Completely Positive Trace Preserving Numerical Methods for Long-Term Generalized Maxwell-Bloch Simulations

The Maxwell-Bloch equations describe the interaction of light (treated classically with Maxwell’s equations) and matter, where the latter is modeled as an ensemble of quantum mechanical systems with two energy levels. The dynamical behavior of the systems is described by the optical Bloch equations. This concept can be generalized to an arbitrary number of energy levels with the help of the density matrix 𝜌̂ and the Lindblad master equation ∂𝑡𝜌̂=−𝑖ℏ−1[𝐻̂,𝜌̂]+𝒟(𝜌̂), where 𝐻̂ is the Hamiltonian of the system and 𝒟 accounts for dissipation.     «

The Maxwell-Bloch equations describe the interaction of light (treated classically with Maxwell’s equations) and matter, where the latter is modeled as an ensemble of quantum mechanical systems with two energy levels. The dynamical behavior of the systems is described by the optical Bloch equations. This concept can be generalized to an arbitrary number of energy levels with the help of the density matrix 𝜌̂ and the Lindblad master equation ∂𝑡𝜌̂=−𝑖ℏ−1[𝐻̂,𝜌̂]+𝒟(𝜌̂), where 𝐻̂ is the Hamiltonian of...     »