Dispersive probing of driven pseudo-spin dynamics in a gradient field

We have studied the coherent evolution of ultracold atomic rubidium clouds subjected to a microwave field driving Rabi oscillations between the stretched states of the F=1 and F=2 hyperfine levels. A phase winding of the two-level system pseudo-spin vector is encountered for elongated samples of atoms exposed to an axial magnetic field gradient and can be observed directly in state-selective absorption imaging. When dispersively recording the sample-integrated spin population during the Rabi drive, we observe a damped oscillation directly related to the magnetic field gradient, which we quantify using a simple dephasing model. By analyzing such dispersively acquired data from millimeter sized atomic samples, we demonstrate that field gradients can be determined with an accuracy of $\sim25$ nT/mm. The dispersive probing of inhomogeneously broadened Rabi oscillations in prolate samples opens up a path to gradiometry with bandwidths in the kilohertz domain.