Highly Resolved Measurements of Stark-Tuned Forster Resonances between Rydberg Atoms

We report on experiments exploring Stark-tuned Forster resonances between Rydberg atoms with high resolution in the Forster defect. The individual resonances are expected to exhibit different angular dependencies, opening the possibility to tune not only the interaction strength but also the angular dependence of the pair state potentials by an external electric field. We achieve a high resolution by optical Ramsey interferometry for Rydberg atoms combined with electric field pulses. The resonances are detected by a loss of visibility in the Ramsey fringes due to resonances in the interaction. We present measurements of the density dependence as well as of the coherence time at and close to Forster resonances. Rydberg atoms in ultra cold atomic systems are particu- larly interesting for negligible motional dephasing (''frozen Rydberg gas''), strong interactions, and various options to control them coherently. With this they are promising ingredients for quantum information processing (1-3) and quantum simulation (4). Also exotic phases for Rydberg dressed ensembles of atoms (5-7) are proposed. These applications rely on coherent control of the strong interactions. Here we study the coherence in the presence of these interactions. One possibility to control interactions between Rydberg atoms are so-called Forster resonances. Two dipole coupled pair states become degenerate and create a resonant dipole-dipole interaction between the atoms. As accidental degeneracy is unlikely, certain Rydberg states can be tuned into Forster resonance by microwave fields (8,9) or a small electric field (10). Different magnetic substates can be coupled by different polarizations of the coupling dipole. This generates diverse angular dependences for different Forster resonances. Thereby Stark-tuned Forster resonances offer the possibil- ity to control both, the interaction strength and the angular dependence by switching small electric fields. They have been studied in several seminal experiments in terms of dipole blockade (11), line shape analysis (12), double- resonance spectroscopy (13), and excitation statistics (14). Until now these experiments did not resolve the splitting of the d state Forster resonance used here. In order to study coherent control of these interactions, interferometric methods offering phase sensitivity are well suited. As already pointed out by Ramsey in 1950 (15) interferometric schemes relying on separated oscillating fields are advantageous in many aspects compared to a single pulse of the coupling field. Besides an increased spectral resolution it allows us to study coherent phe- nomena while not being limited by spatial inhomogeneities of the coupling field. Ramsey interference methods were already used to investigate the coherence in the resonant microwave coupling of single-atom Rydberg states (16) and in the coupling between pair states (17). These experi- ments could not coherently control the excitation and could not study the decoherence directly at the Forster resonance. To our knowledge so far no experiment has been performed that coherently controls both the laser excitation and the interaction of Rydberg atoms. Here, we apply optical Ramsey spectroscopy to coher- ently excite and deexcite 87 Rb atoms to the 44d Rydberg state. These experiments can be viewed as an atom inter- ferometer, similar to the atom-molecule interferometer in (18). The phase of the two arms of the interferometer can be tuned independently by small electric fields. A full coherent control over the electronic state and the phase of the atoms is realized. Using this Ramsey spectroscopy we explore the dephasing at Forster resonances of the channel