  The valley degree of freedom is intrinsic to spin qubits in Si/SiGe quantum
dots. It has been viewed alternately as a hazard, especially when the lowest
valley-orbit splitting is small compared to the thermal energy, or as an asset,
most prominently in proposals to use the valley degree of freedom itself as a
qubit. Here we present experiments in which microwave electric field driving
induces transitions between both valley-orbit and spin states. We show that
this system is highly nonlinear and can be understood through the use of
dressed photon-orbital states, enabling a unified understanding of the six
microwave resonance lines we observe. Some of these resonances are inter-valley
spin transitions that arise from a non-adiabatic process in which both the
valley and the spin degree of freedom are excited simultaneously. For these
transitions, involving a change in valley-orbit state, we find a tenfold
increase in sensitivity to electric fields and electrical noise compared to
pure spin transitions, strongly reducing the phase coherence when changes in
valley-orbit index are incurred. In contrast to this non-adiabatic transition,
the pure spin transitions, whether arising from harmonic or subharmonic
generation, are shown to be adiabatic in the orbital sector. The non-linearity
of the system is most strikingly manifest in the observation of a dynamical
anti-crossing between a spin-flip, inter-valley transition and a three-photon
transition enabled by the strong nonlinearity we find in this seemly simple
system.
