Abstract
Levitating nanoparticles trapped in optical potentials at low pressure open the experimental investigation of nonlinear ballistic phenomena. With engineered non-linear potentials and fast optical detection, the observation of autonomous transient mechanical effects, such as instantaneous speed and acceleration stimulated purely by initial position uncertainty, are now achievable. By using parameters of current low pressure experiments, we simulate and analyse such uncertainty-induced particle ballistics in a cubic optical potential demonstrating their evolution, faster than their standard deviations, justifying the feasibility of the experimental verification. We predict, the maxima of instantaneous speed and acceleration distributions shift alongside the potential force, while the maximum of position distribution moves opposite to it. We report that cryogenic cooling is not necessary in order to observe the transient effects, while a low uncertainty in initial particle speed is required, via cooling or post-selection, to not mask the effects. These results stimulate the discussion for both attractive stochastic thermodynamics, and extension of recently explored quantum regime.
Highlights
Levitating nanoparticles trapped in optical potentials at low pressure open the experimental investigation of nonlinear ballistic phenomena
We describe the properties of the stochastic motion of an underdamped Brownian particle in the unstable cubic potential
The dynamics of the damped Brownian particle in the cubic potential V (x) = Kx3/3 is described by the following Langevin equation x + γ x + κx2 = 2 kBTγ ξ(t), ξ(t) = 0, ξ(t)ξ(t′) = δ(t − t′)
Summary
Levitating nanoparticles trapped in optical potentials at low pressure open the experimental investigation of nonlinear ballistic phenomena. Stochastic levitating optomechanics in vacuum is a dynamically expanding experimental platform with a unique potential to test and exploit strong nonlinear motional effects without any friction, and bring them close to the quantum domain This uniqueness arises from the possibility to combine manipulation of the optical trapping potential by a spatial light modulator, inducing new unexplored nonlinearities, and fast optical measurement to verify rapid transient effects using modern optical detectors. At low pressure, it allows direct observation of stochastic underdamped mechanical p henomena[1,2,3,4,5,6,7], which allow access to the instantaneous particle speed not measurable in the overdamped m otion[8,9]. It is a crucial step to further accumulate such uncertaintyinduced phenomena, and later use them in the aforementioned applications
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