Decoherence of localized spins interacting via RKKY interaction

We theoretically study decoherence of two localized spins interacting via the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in one-, two-, and three-dimensional electron gas. We derive the kinetic equation for the reduced density matrix of the localized spins and show that energy relaxation caused by singlet-triplet transition is suppressed when the RKKY interaction is ferromagnetic. We also estimate the decoherence time of the system consisting of two quantum dots embedded in a two-dimensional electron gas.

Figure 1

The range functions for a one-dimensional system $F_1\left(2k_{F}R\right)$ and $G_1\left(2k_{F}R\right)$ are plotted as a function of $2k_{F}R$ in panel (a). Panels (b) and (c) are the same plot for two- and three-dimensional systems, respectively.

Figure 2

(a) The time evolution of ${\rho }_{\uparrow \downarrow ,\uparrow \downarrow }\left(t\right)$. The initial state is taken to be ∣↑↓⟩ and the time is normalized by $h∕J_{\mathrm{RKKY}}$. (b) The same plot for ${\rho }_{\uparrow \downarrow ,\downarrow \uparrow }\left(t\right)$ with the initial state $(\mid \uparrow \downarrow ⟩-\mid \downarrow \uparrow ⟩)∕\sqrt{2}$. For both panels, the thin solid line represents the result for $\gamma ={\gamma }_{\mathrm{ex}}=0$, while all the other lines are for $\gamma =0.05J_{\mathrm{RKKY}}$. The parameter ${\gamma }_{\mathrm{ex}}$ is taken to be 0, 0.025, 0.045, and $0.05J_{\mathrm{RKKY}}$ for the thick solid, dotted, dashed, and dotted-dashed lines, respectively.