In this latest experiment, the researchers were able to levitate a diamond as small as 100 nanometers (about one-thousandth the diameter of a human hair) in free space. How did they manage it? They used a technique called laser trapping. Essentially, they trapped nanodiamonds in space and, using another laser, caused the diamonds to emit light at certain frequencies. The light emitted by the nanodiamonds was due to photoluminescence. The defects inside the nanodiamonds absorbed photons from the second laser, which excited the system and changed the spin. The system then relaxed and other photons were emitted.
While levitating nanodiamonds doesn't seem like it would have useful applications, it certainly does. It could be used to create optomechanical resonators, which are structures in which the vibrations of the system can be controlled by light. In theory, it could allow researchers to encode information in the vibrations of the diamonds and extract it using the light that they emit.