Rotations and the Spin $$\frac{1}{2}$$ Particle in a Magnetic Field

Alexander J. Silenko

Yan Yu-zhen

The evolutions of spin particles in a rotating magnetic field are discussed. We obtained the wavefunctions of the spin 1/2 and spin 3/2 particles by the trial function method. The Berry phase of the system are also discussed after an evolution period.

Hitoshi Kuwabara, Yasushi Yamauchi, Andrew Pratt

The spin rotation of a particle after a quarter rotation of an external magnetic field is calculated numerically and discussed both in the adiabatic and the nonadiabatic schemes. Adding to the well-known fully adiabatic case, we find that the spin rotates a quarter turn along the magnetic field’s direction when the transient time of the magnetic field matches closely but not exactly the Larmor precession period or its multiples.

Brian P. Anderson

C. E. Creffield

We consider the dynamics of a quantum particle held in a lattice potential and subjected to a time-dependent spin-orbit coupling. Tilting the lattice causes the particle to perform Bloch oscillations, and by suitably changing the Rashba interaction during its motion, the spin of the particle can be gradually rotated. Even if the Rashba coupling can only be altered by a small amount, large spin rotations can be obtained by accumulating the rotation from successive oscillations. We show how the time dependence of the spin-orbit coupling can be chosen to maximize the rotation per cycle, and thus how this method can be used to produce a precise and controllable spin rotator, which we term the Bloch-Rashba rotator, without requiring an applied magnetic field.

Jędrzej Śniatycki