The bands that Quasar wears are called the "Quantum bands" and they give complete control over, among other things, all forms of Quantum Energy. It is the foundation of the Quasar Character.
They bands were created by Eon, a "Foundation Abstract of the 616".
The reason that Quasar is able to control all forms of energy is due to the view that Quantum Energy is the base of all other forms in the universe. Was that ever explained more accurately? I don't know.
But, character profile, story arc history and statements made that Quasar has complete control of all forms of Quantum and other forms of energy, should trump a lack of history, lack of feats and lack of statements to the contrary.
In other words, if the entire history of the character on-panel, disagrees with your opinion, you lose.
He can and has stolen, controlled and used energy from the most powerful beings in the universe, including Thanos, Surfer, Phoenix and the Watcher, among many, many others.
Quasar's limitations are Darkforce and Mind, although he is able to protect himself from the most powerful wielders of thought manipulation. The Cosmic Control Rod is not outside of his abilities.
The loss to Annihilus was a fault in strategy. Just using a shield against the power of the Rod was the end of him. There is nothing to show that his other powers were unable to effect the power of the control rod.
If you are talking about his battle with Maelstrom, you are taking it out of context. Maelstrom not only had the backing of Oblivion, but he had gained the mantle of the Abstract Entity known as Anomaly. This granted him the status of having a nature that was unlike any other, thus difficult, and sometimes impossible to effect or attack successfully.
Captain Atom does not use the Darkforce or powers of the Mind. His powers are firmly based in Quasars toolbox.