The interaction between a dielectric particle with polarizability α α and an electric field E → → is given by the gradient force F → → g r a d = − − α α ∇ ∇ → → E → → 2 / 2 . When a particle is trapped and optically levitated in the focus of a Gaussian laser beam, the force can be approximated to first order by F g r a d , q = − − k q q with q ∈ ∈ { x , y , z } , i.e. a harmonic oscillator with frequency ω ω q = k q / M , where M is the particle's mass. Including passive damping, active external feedback and coupling results in the Langevin equations of motion: