  We propose to use optical tweezers to probe the Casimir interaction between
microspheres inside a liquid medium for geometric aspect ratios far beyond the
validity of the widely employed proximity force approximation. This setup has
the potential for revealing unprecedented features associated to the
non-trivial role of the spherical curvatures. For a proof of concept, we
measure femtonewton double layer forces between polystyrene microspheres at
distances above $400$ nm by employing very soft optical tweezers, with
stiffness of the order of fractions of a fN/nm. As a future application, we
propose to tune the Casimir interaction between a metallic and a polystyrene
microsphere in saline solution from attraction to repulsion by varying the salt
concentration. With those materials, the screened Casimir interaction may have
a larger magnitude than the unscreened one. This line of investigation has the
potential for bringing together different fields including classical and
quantum optics, statistical physics and colloid science, while paving the way
for novel quantitative applications of optical tweezers in cell and molecular
biology.
