Ultra-fast evolution via PT-symmetry and entanglement: extending the BBJM brachistochrone

The basics of quantum mechanical brachistochrones are briefly sketched for Hermitian systems as well as for PT-symmetric systems --- as the latter have been recently proposed by Bender, Brody, Jones and Meister (BBJM) in [C. M. Bender et al, Phys. Rev. Lett. 98, 040403 (2007)]. Using a mainly geometric approach, the hidden new features of this PT-symmetric brachsistochrone with its close relation to non-diagonalizable operator realizations with non-trivial Jordan block structures and spectral singularities (spectral exceptional points) are discussed. Furthermore the Naimark dilation technique as basic tool for an extension toward possible experimental implementations is explained. The remarkable links to wormhole-type setups and entangled states (Einstein's 'spooky action') are highlighted and sketched geometrically. The talk is mainly based on [Phys. Rev. Lett. 101, 230404 (2008)].