Nonlinear Mode Coupling and Synchronization of a Vacuum-Trapped Nanoparticle

Abstract

We study the dynamics of a laser-trapped nanoparticle in high vacuum. Using parametric coupling to an external excitation source, the linewidth of the nanoparticle's oscillation can be reduced by three orders of magnitude. We show that the oscillation of the nanoparticle and the excitation source are synchronized, exhibiting a well-defined phase relationship. Furthermore, the external source can be used to controllably drive the nanoparticle into the nonlinear regime, thereby generating strong coupling between the different translational modes of the nanoparticle. Our work contributes to the understanding of the nonlinear dynamics of levitated nanoparticles in high vacuum and paves the way for studies of pattern formation, chaos, and stochastic resonance. PACS numbers:Synchronization of spatially separate processes occur in biological, chemical, physical, and social systems, and have attracted the interest of scientists for centuries. Nanomechanical oscillators naturally lend themselves to the experimental [1-5] and theoretical [6] study of nonlinear behavior and synchronization. The nonlinear regime can be exploited for applications including phonon-cavity cooling [7,8], precision frequency measurements [9], signal amplification via stochastic resonance [10,11], mass sensing [12] and quantum non-demolition measurements [13][14][15]. In addition, nonlinear mechanical oscillators have been proposed as memory elements [16,17] and to hallmark classical to quantum transitions [18].

Optically levitated nanoparticle as a model system for stochastic bistable dynamics

“…By optimizing the feedback settings (Supplementary Note 2) and carefully screening important sources of noise such as mechanical vibrations and air turbulences, we obtain a highly stable resonator with frequency fluctuations improved by one to two orders of magnitude compared to previous works121 (Supplementary Note 3). When one of the spatial modes is parametrically driven at resonance21, the particle explores the anharmonic part of the optical potential, which can be modelled as a Duffing nonlinearity1. As a result, the equation of motion for the driven coordinate, which we choose to be x , reads…”

Ultrasensitive hysteretic force sensing with parametric nonlinear oscillators

“…We present estimates for the range of forces which can be detected with two different resonators. We first consider a laser-trapped nanoparticle in high vacuum [26] with a very high quality factor and a negative Duffing coefficient α. This system allows for a wide manipulation of the system parameters with small thermal noise.…”

An analytical model for the detection of levitated nanoparticles in optomechanics

“…4 We believe that for the larger particles it is relatively easy to move outside the linear region of the trap to the non-linear part. This introduces coupling between the different modes of oscillations 8,9 and hence the appearances of frequencies other than the desired one. It is also plausible that strong scattering from large particles and the ensuing interference around the trapping region alters the trapping potential profile which introduces coupling between different axes that is otherwise assumed decoupled.…”

“…Subsequently, these frequencies are used for parametric feedback cooling to actively control the motion of a levitated particle. [1][2][3]5,[8][9][10][11][12][13][14] As with other interferometric schemes, this system is well known for its high precision and resilience to noise. In optomechanical setups, this is further enhanced by a balanced detection system.…”