Light carries momentum, so when light hits something, it applies a force. With enough light, it is possible to push objects around. This has been done under microscopes for some years using "optical tweezers" and also in space to push spacecraft around using solar sails. We aim to levitate a mirror that is held up by 3 optical resonators in a tripod configuration. One of the interesting things about this system is that there is no scattering. That is, the levitated mirror will be not be pushed randomly by light that bounces off in all directions, but only by the light that is coherently reflected by the levitated mirror.
Such a levitated system could be used to measure changes in the gravitational force, investigation of quantum opto-mechanical effects and perhaps allow us to build a system that is sensitive to both gravitational and quantum effects, allowing tests of quantum gravity theories.
You can read our original proposal in Phys. Rev. Lett. 111, 183001 (2013) and a more general article in The Conversation: "Levitation is just part of the power of pushy light".