Dephasing of a quantum dot due to the Coulomb interaction with a gate electrode

Dephasing of quantum dots presents an intrinsic limitation on their use for quantum computing. We consider the dephasing of a double quantum dot caused by the Coulomb interaction with nearby gate electrodes and show that this occurs on a much longer time scale than dephasing due to phonons. However, the effect grows rapidly stronger as the system size decreases, and therefore it is expected to limit potential miniaturization of these systems.

Figure 1

(a) A schematic drawing of a double-quantum-dot system. The electrodes define the quantum dots (indicated by the dashed lines), control tunneling into the source or drain electrodes (not shown), and determine the tunnel barrier. (b) An approximated system, in which the electrodes are replaced by a single, infinite electrode and the double-quantum-dot system is represented with a pair of square well potentials of equal height connected via a tunnel barrier. The gate electrode is assumed thick enough that it may be approximated as a bulk metal (filling the region $z>d$).

Figure 2

The dephasing rate of the double-quantum-dot system, due to the interaction with the gate electrode, as a function of tunneling energy (a), distance between the gate and the quantum dots (b), distance between the quantum dots (c), and temperature (d). In (a) we set $d=50\mathrm{nm}$, $s=100\mathrm{nm}$, and $T=100\mathrm{mK}$. In (b) $E_{21}=8\mu \mathrm{eV}$, $s=100\mathrm{nm}$, and $T=100\mathrm{mK}$. In (c) $E_{21}=8\mu \mathrm{eV}$, $d=50\mathrm{nm}$, and $T=100\mathrm{mK}$, and finally in (d) we used $E_{21}=8\mu \mathrm{eV}$, $d=50\mathrm{nm}$, and $s=100\mathrm{nm}$.

Figure 3

The pure dephasing rate, as defined in Eq. (20), as a function of tunneling energy (a), distance between the gate and the quantum dots (b), distance between the quantum dots (c), and temperature (d). The other parameters are chosen as in Figs. 2a, 2b, 2c, 2d, respectively.

Figure 4

The asymptotic value of ${\rho }_{11}$, as a function of $E_{21}$ (with $T=100\mathrm{mK}$) and $T$ (with $E_{21}=8\mu \mathrm{eV}$). The solid line indicates the thermal equilibrium value, while the circles are the numerically calculated asymptotes (calculated from the residue of the $z=0$ pole of the Laplace transform). In both figures, $s=100\mathrm{nm}$ and $d=50\mathrm{nm}$.