Theory on Electron-Phonon Spin Dephasing in GaAs Multi-Electron Double Quantum Dots

Recent studies reveal that a double-quantum-dot system hosting more than two electrons may be superior in certain aspects as compared to the traditional case in which only two electrons are confined (a singlet-triplet qubit). The electron-phonon dephasing occurring in a GaAs multi-electron double-quantum-dot system is studied, in a biased case in which the singlet state is hybridized, as well as in an unbiased case in which the hybridization is absent. It is found that while the electron-phonon dephasing rate increases with the number of electrons confined in the unbiased case, this does not hold in the biased case. A merit figure is defined as a ratio between the exchange energy and the dephasing rate, and have shown that in experimentally relevant range of the exchange energy, the merit figure actually increases with the number of electrons in the biased case. The results show that the multi-electron quantum-dot system has another advantage in mitigating the effect of electron-phonon dephasing, which is previously under-appreciated in the literature.