EUROISMAR 2019

So-called phase-space representations such as Wigner functions, are a powerful tool for representing quantum states and characterizing their time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum optics and beyond. Continuous phase spaces have also been studied for the finite-dimensional quantum systems of individual spins. However, much less was known for coupled spin systems, and we present a complete theory of Wigner functions for this case. In particular, we provide a self-contained Wigner formalism for describing and predicting the time evolution of coupled spins which lends itself to visualizing the high-dimensional state space in a structured and intuitive way. We completely treat the case of an arbitrary number of coupled spins 1/2, thereby establishing the equation of motion using Wigner functions. The explicit form of the time evolution is then calculated for up to three spins 1/2. The underlying physical principles of our Wigner representations for coupled spin systems are illustrated for several NMR examples. This talk is based on Annals of Physics DOI 10.1016/j.aop.2018.11.020 (in press).