Hyperfine-induced decay in triple quantum dots

We analyze the effects of hyperfine interactions on coherent control experiments in triple quantum dots. By exploiting Hamiltonian symmetries and the SU(3) structure of the triple-dot system under pseudoexchange and longitudinal hyperfine couplings, we provide analytic formulas for the hyperfine decay of triple-dot Rabi and dephasing experiments.

Figure 1

(a) Schematic of energy levels of triple-dot system, above a sketch of triple-dot energy potentials. The black dot and black dashed arrow indicate the initialization and pulsing of a triple-dot Rabi or dephasing experiment. (b) SU(3) structure of triple-dot system.

Figure 2

Numeric example of $P_0\left(t\right)$ for three values of $J_n.$ The example values for the hyperfine deviations for the three dots used for this plot are ${\sigma }_j=(j/2){\sigma }_{hf}.$ The black curve shows numeric integration of Eq. (9), featuring no approximation relative to full $8\times 8$ diagonalization and three-dimensional averaging. The blue dashed line shows the high-$J_n$ approximation [Eqs. (14, 15, 16)]. The red line (short dashes) shows the low-$J_n$ approximation [Eq. (18)]. For each $J_n$ a Bloch sphere is shown, in which the three cardinal directions are the expectation value of the first three Gell-Mann matrices ${\lambda }_1,{\lambda }_2$, and ${\lambda }_3$. Hence the surface is the space of DFS qubit states, while the interior corresponds to leakage. The eight colored trajectories represent the unitary evolution under eight different hyperfine fields, sampled from the three independent Gaussian distributions of the three dots. $P_0\left(t\right)$ is the average projection of these trajectories onto the $z$ axis, from which all trajectories begin.