  The superposition of frequency-shifted Laguerre-Gauss modes can produce a
rotating saddle-like intensity profile. When spinning fast enough, the optical
forces produced by this structured light saddle generate a dynamically stable
equilibrium point capable of trapping nanoparticles in a high vacuum, akin to a
Paul trap but with its unique characteristics. We analyze the stability
conditions and center-of-mass motion, dynamics and cooling of a nanoparticle
levitated in the optical saddle trap. We expect the optical saddle to find
applications in levitated optomechanics experiments requiring fast parametric
modulation and inverted squeezing potential landscapes.
