The OP is definitely talking about potential quantum effects of the type expect in the ergoregion of a Black Hole, or event horizon. In THEORY in QM there could be regions of negative energy density, but as an earlier poster said this is mostly Kip Thorne wanting a way to keep open ERBs.
The idea, completely without evidence, but with some math behind it, is that the "throat" of an ERB could be prevented from closing instantly by using energy or matter with a REPULSIVE force in relation to normal matter. This "Negative Matter/Energy" would counterbalance the attractive force that would normally turn you into whatever baby singularities are made of.
As far as I know it is more of a local effect or imbalance as a result of GR/QM than a real thing you could make in an accelerator.
From Wikipedia: "Negative mass in general relativity
In general relativity, negative mass is generalized to refer to any region of space in which for some observers the mass density is measured to be negative. This can occur due to negative mass, or could be a region of space in which the stress component of the Einstein stress-energy tensor is larger in magnitude than the mass density. All of these are violations of one or another variant of the positive energy condition of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory. (Various versions of the positive energy condition, weak energy condition, dominant energy condition, etc., are discussed in mathematical detail by Visser[3].)
Morris, Thorne and Yurtsever[4] pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass-negative region of space-time. In this article, and subsequent work by others, they showed that negative matter could be used to stabilize a wormhole. Cramer et al. argue that such wormholes might have been created in the early universe, stabilized by negative-mass loops of cosmic string[5]. Stephen Hawking has proved that negative energy is a necessary condition for the creation of a closed timelike curve by manipulation of gravitational fields within a finite region of space;[6] this proves, for example, that a finite Tipler cylinder cannot be used as a time machine."
The Dirac Vaccuum explanation has already been provided by Bob S.
For the record, I don't know much about this beyond its utility in sci-fi.