Probing the dynamics of an optically trapped particle by phase sensitive back focal plane interferometry

The dynamics of an optically trapped particle are often determined by measuring intensity shifts of the back-scattered light from the particle using position sensitive detectors. We present a technique which measures the phase of the back-scattered light using balanced detection in an external Mach-Zehnder interferometer scheme where we separate out and beat the scattered light from the particle and that from the top surface of our trapping chamber. The technique has improved axial motion resolution over intensity-based detection, and can also be used to measure lateral motion of the trapped particle. In addition, we are able to track the Brownian motion of trapped 1.1 and 3 μm diameter particles from the phase jitter and show that, similar to intensity-based measurements, phase measurements can also be used to simultaneously determine displacements of the trapped particle as well as the spring constant of the trap. For lateral displacements, we have matched our experimental results with a simulation of the overall phase contour of the back-scattered light by using plane wave decomposition in conjunction with Mie scattering theory. The position resolution is limited by path drifts of the interferometer which we have presently reduced to demonstrate the capability of sub-nm displacement resolution in the axial direction for 1.1 μm diameter particles by locking the interferometer to a frequency stabilized diode laser.