We have realized a magnetic tensor gradiometer by interferometrically measuring the relative phase between two spatially separated Bose-Einstein condensates (BECs). We perform simultaneous Ramsey interferometry of the proximate 87 Rb spin-1 condensates in freefall and infer their relative Larmor phase -and thus the differential magnetic field strength -with a common-mode phase noise suppression exceeding 50 dB. By appropriately biasing the magnetic field and separating the BECs along orthogonal directions, we measure the magnetic field gradient tensor of ambient and applied magnetic fields with a nominal precision of 0.30 nT mm −1 and a sensor volume of 2 × 10 −5 mm 3 . We predict a spin-projection noise limited magnetic energy resolution of order ∼ 10 for typical Zeeman coherence times of trapped condensates with this scheme, even with the low measurement duty cycle of current BEC experiments.

We present a high resolution objective lens made entirely from catalog singlets that has a numerical aperture of 0.36. It corrects for aberrations introduced by a glass window and has a long working distance of 35 mm, making it suitable for imaging objects within a vacuum system. This offers simple high resolution imaging for many in the quantum gas community. The objective achieves a resolution of 1.3 μm at the design wavelength of 780 nm, and a diffraction-limited field of view of 360 μm when imaging through a 5 mm thick window. Images of a resolution target and a pinhole show quantitative agreement with the simulated lens performance. The objective is suitable for diffraction-limited monochromatic imaging on the D2 line of all the alkalis by changing only the aperture diameter, retaining numerical apertures above 0.32. The design corrects for window thicknesses of up to 15 mm if the singlet spacings are modified.