How do scientists stop light?
So to my knowledge they have not been able to actually "stop" light. However, in some laboratory tests they have been able to slow it enough to be able to study it more in depth with temperatures nearing absolute zero. It is presumed that if they are able to reach absolute zero they would be able to actually stop light... but that hasn't happened, yet.
In a vacuum, light travels at the speed, c. In a medium composed of atoms in some arrangement, be it gas, liquid or solid, light naturally slows down. This slowing is due to the coherent response of all the atoms in the medium that react to and are distorted by the electromagnetic field of the light. In a sense, light in such a medium is actually a composite of the electromagnetic field and the atomic response to the field. In a transparent medium the response is mainly a distortion of the atomic charge distribution.
In general, we make no real distinction between light in some atomic medium and light in a vacuum, apart from the change in the propagation speed. However, therein lies the key to understanding how light can be stopped.
It is possible with certain media to engineer a response that ultimately creates an internal distortion that cancels the forward propagation of the light. This is actually a very special state, as it exists as a coherent response to the incoming light. A coherent response is important because it is lossless and can be reversed. In fact it is possible to send a control pulse into the medium that actually reverses the coherent response of the medium and releases the original pulse. This is light being trapped and then released. An optical memory device.
The physics of slow light and optical memory development is fascinating as it works all the way down to the single photon level. If you are interested in looking into the subject further, then do a search for "photon echo" or "Hahn echo".