Alkali metal-noble gas NMR gyroscope is widely used for precision rotation measurement in fundamental and applied physics. By numerically simulating the alkali-nuclear-nuclear tri-spin dynamics, we investigate the dependence of gyroscope response on alkali spin relaxation time and nuclear spin magnetization. We found additional resonance peaks appear due to a new source of instability, namely the inherent multistability of tri-spin dynamics. The numerical simulation results agree well with the recent experiment, enabling a better understanding and exploitation of the gyroscope signal.
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