  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-Zender
interferometer scheme where we separate out and beat the scattered light from
the bead 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 and 3 $\mu$m diameter beads
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 bead 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 for lateral displacements
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 obtain a displacement resolution of around 2 nm
for 1.1 $\mu$m diameter probes by locking the interferometer to a frequency
stabilized diode laser.
