Floquet Lindbladian Exceptional Point Contours in Dissipative Qubit and Qutrit Systems.

We investigate the landscape of exceptional points (EPs) in the transient Lindblad dynamics of two or three-level systems periodically coupled to low positive and negative temperature baths. Alternating spontaneous absorption and emission dissipators σ± with equal strengths γ are used to calculate the Floquet time-evolution operator G_F(T) for the vectorized density matrix over one period T = 2π/ω. By analyzing eigenvalue degeneracies and eigenvector coincidences we map the EP landscape as a function of dissipator strength γ/J and coupling-modulation frequency ω/J. For a qubit this problem maps to one with time-dependent drive and a static dissipator while for a qutrit EP lines emerge at small dissipator strengths γ/J≪1. These semi-analytical results are supported by density matrix temporal dynamics across the EP lines.

We also consider a three-level quantum system governed by a non-Hermitian Hamiltonian with periodic dissipation modulating the interaction between coherent and dissipative processes. Using the Lindblad master equation we focus on the transient behavior of the density matrix under varying dissipation rates. Periodic modulation of dissipation shapes dynamics with rich structures in parameter space and critical points mark transitions between damped and oscillatory behaviors driven by eigenmode coalescences. The interplay between the non-Hermitian Hamiltonian and time-dependent decay terms produces rich dynamics controllable via modulation of pump and dissipation strengths.