We use an optimal control protocol to cool one mode of the center of mass motion of an optically levitated nanoparticle. The feedback technique relies on exerting a Coulomb force on a charged particle with a pair of electrodes and follows the control law of a linear quadratic regulator, whose gains are optimized by a machine learning algorithm in under 5 s. With a simpler and more robust setup than optical feedback schemes, we achieve a minimum center of mass temperature of 5 mK at 3 × 10 −7 mbar and transients 10 to 600 times faster than cold damping. This cooling technique can be easily extended to 3D cooling and is particularly relevant for studies demanding high repetition rates and force sensing experiments with levitated objects.

Nanomechanical resonators are widely operated as force and mass sensors with sensitivities in the zepto-Newton (10 −21 ) and yocto-gram (10 −24 ) regime, respectively. Their accuracy, however, is usually undermined by high uncertainties in the effective mass of the system, whose estimation is a non-trivial task. This critical issue can be addressed in levitodynamics, where the nanoresonator typically consists of a single silica nanoparticle of well-defined mass Yet, current methods assess the mass of the levitated nanoparticles with uncertainties up to a few tens of percent, therefore preventing to achieve unprecedented sensing performances. Here, we present a novel measurement protocol that uses the electric field from a surrounding plate capacitor to directly drive a charged optically levitated particle in moderate vacuum. The developed technique estimates the mass within a statistical error below 1% and a systematic error of ∼ 2%, and paves the way toward more reliable sensing and metrology applications of levitodynamics systems.

Levitation optomechanics exploits the unique mechanical properties of trapped nano-objects in vacuum to address some of the limitations of clamped nanomechanical resonators. In particular, its performance is foreseen to contribute to a better understanding of quantum decoherence at the mesoscopic scale as well as to lead to novel ultrasensitive sensing schemes. While most efforts have focused so far on the optical trapping of low-absorption silica particles, further opportunities arise from levitating objects with internal degrees of freedom, such as color centers. Nevertheless, inefficient heat dissipation at low pressures poses a challenge because most nano-objects, even with low-absorption materials, experience photodamage in an optical trap. Here, by using a Paul trap, we demonstrate levitation in vacuum and center-of-mass feedback cooling of a nanodiamond hosting a single nitrogen-vacancy center. The achieved level of motion control enables us to optically interrogate and characterize the emitter response. The developed platform is applicable to a wide range of other nano-objects and represents a promising step toward coupling internal and external degrees of freedom.

We study the dynamics of the center of mass of a Brownian particle levitated in a Paul trap. We focus on the overdamped regime in the context of levitodynamics, comparing theory with our numerical simulations and experimental data from a nanoparticle in a Paul trap. We provide an exact analytical solution to the stochastic equation of motion, expressions for the standard deviation of the motion, and thermalization times by using the WKB method under two different limits. Finally, we prove the power spectral density of the motion can be approximated by that of an Ornstein-Uhlenbeck process and use the found expression to calibrate the motion of a trapped particle.

The levitation of condensed matter in vacuum allows the study of its physical properties under extreme isolation from the environment. It also offers a venue to investigate quantum mechanics with large systems, at the transition between the quantum and classical worlds. In this work, we study a novel hybrid levitation platform that combines a Paul trap with a weak but highly focused laser beam, a configuration that integrates a deep potential with excellent confinement and motion detection. We combine simulations and experiments to demonstrate the potential of this approach to extend vacuum trapping and interrogation to a broader range of nanomaterials, such as absorbing particles. We study the stability and dynamics of different specimens, such as fluorescent dielectric crystals and gold nanorods, and demonstrate stable trapping down to pressures of 1 mbar.