Ultra-low noise magnetic field is essential for many branches of scientific
research. Examplesinclude experiments conducted on ultra-cold atoms, quantum
simulations, as well as precisionmeasurements. In ultra-cold atom experiments
specifically, a bias magnetic field will be oftenserved as a quantization axis
and be applied for Zeeman splitting. As atomic states areusually sensitive to
magnetic fields, a magnetic field characterized by ultra-low noise as wellas
high stability is typically required for experimentation. For this study, a
bias magneticfield is successfully stabilized at 14.5G, with the root mean
square (RMS) value of the noisereduced to 18.5{\mu}G (1.28ppm) by
placing{\mu}-metal magnetic shields together with a dynamicalfeedback circuit.
Long-time instability is also regulated consistently below 7{\mu}G. The level
ofnoise exhibited in the bias magnetic field is further confirmed by evaluating
the coherencetime of a Bose-Einstein condensate characterized by Rabi
oscillation. It is concluded thatthis approach can be applied to other physical
systems as well.Comment: 7 pages, 5 figure