The common term for averaged null energy condition (ANEC)-violating negative energy, also sometimes known as phantom energy. Technically known as negative stress-energy tensor fields.
Exotic energy is used to keep traversable wormholes open. Macroscale traversable wormholes use a relatively small quantity of exotic energy, but need to be located in a region of asymptotically flat space at least 327 AU in radius. Microscale Hayward wormholes have a much less restrictive requirement for a flatspace environment, but require considerably greater amounts of exotic energy.
Exotic energy is also required for the operation of reactionless drives, as the void bubbles used in such propulsion systems are stabilized using negative energy.
Exotic Atoms - Text by Stephen Inniss A term used for matter that is not composed of the usual protons, neutrons and electrons but that forms analogous structures. The constituent particles of monopolium/magmatter are an example. Some such "atoms" may be said to form "molecules" or analogues of metals or ionic compounds and may be used in the construction of such things as Banks Orbitals.