Unified quantum-statistical approach to open three-level atomic Lambda configurations: Constructing master equations for various evolution types

A unified quantum-statistical framework is proposed for open three-level atomic systems when two lower-energy states are coupled to a single upper state. We suggest a non-Hermitian generalization of the closed model’s Hamiltonian by the analytical continuation of real-valued parameters related to the energies into a complex domain, as well as by considering some terms previously neglected by the procedure of Hermitian conjugation. We show that such systems can have two types of density operator’s evolution, depending on whether they are expected to be sustainable, or in a process of irreversible decay. This approach not only explains previously heuristically introduced terms in equations of motion for the density matrix but also suggests new terms which predict new dissipative effects. We then consider a special case, namely the evolution of pure states described by a generalized Schrödinger equation, which turns out to be nonlinear with respect to the atomic wavefunctions. As a final step towards unification, in addition to the non-Hermitian Hamiltonian generalization, we also include Markovian quantum jumps by adding the Lindblad dissipator. The resulting equations not only expand the range of applicability of open three-level models, but also suggest that dissipative phenomena in quantum-optical systems in vivo are more diverse and significant than previously believed.