A Rydberg atom is special because it has one electron alone in an outermost orbit - very far, in atomic terms, from its nucleus.
Back in 1934 Enrico Fermi predicted that if another atom were to "find" that lone, wandering electron, it might interact with it.
"But Fermi never imagined that molecules could be formed," explained Chris Greene, the theoretical physicist from the University of Colorado who first predicted that Rydberg molecules could exist.
"We recognised, in our work in the 1970s and 80s, the potential for a sort of forcefield between a Rydberg atom and a groundstate [or normal] atom.
"It's only now that you can get systems so cold, that you can actually make them."
Unimaginably cold temperatures are needed to create the molecules, as Vera Bendkowsky from the University of Stuttgart who led the research explained.
"The nuclei of the atoms have to be at the correct distance from each other for the electron fields to find each other and interact," she said.
"We use an ultracold cloud of rubidium - as you cool it, the atoms in the gas move closer together."
The researchers excite an atom to the "Rydberg state" using a laser
At temperatures very close to absolute zero - minus 273C - this "critical distance" of about 100nm (nanometres - 1nm = one millionth of a millimetre) between the atoms is reached.
When one is a Rydberg atom, the two atoms form a Rydberg molecule. This 100nm gap is vast compared to ordinary molecules.
"The Rydberg electron resembles a sheepdog that keeps its flock together by roaming speedily to the outermost periphery of the flock, and nudging back towards the centre any member that might begin to drift away," said Professor Greene.
Pushing this electron out to its lonely periphery - and make a Rydberg atom - requires energy.
"We excite the atoms to the Rydberg stage with a laser," explained Dr Bendkowsky.
"If we have a gas at the critical density, with two atoms at the correct distance that are able to form the molecule, and we excite one to the Rydberg state, then we can form a molecule."
This ultracold experiment is also ultra-fast - the longest lived Rydberg molecule survives for just 18 microseconds.