  In this work we show how constructing Wigner functions of heterogeneous
quantum systems leads to new capability in the visualization of quantum states
of atoms and molecules. This method allows us to display quantum correlations
(entanglement) between spin and spatial degrees of freedom (spin-orbit
coupling) and between spin degrees of freedom, as well as more complex
combinations of spin and spatial entanglement for the first time. This is
important as there is growing recognition that such properties affect the
physical characteristics, and chemistry, of atoms and molecules. Our
visualizations are sufficiently accessible that, with some preparation, those
with a non-technical background can gain an appreciation of subtle quantum
properties of atomic and other systems. By providing new insights and modelling
capability, our phase-space representation will be of great utility in
understanding aspects of atomic physics and chemistry not available with
current techniques.
