Cold and ultracold Rydberg atoms in strong magnetic fields

Cold Rydberg atoms exposed to strong magnetic fields possess unique properties which open the pathway for an intriguing many-body dynamics taking place in Rydberg gases, consisting of either matter or anti-matter systems. We review both the foundations and recent developments of the field in the cold and ultracold regime where trapping and cooling of Rydberg atoms have become possible. Exotic states of moving Rydberg atoms, such as giant dipole states, are discussed in detail, including their formation mechanisms in a strongly magnetized cold plasma. Inhomogeneous field configurations influence the electronic structure of Rydberg atoms, and we describe the utility of corresponding effects for achieving tightly trapped ultracold Rydberg atoms. We review recent work on large, extended cold Rydberg gases in magnetic fields and their formation in strongly magnetized ultracold plasmas through collisional recombination. Implications of these results for current antihydrogen production experiments are pointed out, and techniques for the trapping and cooling of such atoms are investigated.