Energy minimization problem in two-level dissipative quantum control: meridian case

International audienceWe analyze the energy-minimizing problem for a two-level dissipative quantum system described by the Kossakowsky-Lindblad equation. According to the Pontryagin Maximum Principle (PMP), minimizers can be selected among normal and abnormal extremals whose dynamics are classified according to the values of the dissipation parameters. Our aim is to improve our previous analysis concerning 2D solutions in the case where the Hamiltonian dynamics are integrable

Dynamics of generalized PT-symmetric dimers with time-periodic gain–loss

A parity-time (PT)-symmetric system with periodically varying-in-time gain and loss modeled by two coupled Schrödinger equations (dimer) is studied. It is shown that the problem can be reduced to a perturbed pendulum-like equation. This is done by finding two constants of motion. Firstly, a generalized problem using Melnikov-type analysis and topological degree arguments is studied for showing the existence of periodic (libration), shift- periodic (rotation), and chaotic solutions. Then these general results are applied to the PT-symmetric dimer. It is interestingly shown that if a sufficient condition is satisfied, then rotation modes, which do not exist in the dimer with constant gain–loss, will persist. An approximate threshold for PT-broken phase corresponding to the disappearance of bounded solutions is also presented. Numerical study is presented accompanying the analytical results