Spin Precession in a Quasi-1D Rashba Quantum Loop

In this paper we study the spin and subbands populations, as functions of time, for electrons in a quasi-1D Rashba quantum loop, in a strong perpendicular magnetic field. By explicitly including the confining potential and the Rashba spin-orbit coupling, we calculate the time evolution operator, from which the spin states and subbands populations, as functions of time, are obtained. Our calculations show that the spin, while wobbling, precesses about the magnetic field. In sharp contrast to the case of 1 D Rashba wire, here the precession occurs on either an ellipse or a circle, depending on the location of the electron in the loop. We further show that wherever a component of spin lies in the confined direction, S(x) at theta = 0, pi or S(y) at theta = pi/2, 3 pi/2, its expectation oscillates under a sinusoidal envelope. The expectations of other components, S(y) at theta = 0, pi or S(x) at theta = pi/2, 3 pi/2, however, periodically collapse and revive. At other locations along the loop both components lie in the confined directions, so that they oscillate sinusoidally.