Bi-planar magnetic stabilisation coils for an inertial sensor based on atom interferometry

Inertial sensors that measure the acceleration of ultracold atoms promise unrivalled accuracy compared to classical equivalents. However, atomic systems are sensitive to various perturbations, including magnetic fields, which can introduce measurement inaccuracies. To address this challenge, we have designed, manufactured, and validated a magnetic field stabilisation system for a quantum sensor based on atom interferometry. We solve for the magnetic field generated by surface currents in-between a pair of bi-rectangular coils and approximate the surface current using discrete wires. The wires are wound by-hand onto machined panels which are retrofitted onto the existing mounting structure of the sensor without interfering with any experimental components. Along the central $60\mathrm{mm}$ of the $y$-axis, which aligns with the trajectory of the atoms during interferometry, the coils are measured to generate an independent uniform axial magnetic field with a strength of $B_z=\left(22.81\pm 0.01\right)$ $\mu$T/A [$\mathrm{mean}\pm 2\sigma \mathrm{std.\; error}$] and an independent linear axial field gradient of strength $d{B}_z/dy=\left(10.6\pm 0.1\right)$ $\mu$T/Am. The uniform $B_z$ field is measured to deviate by a maximum value of 1.3% in the same region, which is a factor of three times more uniform than the previously-used on-sensor rectangular $B_z$ compensation set.