Brownian Motion of elliptical particles in an optical trap

Master thesis in the group of Thomas Franosch

Thermally agitated particle confined by an optical trap (Figure: Courtesy Sylvia Jeney and Alain Doyon)
Optical trapping constitutes one of the major tools in biophysics to position and manipulate microsized objects. Recent experimental advances allowed to combine optical trapping with high bandwidth ultrasensitive detectors to investigate the fundamentals of Brownian motion with unprecedented accuracy. The trap exerts essentially a harmonic force on a spherical particle towards the laser focus due to the difference in the refractive index relative to the solvent. These forces are counteracted by the friction in the fluid and the motion is incessantly agitated by thermal noise.

Elliptical particles display orientation as an additional degree of freedom. Two non-trivial phenomena arise. First, since the trap is generated by focussing the light the intensity profile close to the center is anisotropic giving rise to torques on the trapped particle. One expects that the torques are not independent of the forces, thus translational excursions from the center are more likely when the particle's axis is aligned with the displacement. A second ingredient is the anisotropic friction experienced by the particle. By hydrodynamics the resistance to translation is different for motion along the axis of symmetry and perpendicular to it. While the motion allows for a simple description in the body-fixed frame, the experiment monitors a complex dynamics in the lab frame.

In this project we want to formulate a theory for the coupled translational-orientational motion based on the underlying Langevin equation. Since an exact solution appears not to be feasible, approximation strategies starting from an exact reformulation of the problem by projection operator techniques shall be implemented for the memory kernel. The theoretical approach should be complemented by Brownian dynamics simulations.


The successful candidate should have a strong background in theoretical physics, in particular statistical physics, and be skilled in computing which is a prerequisite to implement the brownian dynamics simulations. Furthermore, good analytic skills are required to develop the theoretical description of the complex motion. The new group member should look forward to participate in many discussions within the team as well as with experimentalists.


Thomas Franosch