Low frequency dynamical stabilisation in optical tweezers

Abstract

It is well known that a rigid pendulum with minimal friction will occupy a stable equilibrium position vertically upwards when its suspension point is oscillated at high frequency. The phenomenon of the inverted pendulum was explained by Kapitza by invoking a separation of timescales between the high frequency modulation and the much lower frequency pendulum motion, resulting in an effective potential with a minimum in the inverted position. We present here a study of a microscopic optical analogue of Kapitza's pendulum that operates in different regimes of both friction and driving frequency. The pendulum is realized using a microscopic particle held in a scanning optical tweezers and subject to a viscous drag force. The motion of the optical pendulum is recorded and analyzed by digital video microscopy and particle tracking to extract the trajectory and stable orientation of the particle. In these experiments we enter the regime of low driving frequency, where the period of driving is comparable to the characteristic relaxation time of the radial motion of the pendulum with finite stiffness. In this regime we find stabilization of the pendulum at angles other than the vertical (downwards) is possible for modulation amplitudes exceeding a threshold value where, unlike the truly high frequency case studied previously, both the threshold amplitude and equilibrium position are found to be functions of friction. Experimental results are complemented by an analytical theory for induced stability in the low frequency driving regime with friction. © (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.