Optical trapping has proven to be a valuable experimental technique for
precisely controlling small dielectric objects. However, due to their very
nature, conventional optical traps are diffraction limited and require high
intensities to confine the dielectric objects. In this work, we propose a novel
optical trap based on dielectric photonic crystal nanobeam cavities, which
overcomes the limitations of conventional optical traps by significant factors.
This is achieved by exploiting an optomechanically induced backaction mechanism
between a dielectric nanoparticle and the cavities. We perform numerical
simulations to show that our trap can fully levitate a submicron-scale
dielectric particle with a trap width as narrow as 56 nm. It allows for
achieving a high trap stiffness, therefore, a high Q-frequency product for the
particle's motion while reducing the optical absorption by a factor of 43
compared to the cases for conventional optical tweezers. Moreover, we show that
multiple laser tones can be used further to create a complex, dynamic potential
landscape with feature sizes well below the diffraction limit. The presented
optical trapping system offers new opportunities for precision sensing and
fundamental quantum experiments based on levitated particles