In order to separate the timescales of the vibrational state inversion and of the TAB emission, Optimal control was used to design a fast state preparation ramp. We implemented it successfully, obtaining a 99.3(6) % fidelity of the prepared state, and characterized its robustness. The results are described in van Frank et al, Scientific Reports 6, 34187 (2016). We investigated the atom-atom correlations of TAB and their time evolution for different regimes of emission, showing a spreading of correlations for the fast emission regime. We also investigated the dynamics after preparation of superpositions of the ground and first excited vibrational state, showing a strong dependence of the relaxation timescale on the atom number. These different results were presented at international workshop and conferences.
In order to trigger TAB emission in a double-well potential we developed a new optimal control scheme, based on modulation of the separation between the wells. Thanks to our extremely accurate control of the potential this scheme was successfully implemented, and emission of TAB with the expected momentum was observed. We elaborated a method for characterization of two-atom entanglement in our configuration, which we plan to use to demonstrate the entanglement of the TAB produced in the double wells.