Spin-entangled two-particle dark state in quantum transport through coupled quantum dots

We present a transport setup of coupled quantum dots that enables the creation of spatially separated spin-entangled two-electron dark states. We prove the existence of an entangled transport dark state by investigating the system Hamiltonian without coupling to the electronic reservoirs. In the transport regime, the entangled dark state, which corresponds to a singlet, has a strongly enhanced Fano factor compared to the dark state, which corresponds to a mixture of the triplet states. Furthermore, we calculate the concurrence of the occupying electrons to show the degree of entanglement in the transport regime.

Figure 1

Both TQDs are in the strong Coulomb blockade regime such that up to one electron is allowed in each TQD. The electrons in the TQDs interact with each other capacitively due to the charging energies $U_{ij}$ and due to the exchange interaction switching the spins of the electrons. (The exchange interaction $J_1$ is indicated in the sketches.) Each TQD is connected to two sources and one drain. Here, two possible configurations are shown where (a) the two TQDs are triangular and lie above each other and (b) the TQDs are serial and parallel to each other.

Figure 2

(a) Steady-state current $\langle I\rangle /\Gamma$ as a function of the exchange energy $J$ and $\delta U$ normalized by $T_C$ for $\Gamma /T_C=1$. The thin dark line (zero-current line) in the density plot indicates the formation of the singlet DS and the thick dark line indicates the formation of the triplet DS. (b) Fano factor [corresponding to (a)] is highly super-Poissonian around both DSs. But the Fano factor near the singlet DS is around four times higher than around the triplet DS. (c) Current as a function of $\delta U/T_C$, for different coupling strength $T_C/\Gamma$ at $J=0.4T_C$. The curve for $T_C=1\Gamma$ corresponds to a section through the density plot above. (d) The Fano factors show that the maximum value of the Fano factor near both DSs is independent of the ratio $T_C/\Gamma$. Parameter: $V=10T_C$.

Figure 3

(a) Concurrence as a function of the exchange energy $J$ and $\delta U$ normalized by $T_C$ for $T_C=1\Gamma$. (b) Concurrence as a function of $\delta U$ normalized by $T_C$ at $J=0.4T_C$ for different ratios of $T_C/\Gamma$. Parameter: $V=10T_C$.