What if θ13\theta_{13} Is Small?

In the basis where the charged lepton mass matrix is diagonal, the left-handed neutrino mass matrix is invariant under the permutation of the second and third generations if, and only if, the reactor angle $\theta_{13}$ is zero and the atmospheric mixing angle $\theta_{23}$ is maximal. In the presence of the seesaw mechanism, this symmetry leads to an inverted hierarchy, with $m_3=0$. This inverted mass spectrum is doubly protected if the right-handed neutrinos also have a 2-3 symmetry

An equivalence principle for scalar forces

The equivalence of inertial and gravitational masses is a defining feature of general relativity. Here, we clarify the status of the equivalence principle for interactions mediated by a universally coupled scalar, motivated partly by recent attempts to modify gravity at cosmological distances. Although a universal scalar-matter coupling is not mandatory, once postulated, it is stable against classical and quantum renormalizations in the matter sector. The coupling strength itself is subject to renormalization of course. The scalar equivalence principle is violated only for objects for which either the graviton self-interaction or the scalar self-interaction is important---the first applies to black holes, while the second type of violation is avoided if the scalar is Galilean-symmetric.Comment: 4 pages, 1 figur

Generalized Background-Field Method

The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than the ordinary background-field gauge, in that even the triple-gluon vertices for internal lines contain only four terms, not the usual six. This reduction simplifies the calculation inspite of the necessity to include other vertices for compensation. Like the ordinary background-field gauge, this generalized background-field gauge also preserves gauge invariance of the external particles. As a check of the result and an illustration for the reduction in labour, an explicit calculation of the two-loop QCD $\beta$-function is carried out in this new gauge. It results in a saving of 45% of computation compared to the ordinary background-field gauge.Comment: 17 pages, Latex, 18 figures in Postscrip

High efficiency coherent optical memory with warm rubidium vapour

By harnessing aspects of quantum mechanics, communication and information processing could be radically transformed. Promising forms of quantum information technology include optical quantum cryptographic systems and computing using photons for quantum logic operations. As with current information processing systems, some form of memory will be required. Quantum repeaters, which are required for long distance quantum key distribution, require optical memory as do deterministic logic gates for optical quantum computing. In this paper we present results from a coherent optical memory based on warm rubidium vapour and show 87% efficient recall of light pulses, the highest efficiency measured to date for any coherent optical memory. We also show storage recall of up to 20 pulses from our system. These results show that simple warm atomic vapour systems have clear potential as a platform for quantum memory

An AC Stark Gradient Echo Memory in Cold Atoms

The burgeoning fields of quantum computing and quantum key distribution have created a demand for a quantum memory. The gradient echo memory scheme is a quantum memory candidate for light storage that can boast efficiencies approaching unity, as well as the flexibility to work with either two or three level atoms. The key to this scheme is the frequency gradient that is placed across the memory. Currently the three level implementation uses a Zeeman gradient and warm atoms. In this paper we model a new gradient creation mechanism - the ac Stark effect - to provide an improvement in the flexibility of gradient creation and field switching times. We propose this scheme in concert with a move to cold atoms (~1 mK). These temperatures would increase the storage times possible, and the small ensemble volumes would enable large ac Stark shifts with reasonable laser power. We find that memory bandwidths on the order of MHz can be produced with experimentally achievable laser powers and trapping volumes, with high precision in gradient creation and switching times on the order of nanoseconds possible. By looking at the different decoherence mechanisms present in this system we determine that coherence times on the order of 10s of milliseconds are possible, as are delay-bandwidth products of approximately 50 and efficiencies over 90%

Residue codes of extremal Type II Z_4-codes and the moonshine vertex operator algebra

In this paper, we study the residue codes of extremal Type II Z_4-codes of length 24 and their relations to the famous moonshine vertex operator algebra. The main result is a complete classification of all residue codes of extremal Type II Z_4-codes of length 24. Some corresponding results associated to the moonshine vertex operator algebra are also discussed.Comment: 21 pages, shortened from v

Storage and Manipulation of Light Using a Raman Gradient Echo Process

The Gradient Echo Memory (GEM) scheme has potential to be a suitable protocol for storage and retrieval of optical quantum information. In this paper, we review the properties of the $\Lambda$-GEM method that stores information in the ground states of three-level atomic ensembles via Raman coupling. The scheme is versatile in that it can store and re-sequence multiple pulses of light. To date, this scheme has been implemented using warm rubidium gas cells. There are different phenomena that can influence the performance of these atomic systems. We investigate the impact of atomic motion and four-wave mixing and present experiments that show how parasitic four-wave mixing can be mitigated. We also use the memory to demonstrate preservation of pulse shape and the backward retrieval of pulses.Comment: 26 pages, 13 figure

A pseudo-spectral approach to inverse problems in interface dynamics

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles, is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation, is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it is shown to reproduce the input parameters very accurately. When applied to microscopic models of growth, it provides the values of the coupling parameters associated with the corresponding continuum equations. This technique favorably compares with previous methods based on real space schemes.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys. Rev.

Configurable unitary transformations and linear logic gates using quantum memories

We show that a set of optical memories can act as a configurable linear optical network operating on frequency-multiplexed optical states. Our protocol is applicable to any quantum memories that employ off-resonant Raman transitions to store optical information in atomic spins. In addition to the configurability, the protocol also offers favourable scaling with an increasing number of modes where N memories can be configured to implement an arbitrary N-mode unitary operations during storage and readout. We demonstrate the versatility of this protocol by showing an example where cascaded memories are used to implement a conditional CZ gate.Comment: 5 pages, 2 figure