The Naimark dilated PT-symmetric brachistochrone

Abstract

The quantum mechanical brachistochrone system with PT-symmetric Hamiltonian is Naimark dilated and reinterpreted as subsystem of a Hermitian system in a higher-dimensional Hilbert space. This opens a way to a direct experimental implementation of the recently hypothesized PT-symmetric ultra-fast brachistochrone regime of [C. M. Bender et al, Phys. Rev. Lett. {\bf 98}, 040403 (2007)] in an entangled two-spin system.

4 pages

References in corpus (9)

• Making Sense of Non-Hermitian Hamiltonians
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Faster than Hermitian Quantum Mechanics
• Quantum Brachistochrone
• Quantum Brachistochrone Problem and the Geometry of the State Space in Pseudo-Hermitian Quantum Mechanics
• Projective Hilbert space structures at exceptional points
• Elementary Derivation for Passage Times
• On optimum Hamiltonians for state transformations
• The PT-symmetric brachistochrone problem, Lorentz boosts and non-unitary operator equivalence classes

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