Atomistic subsemirings of the lattice of subspaces of an algebra

Let A be an associative algebra with identity over a field k. An atomistic subsemiring R of the lattice of subspaces of A, endowed with the natural product, is a subsemiring which is a closed atomistic sublattice. When R has no zero divisors, the set of atoms of R is endowed with a multivalued product. We introduce an equivalence relation on the set of atoms such that the quotient set with the induced product is a monoid, called the condensation monoid. Under suitable hypotheses on R, we show that this monoid is a group and the class of k1_A is the set of atoms of a subalgebra of A called the focal subalgebra. This construction can be iterated to obtain higher condensation groups and focal subalgebras. We apply these results to G-algebras for G a group; in particular, we use them to define new invariants for finite-dimensional irreducible projective representations.Comment: 14 page

Trapped-Ion Quantum Computing: Progress and Challenges

Trapped ions are among the most promising systems for practical quantum computing (QC). The basic requirements for universal QC have all been demonstrated with ions and quantum algorithms using few-ion-qubit systems have been implemented. We review the state of the field, covering the basics of how trapped ions are used for QC and their strengths and limitations as qubits. In addition, we discuss what is being done, and what may be required, to increase the scale of trapped ion quantum computers while mitigating decoherence and control errors. Finally, we explore the outlook for trapped-ion QC. In particular, we discuss near-term applications, considerations impacting the design of future systems of trapped ions, and experiments and demonstrations that may further inform these considerations.Comment: The following article has been submitted to Applied Physics Review

The Nature of Nearby Counterparts to Intermediate Redshift Luminous Compact Blue Galaxies II. CO Observations

We present the results of a single-dish beam-matched survey of the three lowest rotational transitions of CO in a sample of 20 local (D < 70 Mpc) Luminous Compact Blue Galaxies (LCBGs). These ~L*, blue, high surface brightness, starbursting galaxies were selected with the same criteria used to define LCBGs at higher redshifts. Our detection rate was 70%, with those galaxies having Lblue<7e9 Lsun no detected. We find the H2 masses of local LCBGs range from 6.6e6 to 2.7e9 Msun, assuming a Galactic CO-to-H2 conversion factor. Combining these results with our earlier HI survey of the same sample, we find that the ratio of molecular to atomic gas mass is low, typically 5-10%. Using a Large Velocity Gradient model, we find that the average gas conditions of the entire ISM in local LCBGs are similar to those found in the centers of star forming regions in our Galaxy, and nuclear regions of other galaxies. Star formation rates, determined from IRAS fluxes, are a few solar masses per year, much higher per unit dynamical mass than normal spirals. If this rate remains constant, the molecular hydrogen depletion time scales are short, 10-200 Myr.Comment: accepted for publication in the ApJ (vol 625

Inelastic collisions of ultra-cold heteronuclear molecules in an optical trap

Ultra-cold RbCs molecules in high-lying vibrational levels of the a$^3\Sigma^+$ ground electronic state are confined in an optical trap. Inelastic collision rates of these molecules with both Rb and Cs atoms are determined for individual vibrational levels, across an order of magnitude of binding energies. A simple model for the collision process is shown to accurately reproduce the observed scattering rates

Ion traps fabricated in a CMOS foundry

We demonstrate trapping in a surface-electrode ion trap fabricated in a 90-nm CMOS (complementary metal-oxide-semiconductor) foundry process utilizing the top metal layer of the process for the trap electrodes. The process includes doped active regions and metal interconnect layers, allowing for co-fabrication of standard CMOS circuitry as well as devices for optical control and measurement. With one of the interconnect layers defining a ground plane between the trap electrode layer and the p-type doped silicon substrate, ion loading is robust and trapping is stable. We measure a motional heating rate comparable to those seen in surface-electrode traps of similar size. This is the first demonstration of scalable quantum computing hardware, in any modality, utilizing a commercial CMOS process, and it opens the door to integration and co-fabrication of electronics and photonics for large-scale quantum processing in trapped-ion arrays.Comment: 4 pages, 3 figure