Phase portrait of the qutrit system

We investigate the structure of the Bloch space for the qutrit system by analyzing its properties and phase portraits. Within the framework of the SU(3) representation theory and transition features between various states, the qutrit system is categorized as lambda, vee, and cascade type three-level systems. Each of these systems has its own Bloch equation, resulting in distinct dynamics with unique dynamical trajectories. Expanding upon our earlier work (S. Sen, M. R. Nath, T. K. Dey and G. Gangopadhyay, Ann. Phys. 327 (2012) 224–252), which demonstrated the splitting of the Bloch sphere into two distinct sectors, in this paper we provide their explicit derivation from the dynamical perspective and examine the phase portraits of two sectors separately. These phase portraits, ranging from simple to complex patterns of curves, reveal the characteristic pattern of evolution for each sub-sector of the qutrit Bloch space.