D'Alessandro, DomenicoIsik, Yasemin2024-06-122024-06-1220240005-10981873-2836https://doi.org/10.1016/j.automatica.2024.111595https://hdl.handle.net/20.500.14551/22886We consider the problem of population transfer optimal control for a quantum Lambda system where the control couples pairwise only the lowest two energy levels to the highest level. The cost to be minimized expresses a compromise between minimizing the energy of the control and the average population in the highest level (occupancy), which is the one mostly subject to decay. Such a problem admits a group of symmetries, that is, a Lie group acting on the state space, which leaves dynamics, cost and initial and final conditions unchanged. By identifying a splitting of the tangent bundle into a vertical (tangent to the orbits) and horizontal (complementary) subspace at every point (a connection), we develop a symmetry reduction technique. In this setting, the problem reduces to a real problem on the sphere S2 for which we derive several properties and provide a practical method for the solution. We also describe an explicit numerical example. (c) 2024 Elsevier Ltd. All rights reserved.en10.1016/j.automatica.2024.111595info:eu-repo/semantics/closedAccessOptimal Control Of Quantum SystemsSymmetry ReductionVariational MethodsQuantum Lambda SystemsPontryagin Maximum PrincipleOccupancy CostReduction To The Real CaseArticle163N/AWOS:0012204772000012-s2.0-85186651525Q1