Evolution of anN-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation
From MaRDI portal
Publication:2962799
DOI10.1080/09500340.2013.865806zbMath1356.81130arXiv1309.1130OpenAlexW2077900931MaRDI QIDQ2962799
No author found.
Publication date: 17 February 2017
Published in: Journal of Modern Optics (Search for Journal in Brave)
Abstract: The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. For finding solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N2xN2. When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a fifteen-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy levels.
Full work available at URL: https://arxiv.org/abs/1309.1130
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)
Cites Work
This page was built for publication: Evolution of anN-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation
