  We manipulate correlations between Rydberg excitations in cold atom samples
using a rotary-echo technique. The correlations are due to interactions between
the Rydberg atoms. In the rotary-echo excitation sequence, the phase of the
excitation pulse is flipped at a selected time during the pulse. We measure the
resultant change in the spatial pair correlation function of the excitations
via direct position-sensitive atom imaging. For zero detuning of the lasers
from the interaction-free Rydberg-excitation resonance, the pair-correlation
value at the most likely nearest-neighbor Rydberg-atom distance is
substantially enhanced when the phase is flipped at the middle of the
excitation pulse. In this case, the rotary echo eliminates most uncorrelated
(un-paired) atoms, leaving an abundance of correlated atom pairs at the end of
the sequence. In off-resonant cases, a complementary behavior is observed. We
further characterize the effect of the rotary-echo excitation sequence on the
excitation-number statistics of the atom sample.
