Dynamic evolution for liquid-state nuclear spins and Berry phase of mixed state in a magnetic resonance

Dynamic evolution for liquid-state nuclear spin in a magnetic resonance is investigated based on Bloch sphere structure under the time-dependent modified Bloch equation. We show that the magnetization is related to the magnetic field strength but approximately independent of the initial unpolarized spin state after a very short evolving time. We predict that the Berry phase transition of the nuclear spin system take place in a quasicyclic evolution for some initial states, resulting in that the evolving memory of nuclear spin polarization is kept in terms of the Berry phase. The findings provide another clue to search for quantum memory devices in such a system on the basis of the geometric phase.