Controllability of a Pair of Coupled Quantum Dots

This article studies the controllability of a pair of coupled quantum dots being interrogated by an external electromagnetic field. It is shown that this system is controllable. However, in the limit of large spatial separation between the two dots the dynamical Lie algebra of the problem degenerates to the complex representation of so(4) in su(4). The question of which pure and mixed states for the system are accessible from the initial condition is then studied via an ab initio approach. This is achieved by finding an explicit conjugation, within su(4), between the complex representation of so(4) and su(2)⊗ su(2), and then using the greater structure of the group SU(2)⊗ SU(2).