Quantum control in infinite dimensions

Accurate control of quantum evolution is an essential requirement for quantum state engineering, laser chemistry, quantum information and quantum computing. Conditions of controllability for systems with a finite number of energy levels have been extensively studied. By contrast, results for controllability in infinite dimensions have been mostly negative, stating that full control cannot be achieved with a finite dimensional control Lie algebra. Here we show that by adding a discrete operation to a Lie algebra it is possible to obtain full control in infinite dimensions with a small number of control operators.