Double quantum dot

Two capacitively and tunnel-coupled electron islands with separately tunable occupations. Detuning controls which dot holds an electron and whether two-electron charge states such as $(1,1)$ and $(0,2)$ are accessible.

A single electron shared by two dots has a left/right charge basis. In that basis, a two-level model is $H=(\epsilon {\sigma }_z+2t_c{\sigma }_x)/2$, where detuning sets the energy imbalance and tunnelling mixes the states. Electrical control and charge sensing are direct, but electric-potential fluctuations also couple strongly to the encoded information.

An effective coupling that separates the two-electron singlet state and triplet states by energy $J$. For a symmetric two-site Hubbard model with weak tunnelling $t_c$ and charging cost $U$, $J\simeq 4t_c^2/U$. Gate-controlled detuning and tunnelling change the interaction; the simple expression does not hold at arbitrary detuning or strong charge hybridization.