  The narrow s-wave Feshbach resonance of a $^6$Li Fermi gas shows strong
three-body loss, which is proposed to be used to measure the minute change of a
magnetic field around the resonance. However, the eddy current will cause
ultracold atom experiencing a magnetic field delayed to the desired magnetic
field from the current of the magnetic coils. The elimination of the eddy
current effect will play a key role in any experiments that motivated to
measure the magnetic field to the precision of a part per million stability.
Here, we apply a method to correct the eddy current effect for precision
measurement of the magnetic field. We first record the three-body loss
influenced by the effect of induced eddy current, then use a certain model to
obtain the time constant of the actual magnetic field by fitting the atom loss.
This precisely determines the actual magnetic field according to the time
response of the three-body loss. After that, we implement the desired magnetic
field to the atoms so that we can analyze the three-body loss across the whole
narrow Feshbach resonance. The results show that the three-body recombination
is the dominated loss mechanism near the resonance. We expect this practical
method of correcting the eddy current error of the magnetic field can be
further applied to the future studies of quantum few- and many-body physics
near a narrow Feshbach resonance.
