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We present a formalism that enables the study of the non-Markovian dynamicsof a three-level ladder system in a single structured reservoir. Thethree-level system is strongly coupled to a bath of reservoir modes and twoquantum excitations of the reservoir are expected. We show that the dynamicsonly depends on reservoir structure functions, which are products of the modedensity with the coupling constant squared. This result may enable pseudomodetheory to treat multiple excitations of a structured reservoir. The treatmentuses Laplace transforms and an elimination of variables to obtain a formalsolution. This can be evaluated numerically (with the help of a numericalinverse Laplace transform) and an example is given. We also compare this resultwith the case where the two transitions are coupled to two separate structuredreservoirs (where the example case is also analytically solvable)

Non-Markovian decay of a three-level cascade atom in a structured reservoir