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We derive the exact solution of a system of N-level atoms in contact with aMarkovian reservoir. The resulting Liouvillian expressed in a vectorized basisis mapped to an SU(N) trigonometric Richardson-Gaudin model whose exactsolution for the complete set of eigenmodes is given by a set of non-linearcoupled equations. For N = 2 (SU(2)) we recover the exact solution of Phys.Rev. Lett. 122, 010401 (2019). We then study the SU(3) case for three-levelatom systems and discuss the properties of the steady state and dissipativegaps for finite systems as well as for the thermodynamic limit.

Trigonometric SU(N) Richardson-Gaudin models and dissipative multi-level atomic systems