  We observe clear precessional motion of highly birefringent liquid crystal
(LC) particles trapped in a spherically aberrated optical trap which is built
around a tilted refractive index stratified medium. For input circularly
polarized light, the breaking of azimuthal symmetry induced by the tilt leads
to an asymmetric intensity distribution in the radial direction near the trap
focal plane, which - in combination with the spin-orbit conversion effects for
input circularly polarized light - results in non-uniform canonical and spin
momentum densities in those regions. In addition, while the canonical momentum
remains always oriented towards the axial direction, the spin momentum reverses
direction along spatial loops in the radial direction. As a consequence, the
total momentum precesses around the canonical momentum vector along elliptical
spatial loops - akin to a Larmor-like precession of magnetic moment (total
momentum in our case) around a magnetic field (canonical momentum). We probe
this precession experimentally using the single trapped LC particles - with the
direction of precession determined by the helicity of the input light and the
precession frequency varying linearly with the laser power. Our experimental
results are validated by numerical simulations of the system where we employ
the Debye-Wolf theory for tight focusing in the presence of a tilted stratified
media.
