  We present a multi-modal spectroscopic paradigm that enables independent
measurement of charge and spin degrees of freedom (DOF) in strongly correlated
materials. This spin-based technique probes symmetry-specific Hamiltonian
parameters by analyzing how the time delay between applied pulses ($\tau$)
affects the response. We demonstrate ways in which charge DOF that couple
through the quadrupolar interaction (inversion symmetric) can be independently
measured even in the presence of large magnetic noise (inversion asymmetric).
The method quantifies both the strength of the interactions and its
distribution (noise). We provide protocols to directly and independently
measure the distribution of interaction strengths, even when the average value
of the interaction is zero. By independently measuring distributions of
different forms of disorder, this methodology can elucidate which microscopic
symmetry drives a phase transition. We discuss potential applications to study
complex phase transitions in strongly interacting quantum materials.
