Single-shot readout and relaxation measurements in exchange coupled $^{31}P$ electron spins in silicon

We present the experimental observation of a large exchange coupling $J\approx300$ $\mu$eV between two $^{31}P$ electron spin qubits in silicon (Dehollain, \textbf{PRL} 112, 236801). The singlet and triplet states of the coupled spins are monitored in real time by a single-electron transistor, which detects ionization from tunnel-rate-dependent processes in the coupled spin system, yielding single-shot readout fidelities above 95\%. The triplet to singlet relaxation time $T_1\approx4$ ms at zero magnetic field agrees with the theoretical prediction for the observed $J$-coupling energy in $^{31}P$ dimers in silicon. The three order of magnitude increase in relaxation rate compared to single donors, is caused by a hyperfine interaction mediated mixing of the singlet and triplet states. Additionally, the time evolution of the two-electron state populations reveals an inversion in the energetic hierarchy of the valley-orbit excited states, which had been theoretically predicted for donor pairs with $<6$ nm separation. These results pave the way to the realization of two-qubit quantum logic gates with spins in silicon and highlight the necessity to adopt gating schemes compatible with weak $J$-coupling strengths.