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

TL;DR

This paper introduces a phase-sensitive interferometric technique for measuring the dynamics of optically trapped particles, achieving improved axial resolution and enabling simultaneous displacement and trap stiffness measurements.

Contribution

The authors develop a balanced detection method using a Mach-Zender interferometer to measure phase shifts, enhancing resolution over traditional intensity-based detection methods.

Findings

Achieved around 2 nm displacement resolution for 1.1 μm beads.

Demonstrated simultaneous measurement of particle displacement and trap spring constant.

Matched experimental phase contour results with theoretical simulations.

Abstract

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.