We study the quantum dynamics of a one-dimensional $\mathrm{SU}(3$)-symmetric system of cold atoms in the presence of two-body losses. We exploit the representation theory of $\mathrm{SU}(3$), the so-called eightfold way, as a scheme to organize the dark states of the dissipative dynamics in terms of generalized Dicke states and show how they are dynamically approached, both in the weakly and strongly interacting and dissipative regimes. Our results are relevant for a wide class of alkaline-earth(-like) gas experiments, paving the way to the dissipative preparation and exploitation of generalized Dicke states.

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• Cold gases in optical lattices
• Open quantum systems
• Atomic gases
• Many-body techniques
• Monte Carlo methods
• Quantum master equation