Single-shot readout and relaxation of singlet/triplet states in exchange-coupled ${}^{31}$P electron spins in silicon

Abstract

We present the experimental observation of a large exchange coupling $J\approx 300$ $\mu$eV between two ${}^{31}$P electron spin qubits in silicon. 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 $T_1\approx 4$ ms at zero magnetic field agrees with the theoretical prediction for $J$-coupled ${}^{31}$P dimers in silicon. The time evolution of the 2-electron state populations gives further insight into the valley-orbit eigenstates of the donor dimer, valley selection rules and relaxation rates, and the role of hyperfine interactions. These results pave the way to the realization of 2-qubit quantum logic gates with spins in silicon, and highlight the necessity to adopt gating schemes compatible with weak $J$-coupling strengths.

Main: 5 pages, 4 figures. Supp.Mat: 1 page, 1 figure. Final version with journal reference

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