Dephasing of exchange coupled spin qubits by electron-phonon coupling: Effect of phonon relaxation

Electron-phonon interaction leads to pure dephasing between two-electron singlet and triplet states for two exchange-coupled spin qubits in a semiconductor double quantum dot because of the Coulombic nature of exchange interaction. Here we clarify the effect of phonon relaxation, whether via boundary scattering or phonon anharmonicity, on phonon-induced two-spin dephasing. Specifically, we show that within a spin-boson model, phonon relaxation leads to a complete exponential decay of the phase between the singlet and triplet two-spin states, with the decoherence rate proportional to the phonon relaxation rate. We examine the relevant parameter regimes and clarify the importance of this decoherence effect.