The elimination of polarization-dependent crosstalk between radial displacements of levitated nanospheres in optical tweezers in vacuum

The displacement measurement of the levitated particle is essential in optical tweezers in vacuum. However, crosstalk between the radial axes often occurs and will deteriorate the measurement precision. Common methods are proposed to align the coordinate systems of the motion and measurement, but few have considered the polarizations of the trapping beam and possible crosstalk control. Here single SiO2 particles with a diameter of 200nm are trapped in the single-beam optical tweezers in vacuum. Balanced detectors and D-shaped mirrors are used to measure the particle's displacements. As expected, the crosstalk coefficient can be periodically changed with the control of the linear polarization of the trapping beam. When the polarization direction is along Y axis, the crosstalk on the displacement x from the other radial axis can reach to infinity. When the polarization direction is along X axis, the crosstalk is eliminated. For comparison, crosstalk elimination is also achieved by an inserted Dove prism to rotate the beam along the propagation axis. The crosstalk elimination by polarization control is simpler, but it needs linear-polarized beam and will slightly change the particle's resonant frequencies. The crosstalk elimination by beam rotations will need at least two Dove prisms, but it is adapted to most common conditions and does not change the resonant frequencies. The research is useful for the feedback cooling and the precise measurement of the physical quantities in future.