The team then used the miniscule forces of laser light to hold the sphere with the radiation pressure of light – rather like levitating a beach ball with a jet of water.
They exploited the property of polarisation of the laser light that changed as the light passed through the levitating sphere, exerting a small twist or torque.
Light, of course, can have angular momentum, so if the ball was changing the light from linear to circular polarization (or vice versa), the angular momentum change would have to come from the ball, so it would spin.
If my calculator skills are not failing me, the ball had around 10^17 h-bar of angular momentum, which isn’t a lot for a macroscopic object. 10^17 photons is less than a tenth of a Watt-second’s worth of visible light, or 10 mW for less than 2 minutes.
The technique they are using is actually using the material as a half-wave plate, which is twice as effective at imparting angular momentum to the sphere as I had described. When circularly polarized light is incident upon it it switches the direction of the polarization, imparting 2*h-bar of angular momentum.