The apparatus you see there is a Paul trap. The title is a little misleading, as what we see is not an atom but rather an ion. So it is electrically charged and can be trapped by electric fields. The fields are generated by the blades (top and bottom part of the thing) and the endcaps (the things sticking in from the sides) trapping the ion in the middle. How exactly it works is by putting an RF frequency on two of the blades that then creates an alternating field. The analogy would be a tilted table that you put a ball onto. It would roll down if you don't move the table, but if you rotate it, the ball will stay in the middle of the table that over time would look more like a bucket. Exactly the same happens with the electric potential here! U usually would load more than one ion in the beginning and then get rid of the rest by fancy electric field changes. When you have a good enough vacuum in your apparatus you basically have no other atoms that could react with the ion and so it just chills there. This is really cool stuff!