  The interaction between a qubit and its environment provides a channel for
energy relaxation which has an energy-dependent timescale governed by the
specific coupling mechanism. We measure the rate of inelastic decay in a Si MOS
double quantum dot (DQD) charge qubit through sensing the charge state's
response to non-adiabatic driving of its excited state population. The charge
distribution is sensed remotely in the weak measurement regime. We extract
emission rates down to kHz frequencies by measuring the variation of the
non-equilibrium charge occupancy as a function of amplitude and dwell times
between non-adiabatic pulses. Our measurement of the energy-dependent
relaxation rate provides a fingerprint of the relaxation mechanism, indicating
that relaxation rates for this Si MOS DQD are consistent with coupling to
deformation acoustic phonons.
