Abstract
We address the development of geometric phases in classical and quantum magnetic moments (spin-1/2) precessing in an external magnetic field. We show that nonadiabatic dynamics lead to a topological phase transition determined by a change in the driving field topology. The transition is associated with an effective geometric phase which is identified from the paths of the magnetic moments in a spherical geometry. The topological transition presents close similarities between SO(3) and SU(2) cases but features differences in, e.g. the adiabatic limits of the geometric phases, being and π in the classical and the quantum case, respectively. We discuss possible experiments where the effective geometric phase would be observable.
Highlights
An adiabatic cyclic process involves slowly changing periodic parameters driving a physical system
We show here that precessions of a classical magnetic moment give rise to effective nonadiabatic geometric and dynamic phase angles with an associated topological transition, showing a clear correspondence with those found for spin rotations
In the classical case, the effective geometric phase is associated with the dynamics of precessions of the classical magnetic moment in the S2 sphere, much like it was found to be related to the windings of the spin magnetic moment on the Bloch sphere in the quantum case [23]
Summary
An adiabatic cyclic process involves slowly changing periodic parameters driving a physical system. They play a crucial role when the Born-Oppenheimer approximation breaks down near a conical intersection of two potential energy surfaces In these cases, the electronic part of the wave function may acquire a phase shift when the nuclei traverse a closed path The changing field topology is associated with nonadiabatic dynamics when a degeneracy is placed along the path of the cycle, leading to emergent effective geometric phases undergoing a smooth but distinct transition. We study the nonadiabatic dynamics of a classical and a quantum mechanical (spin) magnetic moment precessing in a time-dependent magnetic field with varying topology due to the combined action of coplanar, homogeneous and rotating, field components. We show here that precessions of a classical magnetic moment give rise to effective nonadiabatic geometric and dynamic phase angles with an associated topological transition, showing a clear correspondence with those found for spin rotations. We suggest experimental setups that would demonstrate the discussed effects
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