Although quantum degenerate gases of neutral atoms have shown remarkable progress in the study of many body quantum physics, condensed matter physics, precision measurements, and quantum information processing, experimental progress is needed in order to reach their full potential in these fields. More complex spatial geometries as well as novel methods for engineering interesting interactions are needed. Here we demonstrate a novel experimental platform for the realization of quantum degenerate gases with a wide range of tune-ability in the spatial geometries experienced by the atoms and with the possibility of non-trivial long-range interactions both within and between multiple 87Rb Bose-Einstein condensates (BECs). We explore the use of a large mode-volume bow-tie ring cavity resonant at two wavelengths, $lambda$ =1560 and 780 nm, for the creation of multiple BECs within a Malleable optical trap which also possesses the ability of photon-mediated long-range interactions. By exciting diverse transverse modes at 1560 nm, we can realize many optical trapping geometries which can open the door to spatial quantum state engineering with cavity-coupled BECs. As representative examples we realize a BEC in the fundamental TEM00 and a double BEC in the TEM01 mode of the cavity. By controlling the power between the fundamental and the higher transverse cavity mode, splitting and merging of cold thermal atomic ensemble is shown as well as the potential of creating more complex trapping geometries such as uniform potentials. Due to the double resonance of the cavity, we can envision a quantum network of BECs coupled via cavity-mediated interactions in non-trivial geometries.
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