  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.
