We propose methods of optical pumping that are applicable to open, high-angular-momentum transitions in atoms and molecules, for which conventional optical pumping would lead to significant population loss. Instead of applying circularly polarized cw light, as in conventional optical pumping, we propose to use techniques for coherent population transfer (e.g., adiabatic fast passage) to arrange the atoms so as to increase the entropy removed from the system with each spontaneous decay from the upper state. This minimizes the number of spontaneous-emission events required to produce a stretched state, thus reducing the population loss due to decay to other states. To produce a stretched state in a manifold with angular momentum J, conventional optical pumping requires about 2J spontaneous decays per atom; one of our proposed methods reduces this to about log 2 2J, while another of the methods reduces it to about one spontaneous decay, independent of J.

Abstract. The joint numerical range W (F ) of three hermitian 3-by-3 matrices F = (F 1 , F 2 , F 3 ) is a convex and compact subset in R 3 . We show that W (F ) is generically a three-dimensional oval. Assuming dim(W (F )) = 3, every one-or two-dimensional face of W (F ) is a segment or a filled ellipse. We prove that only ten configurations of these segments and ellipses are possible. We identify a triple F for each class and illustrate W (F ) using random matrices and dual varieties.

Photomultipliers are commonly used in commercial PET scanner as devices which convert light produced in scintillator by gamma quanta from positron-electron annihilation into electrical signal. For proper analysis of obtained electrical signal, a photomultiplier gain curve must be known, since gain can be significantly different even between photomultipliers of the same model. In this article we describe single photoelectron method used for photomultipliers calibration applied for J-PET scanner, a novel PET detector being developed at the Jagiellonian University. Description of calibration method, an example of calibration curve and gain of few R4998 Hamamatsu photomultipliers are presented.

For a given Hamiltonian H on a multipartite quantum system, one is interested in finding the energy E 0 of its ground state. In the separability approximation, arising as a natural consequence of measurement in a separable basis, one looks for the minimal expectation value λ ⊗ min of H among all product states. For several concrete model Hamiltonians, we investigate the difference λ ⊗ min − E 0 , called separability gap, which vanishes if the ground state has a product structure. In the generic case of a random Hermitian matrix of the Gaussian orthogonal ensemble, we find explicit bounds for the size of the gap which depend on the number of subsystems and hold with probability one. This implies an effective entanglement criterion applicable for any multipartite quantum system: If an expectation value of a typical observable among a given state is sufficiently distant from the average value, the state is almost surely entangled.