Uncertainty-induced instantaneous speed and acceleration of a levitated particle

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.

Nonlinear squeezing of stochastic motion

“…This potential cannot be approximated by a harmonic potential in any limiting cases. Motivated by the short-term deterministic dynamics of a massive particle in a cubic potential [23,24,26] we examine the nonlinear variable p + λx 2 . This variable is chosen as an exemplar, however the principles applied to derive the threshold may be applied to other variables such as p + λx n , providing a collection of thresholds for nonlinear motion.…”

Stroboscopic thermally-driven mechanical motion

“…Unstable asymmetrical systems can turn fluctuations into directional motion. However, the limitation upon observing the effect in a one-dimensional nonlinear system (such as the cubic potential 29 , 51 , 52 ) arises from the rapidly increasing noise from that unstable behaviour. A combination of a thermal bias and stroboscopic cooling can overcome the limitation.…”

“…In the limit of low pressure, the position of the system’s variable x barely moves around its initial conditions . However, the main nonlinear effect is translated to the instantaneous velocity 52 . In the stroboscopic control, while the cooling of the driver y is implemented by feedback control to the desired , the noise from the driver y induces the motion in the mean instantaneous velocity .…”

“…It is an autonomous motion that does not require an external coherent drive. It has been experimentally verified in the overdamped regime 29,51 , and recently investigated in the underdamped limit 52 . However, such phenomena are limited when the directional motion and the fluctuating driver are combined in one degree of freedom (1D).…”

“…It opens a larger space to observe transients of interacting systems 44 and, possibly, even complex systems 45,46 .Levitating optomechanics has opened an extensive theoretical and experimental investigation of transient, unstable motion in nonlinear potentials [47][48][49][50] . A pivotal nonlinear effect uses fluctuations positively to generate directional motion 29,51,52 . It is an autonomous motion that does not require an external coherent drive.…”