The Quantum Field, as stated by Dr. Heinrich Megala, is the underlying essence of all matter and energy. It is believed that whenever Captain Atom 'Quantum Jumps', he moves through the Quantum Field from one place in space-time to another. The Dilustel metal covering his body is a conduit between his mind and the Field itself, responding to Captain Atom's thoughts, instincts, and experience, allowing him to tap into the Quantum Field in order to use it. Primarily, this power source grants Captain Atom with vast superhuman physical abilities (strength, endurance, speed, invulnerability, reflexes, etc), supersonic flight, the ability to manipulate and generate Quantum energy, and energy absorption. There are other various uses, as well.
Major Force, by extension, has a lot of the same powers, save for energy blasts, energy absorption, and flight. Instead, he gained the ability to project blasts of dark matter. Later in his career, he was able to generate energy blasts, energy shields, and take flight much like Captain Atom. But, based on the Quantum Field's use, Captain Atom appeared to be more versatile with it, as he's been able to do things that Major Force has yet to exhibit.
Whenever energy is absorbed, it is normally returned to the flow of the Quantum Field. The location of this power source is unknown, but it was stated to be the space between matter and energy in within the universe. Takion, however, revealed that the Quantum Field actually originates from the Source. Bombshell, another quantum-powered superhero, was bonded to the Dilustel metal without the nuclear explosion that Captain Atom and Major Force were administered. However, the metal still granted her the same powers as the other two, but to a lesser degree.
Silver Shield is an alien who lived in the Quantum Field. He was "swimming" in the Quantum Field where he found a hole in space-time. Wanting to know more about the hole, he traversed it, realizing that it (normal space) was not the same as the Quantum Field. It wasn't until Dr. Heinrich Megala discovered the Silver Shield's landing on Earth, and gathered a group of scientists to study their findings. They were unable to breach the hull of the ship through conventional means, but Babylon had an X-Ionized knife that allowed him to cut through it. As a result, the Silver Shield felt pain for the first time. The Silver Shield told Captain Atom that he was unable to go back home because his form was only useful on Earth and that the damage he sustained (the pieces shaved off by Dr. Megala) left him incomplete which is not allowed in the Quantum Field. Captain Atom was able to find a place for the Silver Shield to stay.
After an attack from Shadowstorm during the War of the Gods event, Captain Atom drove himself into the Quantum Field by force. With the help of a telepath named Rasputin, he learned that the Quantum Field is linked to Quantum Theory, and that it does and doesn't exist; it doesn't come into existence unless Captain Atom calls upon it. He also learned that usage of the Field is limited by his will (it is again revealed by Hal Jordan that Captain Atom's power increases with his willpower) and that, theoretically, he has no limit to his power. After having his mind opened by Rasputin, Atom was able to manipulate the Quantum Field into a universe of his own, much like the original. The only difference was that he was able to make a new life for himself and his family, a life in which he never became Captain Atom. But, whenever he desired to make changes to his universe, he used his powers to tamper with its reality. The more he did it, the more his universe became less real. Tampering with it even more spawned a darker, evil version of Captain Atom. After destroying his universe, the real Captain Atom eventually defeated his evil copy before returning the real universe to defeat Shadowstorm.
Later, during Captain Atom's adventures in Extreme Justice, the real Nathaniel Adam (Monarch II), who had spent years within the Quantum Field, emerges from it after spending years tapping into it. He acquired the armor from Hank Hall himself, who appeared inside of the Quantum Field after traveling through time and battling Captain Atom during the Armageddon event. Through meditation, Nathaniel felt a jolt in the timestream, and used it to find his way out. He revealed that soon after the nuclear experiment in 1968, his body was transported to the Field, but it was covered in the Dilustel metal. During the process, Nathaniel's body was cloned by the metal itself. While he was stuck there, the clone (Captain Atom) made it back to Earth from the Quantum Field. This, however, would suggest that Captain Atom is actually a copy of his original self, assuming Nathaniel Adam's life as his own.
During Infinite Crisis, Breach's containment suit was ruptured by Superboy Prime, sending him to the Quantum Field. As a result, Captain Atom reappeared in his place from the Wildstorm Universe (from the pages of Captain Atom: Armageddon), with no clue as to what was going on. However, this instance was later retconned in both Battle for Bludhaven and in Captain Atom: Armageddon, having Captain Atom reappear in Bludhaven during the aftermath of Infinite Crisis.
In DC Rebirth the son of Captain Atom, Genji Sato was shown to inherit access into the Quantum Field.