Interisotope Determination of Ultracold Rubidium Interactions from Three High-Precision Experiments

Abstract

Combining the measured binding energies of four of the most weakly bound rovibrational levels of the 87 Rb2 molecule with the results of two other recent high-precision rubidium experiments, we obtain exceptionally strong constraints on the atomic interaction parameters in a highly model independent analysis. The comparison of 85 Rb and 87 Rb data, where the two isotopes are related by a mass scaling procedure, plays a crucial role. Using the consistent picture of the interactions that thus arises we are led to predictions for scattering lengths, clock shifts, Feshbach resonance fields and widths with an unprecedented level of accuracy. To demonstrate this, we predict two Feshbach resonances in mixed-spin scattering channels at easily accessible magnetic field strengths, which we expect to play a role in the damping of coherent spin oscillations. Suggested PACS Numbers: 03.75.Fi, 34.20.Cf, 32.80.Pj After the first realization of Bose-Einstein condensation (BEC) in a dilute ultracold gas of rubidium atoms [1], experiments with the two isotopes 87 Rb and 85 Rb further lead to an amazingly rich variety of BEC phenomena, ranging from the controlled collapse of a condensate with tunable attractive interactions [2] to the realization of an atomic matter wave on a microchip [3]. Because of the large number of groups that have started doing experiments with these atomic species and the growing complexity and subtlety of the planned experiments, there is a clear need for a more precise knowledge of the interactions between ultracold rubidium atoms in the electronic ground state, since these determine most of the properties of the condensate. For instance, despite a widespread interest, until now to our knowledge no experimental group has been able to locate the predicted [4] magnetic-field induced Feshbach resonances that can be used to tune the interactions between ultracold 87 Rb atoms. Being able to switch on or off these interactions at will by a mere change of magnetic field may well be one of the main assets of matter waves compared to light waves in the new matter wave devices. In an atomic interferometry device, in particular, a nonlinear interaction between interfering waves may be introduced or eliminated by changing a field applied at the intersection point.In this Letter, combining the results of three very recent high-precision observations, we come close to a complete and model-independent specification of the interaction properties of ultracold rubidium atoms. The fact that two isotopes 85 Rb and 87 Rb are involved in the measurements makes the constraints exceptionally strong and also increases the predictive power: the interaction properties of any other fermionic or bosonic isotope with mass number 82, 83, 84, or 86 are now known with about the same precision. Using mass scaling to relate the different isotopes we are able for the first time to deduce for each of the isotopes the exact numbers of bound Rb 2 states with total spin S = 0 (singlet) and 1 (triplet). As an illustration of the predictive ...

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