  Two level systems that can be reliably controlled and measured hold promise
in both metrology and as qubits for quantum information science (QIS). When
prepared in a superposition of two states and allowed to evolve freely, the
state of the system precesses with a frequency proportional to the splitting
between the states. In QIS,this precession forms the basis for universal
control of the qubit,and in metrology the frequency of the precession provides
a sensitive measurement of the splitting. However, on a timescale of the
coherence time, $T_2$, the qubit loses its quantum information due to
interactions with its noisy environment, causing qubit oscillations to decay
and setting a limit on the fidelity of quantum control and the precision of
qubit-based measurements. Understanding how the qubit couples to its
environment and the dynamics of the noise in the environment are therefore key
to effective QIS experiments and metrology. Here we show measurements of the
level splitting and dephasing due to voltage noise of a GaAs singlet-triplet
qubit during exchange oscillations. Using free evolution and Hahn echo
experiments we probe the low frequency and high frequency environmental
fluctuations, respectively. The measured fluctuations at high frequencies are
small, allowing the qubit to be used as a charge sensor with a sensitivity of
$2 \times 10^{-8} e/\sqrt{\mathrm{Hz}}$, two orders of magnitude better than
the quantum limit for an RF single electron transistor (RF-SET). We find that
the dephasing is due to non-Markovian voltage fluctuations in both regimes and
exhibits an unexpected temperature dependence. Based on these measurements we
provide recommendations for improving $T_2$ in future experiments, allowing for
higher fidelity operations and improved charge sensitivity.
