Recording long-term optical images of a Brownian particle in a Paul trap essentially free of thermally induced positional noise

We show experimentally that the positional uncertainty in long-term images of a microparticle in a Paul trap in air can be reduced to the optical limit, and below the pseudopotential limit. For this damped system, far below any Mathieu instability, the particle's thermally induced positional noise is extremely sensitive to the phase of the driving field. Accumulating images strobed at the proper phase produces a long-term optical image which is essentially free of thermally induced positional noise. Although noise squeezing theory does not apply at such large dissipation, our results may be understood through recent theory of the Brownian parametric oscillator. Use of this theory coupled with our observations suggests that the extreme reduction in spatial variance observed by using our technique results from working in a low Reynolds number regime.