  Atom interferometers allow determining inertial effects to high accuracy.
Quantum-projection noise as well as systematic effects impose demands on large
atomic flux as well as ultra-low expansion rates. Here we report on a high-flux
source of ultra-cold atoms with free expansion rates near the Heisenberg limit
directly upon release from the trap. Our results are achieved in a
time-averaged optical dipole trap and enabled through dynamic tuning of the
atomic scattering length across two orders of magnitude interaction strength
via magnetic Feshbach resonances. We demonstrate BECs with more than $6\times
10^{4}$ particles after evaporative cooling for $170$ ms and their subsequent
release with a minimal expansion energy of $4.5$ nK in one direction. Based on
our results we estimate the performance of an atom interferometer and compare
our source system to a high performance chip-trap, as readily available for
ultra-precise measurements in micro-gravity environments.
