We examine interactions between atoms continuously and coherently driven
between the ground state and a Rydberg state, producing "Rydberg-dressed
atoms." Because of the large dipolar coupling between two Rydberg atoms, a
small admixture of Rydberg character into a ground state can produce an atom
with a dipole moment of a few Debye, the appropriate size to observe
interesting dipolar physics effects in cold atom systems. We have calculated
the interaction energies for atoms that interact via the dipole-dipole
interaction and find that due to blockade effects, the R-dependent two-atom
interaction terms are limited in size, and can be R-independent up until the
dipolar energy is equal to the detuning. This produces R-dependent interactions
different from the expected 1/R^3 dipolar form, which have no direct analogy in
condensed matter physics, and could lead to new quantum phases in trapped
Rydberg systems.Comment: 5 pages, 7 figures; Accepted to Phys. Rev. A, 18 Aug. 201