Orthogonal Operators: Applications, Origin and Outlook

Orthogonal operators can successfully be used to calculate eigenvalues and eigenvector compositions in complex spectra. Orthogonality ensures least correlation between the operators and thereby more stability in the fit, even for small interactions. The resulting eigenvectors are used to transform the pure transition matrix into realistic intermediate coupling transition probabilities. Calculated transition probabilities for close lying levels illustrate the power of the complete orthogonal operator approach.

Orthogonal Operators: Applications, Origin and Outlook

Orthogonal operators can successfully be used to calculate eigenvalues and eigenvector compositions in complex spectra. Orthogonality ensures least correlation between the operators and thereby more stability in the fit, even for small interactions. The resulting eigenvectors are used to transform the pure transition matrix into realistic intermediate coupling transition probabilities. Calculated transition probabilities for close lying levels illustrate the power of the complete orthogonal operator approach.

Universality of beamsplitters

We consider the problem of building an arbitrary N × N real orthogonal operator using a finite set, S, of elementary quantum optics gates operating on m ≤ N modes - the problem of universality of S on N modes. In particular, we focus on the universality problem of an m-mode beamsplitter. Using methods of control theory and some properties of rotations in three dimensions, we prove that any nontrivial real 2-mode and ‘almost’ any nontrivial real 3-mode beamsplitter is universal on m ≥ 3 modes.

Revised analysis of the Zn VI spectrum

The spectrum of zinc was photographed in the 100–300 Å (1 Å = 10−10 m) wavelength region on a 10.7 m grazing-incidence spectrograph. On the basis of these precise and extensive data the 3d7–3d64p transition array of Zn VI was reanalysed. All 19 levels of the ground configuration 3d7 were confirmed but the level values were revised. Out of the 161 levels of the 3d64p configuration reported earlier, 10 levels were rejected and 16 new levels were established thus totalling the known levels to 167. The number of the classified lines is 538, almost doubling the previous number. The least-squares-fitting parametric calculations adequately interpret the observed spectrum. The 3d7 configuration was also described by an orthogonal operator technique.