Gate control of the spin-splitting energy in a quantum dot: Application in single qubit rotation

We numerically calculate modulation of the spin-splitting energy in an asymmetric quantum dot due to an external electrostatic potential (applied via gates) that induces the Rashba spin–orbit interaction. The quantum dot has finite potential barriers and contains a built-in electric field (due to doping or compositional variation) that makes the potential profile asymmetric in space. It is placed in a magnetic field which lifts the spin degeneracy of every subband due to the Zeeman effect and we calculate by how much the Rashba interaction can change the total spin-splitting energy in the lowest subband. In the past, a perturbative solution that ignored “spin texturing” effects indicated that (1) the Rashba interaction always increases the total spin-splitting energy and that (2) the increase is a negligible fraction (<0.1%) of the total spin-splitting energy for reasonable parameters. The more accurate non-perturbative solution presented here accounts for spin texturing and shows that (1) the total spin-splitting energy may actually decrease (instead of increasing) owing to the Rashba effect and that (2) the Rashba interaction can decrease the spin-splitting energy by >50% for reasonable parameters. A modulation this large can be used for single qubit rotation in a quantum gate.