Quantum logic gate analysis for Rabi oscillation driven by a time-dependent Rashba external field

 We study time-dependent (TD) spin phenomena driven by oscillating Rashba spin-orbit interaction (SOI). An electron is confined by a harmonic potential surrounded by a cylindrical hard-wall in a two-dimensional quantum dot (2DQD). An oscillating Rashba external field with a frequency w is applied perpendicular to the 2D plane. We numerically solve the corresponding TD Schödinger equation by employing the real-time, real-space finite difference method. We conduct projection and Fourier transform analyses and investigate the Rabi oscillation caused by the resonant interstate transitions.

 The harmonic confinement ω₀ produces eigenstates with equivalent energy separation. Consequently, the Rashba external field (w= ω₀) produces an infinite number of interstate resonant transitions. The selection rule requests an alternating spin-change between the individual transitions. Eventually, the multiple inter-neighboring-state (INS) transitions result in the complicated spin flip-flopping. Because the predominant INS coupling occurs between the ground and first-excited states, we remake the resulting spin-flip process between these two states and then draw it on the Bloch sphere. Thus, two-state Rabi oscillation driven by the Rashba SOI is expressed by the basic logic gates. By combining these gates, we restudy the complicated spin dynamics confined in the harmonic and cylindrical hard-wall hybrid potential.