Comparison of density matrix and state vector approaches to dissipative evolution of hyperfine levels coupled to optical and radio-frequency fields in the two-level approximation

Zloshchastiev, Konstantin G.2025-05-212025-05-212024-12-14Zloshchastiev, K.G. 2024. Comparison of density matrix and state vector approaches to dissipative evolution of hyperfine levels coupled to optical and radio-frequency fields in the two-level approximation. Journal of Modern Optics. 71(19-21): 781-794. doi:10.1080/09500340.2025.24587330950-03401362-3044 (Online)https://hdl.handle.net/10321/5957We consider a three-level atom interacting with two optical and one microwave fields in the adiabatic approximation resulting in a simplified description in the terms of a two-level system. Working within the reduced density operator framework, we assume this two-level system to be affected by two types of environment, described by some ad hoc non-Hermitian Hamiltonian and Gorini-Kossakowski-Sudarshan-Lindblad’s models. We compare the three types of dissipative evolution which can occur: driven by equations for a normalized density matrix, a non-normalized density matrix and a normalized state vector. Using the latter type, we derive an effective Hamiltonian, which encodes information about not only the Hamiltonian part of an original master equation but also its non-Hamiltonian (Liouvillian) part. The Hamiltonian turns out to be dependent on the wavefunction itself: the effects of above-mentioned environments induce, respectively, cubic and quintic nonlinear terms. For evolutions driven by density operators, we study various indicators of quantum purity. It is shown that if a trace of density operator is not conserved then conventional von Neumann entropy can no longer be used as a purity indicator; therefore we introduce the purity-normalized definition of quantum statistical entropy.15 penAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/Quantum opticsOpen quantum systems0205 Optical Physics0206 Quantum Physics1007 NanotechnologyOptics5102 Atomic, molecular and optical physics5108 Quantum physicsnon-Hermitian HamiltonianHyperfine structureLambda systemMaster equationTwo-level atomComparison of density matrix and state vector approaches to dissipative evolution of hyperfine levels coupled to optical and radio-frequency fields in the two-level approximationArticle10.1080/09500340.2025.2458733