Non-conservative effects in optically trapped, low symmetry particles

The force field experienced by a sphere, trapped in a tightly focused Gaussian beam, is approximately conservative for small displacements. For lower symmetry systems, this is not generally the case. Even when very tightly trapped, a particle in such a system displays the effects of the non-conservative force field to which it is exposed. It does not come to thermal equilibrium, but reaches a steady state in which its stochastic motion is subject to a deterministic, cyclic bias. Here, we examine the dynamics of such a system, and show that the non-conservative nature of the force field manifests itself in both the covariance and the spectral density of the generalized coordinates of the particle. In addition, we show that the coupling between different types of thermal motion of such particles, i.e. rotational and translational, is asymmetric, which leads to the periodic bias to the motion. These points are illustrated through computational simulations of the Brownian dynamics of a trapped silica disk.