Singlet-triplet filtering and entanglement in a quantum dot structure

We consider two interacting electrons in a semiconductor quantum dot structure, which consists of a small dot within a larger dot, and demonstrate a singlet-triplet filtering mechanism which involves spin-dependent resonances and can generate entanglement. By studying the exact time evolution of singlet and triplet states we show how the degree of both filtering and spin entanglement can be tuned using a time-dependent gate voltage.

Figure 1

(Color online) (a) Quantum dot confining potential and effective charge density (in arbitrary units) of the lowest triplet eigenstate. (b) Contour plot of the lowest triplet eigenstate. (c) The two-lowest singlet and triplet pairs.

Figure 2

(Color online) Effective charge density for (a) left and (b) right triplet states. The quantum dot confining potential is also shown.

Figure 3

Effective charge density for singlet and triplet components at the final time for (a) a case in the filtering regime and (b) the most general case.

Figure 4

Energy splitting of the two lowest levels for singlet and triplet components, as a function of time for one cycle in the filtering regime.

Figure 5

(Color online) Dependence (at the final time), as a function of maximum gate voltage for fixed gating rate, of (a) absolute value of $\cos \delta$ and right probabilities for singlet and triplet components, and (b) concurrence, spin-flip, and non-spin-flip probabilities calculated for the right region.

Figure 6

(Color online) Dependence (at the final time) of quantities in Fig. 5 as a function of pulse duration time for two different maximum gate voltages. (a) $V_b=2.75\mathrm{meV}$ and (b) $V_b=5\mathrm{meV}$.

Figure 7

Illustration of the two-electron spin dynamics in a three-step process, I, II, III. The process (a) is allowed only for singlets whereas the process (b) is allowed for both singlets and triplets.