Fermionic artificial matter realized with cold atoms grants access to an unprecedented degree of control on sophisticated many-body effects with an enhanced flexibility of the operating conditions. Here, we consider three-component fermions with attractive interactions to study the formation of complex bound states, whose nature goes beyond the standard fermion pairing occurring in quantum materials. Such systems display clear analogies with quark matter. We address the nature of the bound states of a three-component fermionic system in a ring-shaped trap through the persistent current. In this way, we demonstrate that we can distinguish between color superfluid and trionic bound states. By analyzing finite temperature effects, we show how finite temperature can lead to the deconfinement of bound states. For weak interactions, the deconfinement occurs because of scattering states. In this regime, the deconfinement depends on the trade-off between interactions and thermal fluctuations. For strong interactions the features of the persistent current result from the properties of a suitable gas of bound states.
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