Effects of Multi-pulse Dynamical Decoupling Schemes on Dephasing in a GaAs Spin Qubit

Coherence time ($T_2$) of a singlet-triplet qubit in a GaAs double quantum dot is studied as a function of the number of $\pi$-pulses in a Carr-Purcell-Meiborn-Gill (CPMG) dynamical decoupling sequence. In this system, the dominant forms of dephasing are expected to be hyperfine coupling to the nuclei and electrical noise. For $n_\pi$ ranging from 2 to 32, we find a power law dependence of $T_2$ with the number of pulses, $T_2 \propto n_\pi^\beta$, where $n_\pi$ is the number of pulses and $\beta \sim 0.7$ is a fit parameter.