expressions we find in good agreement with experiments. We measure a torque of 1.9±0.5×10^{-23}  N m at 1×10^{-1}  mbar, with an estimated torque sensitivity of 3.6±1.1×10^{-31}  N m/sqrt[Hz] at 1×10^{-7}  mbar.

[1]  B. Chui,et al.  Single spin detection by magnetic resonance force microscopy , 2004, Nature.

[2]  Christoph Dellago,et al.  Direct measurement of Kramers turnover with a levitated nanoparticle. , 2017, Nature nanotechnology.

[3]  T. S. Monteiro,et al.  Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles. , 2015, Physical review letters.

[4]  A. Geraci,et al.  Zeptonewton force sensing with nanospheres in an optical lattice , 2016, 1603.02122.

[5]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[6]  Mark G. Raizen,et al.  Millikelvin cooling of an optically trapped microsphere in vacuum , 2011, 1101.1283.

[7]  Hendrik Ulbricht,et al.  Force sensing with an optically levitated charged nanoparticle , 2017, 1706.09774.

[8]  Jonghoon Ahn,et al.  Experimental Test of the Differential Fluctuation Theorem and a Generalized Jarzynski Equality for Arbitrary Initial States. , 2017, Physical review letters.

[9]  Lukas Novotny,et al.  Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle. , 2014, Physical review letters.

[10]  Jonghoon Ahn,et al.  Torsional Optomechanics of a Levitated Nonspherical Nanoparticle. , 2016, Physical review letters.

[11]  Jacob P. J. Murphy,et al.  Optical and magnetic measurements of gyroscopically stabilized graphene nanoplatelets levitated in an ion trap , 2016, 1612.05928.

[12]  Stefan Kuhn,et al.  Optically driven ultra-stable nanomechanical rotor , 2017, Nature Communications.

[13]  Stefan Kuhn,et al.  Full Rotational Control of Levitated Silicon Nanorods , 2016, 1608.07315.

[14]  F. J. Rodríguez-Fortuño,et al.  Lateral Casimir Force on a Rotating Particle near a Planar Surface. , 2016, Physical review letters.

[15]  Lukas Novotny,et al.  GHz Rotation of an Optically Trapped Nanoparticle in Vacuum. , 2018, Physical review letters.

[16]  M. Torovs,et al.  Detection of anisotropic particles in levitated optomechanics , 2018, Physical Review A.

[17]  E. B. Aranas,et al.  Thermometry of levitated nanoparticles in a hybrid electro-optical trap , 2017 .

[18]  R Kaltenbaek,et al.  Large quantum superpositions and interference of massive nanometer-sized objects. , 2011, Physical review letters.

[19]  Kishan Dholakia,et al.  Supplementary Figure S1: Numerical Psd Simulation. Example Numerical Simulation of The , 2022 .

[20]  Florian Blaser,et al.  Cavity cooling of an optically levitated submicron particle , 2013, Proceedings of the National Academy of Sciences.

[21]  Lukas Novotny,et al.  Sensing Static Forces with Free-Falling Nanoparticles. , 2017, Physical review letters.

[22]  Yong Li,et al.  Coriolis-force-induced coupling between two modes of a mechanical resonator for detection of angular velocity , 2018 .

[23]  M. Raizen,et al.  Measurement of the Instantaneous Velocity of a Brownian Particle , 2010, Science.

[24]  F. Robicheaux,et al.  Shot-noise-dominant regime for ellipsoidal nanoparticles in a linearly polarized beam , 2017, 1701.04477.

[25]  H. Ulbricht,et al.  Wigner Function Reconstruction in Levitated Optomechanics , 2017, 1707.07859.

[26]  Steven W. Ellingson,et al.  Radio Systems Engineering , 2016 .

[27]  Mauro Paternostro,et al.  Parametric feedback cooling of levitated optomechanics in a parabolic mirror trap , 2016, 1603.02917.

[28]  M. Paternostro,et al.  Non-interferometric test of the continuous spontaneous localization model based on rotational optomechanics , 2017, New Journal of Physics.

[29]  Lukas Novotny,et al.  Thermal nonlinearities in a nanomechanical oscillator , 2013, Nature Physics.

[30]  M. R. Freeman,et al.  Nanoscale torsional optomechanics , 2012, 1210.1852.

[31]  M. Roukes,et al.  Ultimate limits to inertial mass sensing based upon nanoelectromechanical systems , 2003, physics/0309075.

[32]  Christoph Dellago,et al.  Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state. , 2014, Nature nanotechnology.

[33]  James Bateman,et al.  Near-field interferometry of a free-falling nanoparticle from a point-like source , 2013, Nature Communications.

[34]  Qinkai Han,et al.  Optically Levitated Nanodumbbell Torsion Balance and GHz Nanomechanical Rotor. , 2018, Physical review letters.

[35]  Angelo Bassi,et al.  Models of Wave-function Collapse, Underlying Theories, and Experimental Tests , 2012, 1204.4325.

[36]  문정진 § 19 , 2000 .

[37]  J. Anders,et al.  Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere. , 2013, Nature nanotechnology.

[38]  Stefan Kuhn,et al.  Cavity-Assisted Manipulation of Freely Rotating Silicon Nanorods in High Vacuum , 2015, Nano letters.

[39]  Quantum many-body simulation and torsional matter-wave interferometry with a levitated nanodiamond , 2016, 1611.05599.

[40]  J. Ralph,et al.  Real-Time Kalman Filter: Cooling of an Optically Levitated Nanoparticle , 2017, 1712.07921.

[41]  Peter F. Barker,et al.  Laser refrigeration, alignment and rotation of levitated Yb3+:YLF nanocrystals , 2017 .

[42]  Antonio-José Almeida,et al.  NAT , 2019, Springer Reference Medizin.

[43]  Andrew G. Glen,et al.  APPL , 2001 .

[44]  S. Maskell,et al.  Dynamical model selection near the quantum-classical boundary , 2017, Physical Review A.

[45]  Christoph Dellago,et al.  Direct Measurement of Photon Recoil from a Levitated Nanoparticle. , 2016, Physical review letters.