Entanglement distillation by adiabatic passage in coupled quantum dots

The adiabatic passage of two correlated electrons in three coupled quantum dots is shown to provide a robust and controlled way of distilling, transporting, and detecting spin entanglement, as well as measuring the rate of spin disentanglement. By employing tunable interdot coupling the scheme creates from an unentangled two-electron state, a superposition of spatially separated singlet and triplet states. A single measurement of a dot population (charge) collapses the wave function to either of these states, realizing the entanglement to the charge conversion. The scheme is robust, with the efficiency close to 100%, for a large range of realistic spectral parameters.

Figure 1

(Color online) The entanglement distillation by adiabatic passage. Three quantum dots are coupled via electrode-defined barriers giving tunnel couplings $t_{12}$ and $t_{23}$. The ground state energy of dot 2 is shifted by $\Delta$. The charge on dots 1 or 3 is detected by electrometers. On the right-hand side the four figures show the scheme at work [the light bulb in (d) is an electrometer].

Figure 2

(Color online) (a) Temporal evolution of the two-electron spectrum (solid lines) of the Hamiltonian $H$ in the presence of two overlapping Gaussian pulses (dashed) of $t_{12}$ and $t_{23}$. The spectra are plotted for $U=1\mathrm{meV}$, $V=0$, and $\Delta =0.8\mathrm{meV}$. The pulses of $t_{12}\left(t\right)$ and $t_{23}\left(t\right)$ have widths $\tau \approx 500\mathrm{ps}$. (b) States with $S_z=0$ relevant for the EDAP, from the box in (a). There is a level repulsion (anticrossing) inside the circles, where the passage is rapid. At the other two crossings there is no repulsion. The horizontal line is the trapped state ${\Psi }_1$. (c) The counterintuitive passage scheme for ${\Psi }_1$ showing the probabilities $p$ of finding states ${\mid T_0⟩}_{12}$ and ${\mid T_0⟩}_{23}$. (d) The passage scheme for ${\mid S⟩}_{12}$ showing the probabilities $p$ of observing ${\mid S⟩}_{12}$ and $\mid D_1⟩$.

Figure 3

(a) The calculated probabilities and electron populations after the EDAP as a function of $\Delta$, with $\Psi \left(0\right)={\mid S⟩}_{12}$ [(a) and (b)] and $\Psi \left(0\right)=a_{1\uparrow }^{†}{a}_{2\downarrow }^{†}\mid 0⟩$ [(c) and (d)]. The thin dotted lines in (c) are for $V=0.1\mathrm{meV}$. The pulses are the same as in Fig. 2.

Figure 4

(Color online) The calculated efficiency $w$ as a function of the pulse dispersion $\tau$ and offset $\Delta$, for the counterintuitive pulse sequence. The black (darkest) window is for efficiency higher than 98%, while the second darkest window is for $w>90\%$.