Extended Data Fig. 4: T1 processes and temperature dependence.
From: High-fidelity spin qubit operation and algorithmic initialization above 1 K
a, The characteristic time of spin relaxation, T1, and the decay amplitude for various two-qubit states as a function of temperature. We recognise the presence of different relaxation mechanisms at low temperatures, as described in the main text. Here we also look at the evolution of the decay amplitudes, defined as the difference in Pblockade between the starting point and decay equilibrium. At low temperatures where the relaxation to low-energy states dominates, the decay reaches an equilibrium with mostly \(\left|\downarrow \downarrow \right\rangle \). With even-parity initialisation, the decay amplitude should be well below 0.5. With odd-parity initialisation, the decay amplitude should be well above 0.5. At high temperatures where the thermal energy becomes comparable or greater than the qubit energy, the decay equilibrium is a mixed state and Pblockade tends towards 0.5. Therefore, the decay amplitude reduces as the temperature increases, following an \({e}^{-{k}_{{\rm{B}}}T}\)-like reduction, until the degradation of readout starts to dominate. This trend is apparent in the (5, 3) state, but becomes more convoluted in (1, 3), possibly due to lower-lying excited states. Although T1 is not the limiting time scale in this temperature range, we recognise the rich physical processes behind relaxation revealed in this work additional to the previous results15,16 and their potential impact on longer or higher-temperature operation in the future. b, Measured and fitted relaxation decay curves. Since all the decay curves are one-way, they are fit to a single formula \(a{e}^{-{(t/{T}_{1})}^{c}}+d\), where a, c and d are the decay amplitude, exponent and equilibrium. Although fluctuations in the readout level is inevitable before RFSET feedback takes place at the end of each shot, the two-level separation in the charge readout is sufficiently large to maintain an overall correct readout level (Supplementary Information). Error bars represent the 95 % confidence level.