Fig. 1: Experimental optimization.

a A laser (red beam) is focused by a high-NA objective to levitate nanoparticles (red dot) in a vacuum. An SLM (black box) phase-modulates the beam and imprints a non-uniform wavefront (white-to-black concentric circles, \(\phi \left(r\right)\) with \(r\) the spatial coordinate on the SLM) that reshapes the trapping field (i.e., focused field). The transmitted light is collected by a second lens and injected into a fiber bundle to read out the nanoparticle’s motion along \(x\), \(y\), and \(z\). b PSDs \({S}_{{zz}}\) of a \(125\,{{\mathrm{nm}}}\)-radius nanoparticle, measured for a uniform (black curve, black circle in inset) and an optimized wavefront (red curve, black-to-white circles in inset). c Evolution of the stiffness ratios \({\kappa }_{{{\mathrm{opt}}},x}/{\kappa }_{0,x}\) (green), \({\kappa }_{{{\mathrm{opt}}},y}/{\kappa }_{0,y}\) (yellow) and \({\kappa }_{{{\mathrm{opt}}},z}/{\kappa }_{0,z}\) (blue) throughout the optimization procedure. The iterations used in b are marked by the black and red double-arrow lines. d Optimized stiffness ratios obtained after applying the routine to nanoparticles of different radii (same color code as in c). The corresponding optimized wavefronts are reported in the insets. Error bars characterize the fluctuations of the final stiffness ratios under their respective optimized wavefronts.