  We study the Aharonov-Bohm (AB) caging effect in rhombic exciton-polariton
lattices, with the Rashba-Dresselhaus spin-orbit coupling (RDSOC) in acting a
synthetic gauge field. The effective magnetic flux through each plaquette is
controlled by the orientation of the RDSOC and geometry of the rhombic lattice.
The results show that the interplay of lattice geometry and the RDSOC will
dramatically influence the energy band structure, furthermore, determining the
transportation properties of exciton-polariton condensates. Non-Hermitian
effects, which arise from the polariton intrinsic loss mechanism, on the AB
caging is also discussed in detail. Meanwhile, the effect of disorder on the
dynamics of AB caging is investigated, and we find that the disorder will lead
to the inverse Anderson localization. We propose that using the AB caging
effect allows to trap and steer the propagation of polaritons in a given
parameter regime. Considering the specific example of a photonic liquid crystal
microcavity to achieve our theoretical predictions, the AB caging could be
switched on and off by applying an external voltage.

Quantum Gases