Rapid generation of all-optical $^{39}$K Bose-Einstein condensates using a low-field Feshbach resonance

Ultracold potassium is an interesting candidate for quantum technology applications and fundamental research as it allows controlling intra-atomic interactions via low-field magnetic Feshbach resonances. However, the realization of high-flux sources of Bose-Einstein condensates remains challenging due to the necessity of optical trapping to use magnetic fields as free parameter. We investigate the production of all-optical $^{39}$K Bose-Einstein condensates with different scattering lengths using a Feshbach resonance near $33$ G. By tuning the scattering length in a range between $75\, a_0$ and $300\, a_0$ we demonstrate a trade off between evaporation speed and final atom number and decrease our evaporation time by a factor of $5$ while approximately doubling the evaporation flux. To this end, we are able to produce fully condensed ensembles with $5.8\times10^4$ atoms within $850$ ms evaporation time at a scattering length of $232\, a_0$ and $1.6\times10^5$ atoms within $3.9$ s at $158\, a_0$, respectively. We deploy a numerical model to analyse the flux and atom number scaling with respect to scattering length, identify current limitations and simulate the optimal performance of our setup. Based on our findings we describe routes towards high-flux sources of ultra-cold potassium for inertial sensing.