Magnetic-field diagnostics in a cold-atom trap using Rydberg electromagnetically induced transparency

We perform an in-situ, atom-based measurement of a time-dependent magnetic field in a gas of ultra-cold cesium atoms using Rydberg electromagnetically induced transparency (EIT). The three-level ladder EIT system consists of ground ($6S_{1/2}$), excited ($6P_{3/2}$), and Rydberg levels ($48D_{5/2}$), with a total of 96 magnetic sublevels. The magnetic field we measure in the present demonstration is a superposition of an adjustable field from a set of Helmholtz coils and a rapidly decaying eddy-current field. The EIT spectrum exhibits two dominant lines with a Zeeman splitting of $5.6~$MHz per Gauss, which are employed to measure the time-dependent magnetic field. A quantum Monte Carlo wave-function (QMCWF) approach is used to solve the quantum Master equation of the 96-level problem. The QMCWF results allow us to interpret the EIT spectra in considerable detail, showing good agreement with the experiment, and to gain insight into optical-pumping and radiation-pressure effects. To demonstrate the utility of the in-situ, time-resolved magnetic-field measurement method, we determine the decay time of the eddy-current magnetic field at the location of the cold atom cloud. The field and time resolutions of the measurement are about $5~$mG and $100~\mu$s, respectively.