  We have observed Stueckelberg oscillations in the dipole-dipole interaction
between Rydberg atoms with an externally applied radio-frequency field. The
oscillating RF field brings the interaction between cold Rydberg atoms in two
separated volumes into resonance. We observe multi-photon transitions when
varying the amplitude of the RF-field and the static electric field offset. The
angular momentum states we use show a quadratic Stark shift, which leads to a
fundamentally different behavior than linearly shifting states. Both cases are
studied theoretically using the Floquet approach and are compared. The
amplitude of the sidebands, related to the interaction strength, is given by
the Bessel function in the linearly shifting case and by the generalized Bessel
function in the quadratically shifting case. The oscillatory behavior of both
functions corresponds to Stueckelberg oscillations, an interference effect
described by the semi-classical Landau-Zener-Stueckelberg model. The
measurements prove coherent dipole-dipole interaction during at least 0.6
micro-seconds.
