Higher-Order Traps in Quantum Control Landscapes of Physical Systems

An important problem in quantum control is the analysis of quantum control landscapes and its trapping features. The notion of a trap in quantum control landscape was introduced in [H. Rabitz, M. Hsieh, C. Rosenthal, Quantum optimally controlled transition landscapes, Science 303, 1998 (2004)]. Later, the notion of higher-order traps was introduced [A. Pechen and D.J. Tannor, Are there traps in quantum control landscapes?, Phys. Rev. Lett. 106, 120402 (2011)] and such higher-order traps were shown to exist for a variety of important applications for physical systems such as for example Λ-atoms widely used in quantum optics and superconducting transmon qubit systems used as one of the potential platform for quantum computation. In this note, we provide several results on the existence of higher-order traps in quantum control landscapes.