Phase-sensitive tests of the pairing state symmetry in Sr2RuO4

Exotic superconducting properties of Sr$_{2}$RuO$_{4}$ have provided strong support for an unconventional pairing symmetry. However, the extensive efforts over the past decade have not yet unambiguously resolved the controversy about the pairing symmetry in this material. While recent phase-sensitive experiments using flux modulation in Josephson junctions consisting of Sr$_{2}$RuO$_{4}$ and a conventional superconductor have been interpreted as conclusive evidence for a chiral spin-triplet pairing, we propose here an alternative interpretation. We show that an overlooked chiral spin-singlet pairing is also compatible with the observed phase shifts in Josephson junctions and propose further experiments which would distinguish it from its spin-triplet counterpart.Comment: 4 pages, 1 figur

On ramification theory in the imperfect residue field case

We consider the class of complete discretely valued fields such that the residue field is of prime characteristic p and the cardinality of a $p$-base is 1. This class includes two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It appears that a Hasse-Herbrand type functions can be defined with all the usual properties. Therefore, a theory of upper ramification groups, as well as the ramification theory of infinite extensions, can be developed. Next, we consider an equal characteristic two-dimensional local field $K$. We introduce some filtration on the second K-group of a given field. This filtration is other than the filtration induced by the valuation. We prove that the reciprocity map of two-dimensional local class field theory identifies this filtration with the ramification filtration.Comment: This is a corrected and extended version of my 1998 Nottingham preprint; many details are added. AmSTeX, 28 pages. To appear in Proceedings of the conference "Ramification theory of arithmetic schemes" (Luminy, 1999

Atom state evolution and collapse in ultracold gases during light scattering into a cavity

We consider the light scattering from ultracold atoms trapped in an optical lattice inside a cavity. In such a system, both the light and atomic motion should be treated in a fully quantum mechanical way. The unitary evolution of the light-matter quantum state is shown to demonstrate the non-trivial phase dependence, quadratic in the atom number. This is essentially due to the dynamical self-consistent nature of the light modes assumed in our model. The collapse of the quantum state during the photocounting process is analyzed as well. It corresponds to the measurement-induced atom number squeezing. We show that, at the final stage of the state collapse, the shrinking of the width of the atom number distribution behaves exponentially in time. This is much faster than the square root time dependence, obtained for the initial stage of the state collapse. The exponentially fast squeezing appears due to the discrete nature of the atom number distribution.Comment: 10 pages, 1 figur