A method for optically trapping nanospheres at micron range from a tilted mirror

We propose and experimentally demonstrate a novel optical method for trapping and cooling dielectric nanospheres at (sub)-micron distances from a reflective metallic surface. By translating a tilted mirror towards the focus of a single-beam optical tweezer, the optical trap transitions into an off-axis standing-wave configuration due to interference between the incident and reflected beams. Stable potential minima emerge within a finite overlap region close to the surface, with their number, shape, and distance from the surface tunable via the incidence angle, waist, and polarization of the incoming beam. This configuration enables deterministic selection of trapping sites as the system transitions from the single-beam trap to the off-axis standing wave trap. We validate this approach using a $170$ nm diameter silica sphere in a single-beam trap with a $1.5$ $\mu$m waist and transitioning it into the second or first potential minimum of the standing wave trap, located $1.61$ $\mu$m or $0.55$ $\mu$m from the surface, respectively. The experimental results align well with our theoretical model, supported by numerical simulations of the Langevin equations of motion. Additionally, we perform parametric feedback cooling of all three motional degrees of freedom in a high-vacuum environment. This method provides a robust platform for ultra-sensitive scanning surface force sensing at micron distances from a reflective surface in high vacuum and may open new pathways for short-range gravity or Casimir effect measurements.