Investigation of the benefits and disadvantages of using double-pair anti-Helmholtz coils in BEC-producing MOT setups and optimizing their design

This work has investigated the Magneto-Optical Trap (MOT) system used to produce Bose-Einstein Condensate (BEC). A primary challenge addressed in this study concerns the geometric limitations of traditional single-pair anti-Helmholtz coil configurations, where the magnetic field peaks occur outside the accessible inter-coil region. To overcome this limitation, we have explored the use of double-pair anti-Helmholtz coil configurations that create well-shaped magnetic field potentials centered at the experimentally accessible z=0 location. This investigation encompasses the three sequential processes of atom cooling: cooling in a linear external magnetic field through Doppler cooling, cooling in a well-shaped magnetic field through trapping, and evaporative cooling of atoms to achieve sub-microkelvin temperatures. Through theoretical analysis and numerical simulation, we have determined optimal geometric parameters for the coil configuration and operational parameters including laser detuning, saturation intensity, and initial atom populations for {}⁸⁷Rb BEC production. The results indicate that with the optimized configuration, the system can achieve final temperatures of approximately T_f sim 60 nK and produce condensate populations of sim 10⁵ atoms with a mean density of n₀ = 4.9 times 10¹⁵ m^-3, providing systematic design guidance for experimental BEC systems