78 research outputs found
On the K-theory of C*-algebras arising from integral dynamics
We investigate the -theory of unital UCT Kirchberg algebras
arising from families of relatively prime numbers. It is
shown that is the direct sum of a free abelian group and a
torsion group, each of which is realized by another distinct -algebra
naturally associated to . The -algebra representing the torsion part is
identified with a natural subalgebra of . For
the -theory of , the cardinality of determines the free
part and is also relevant for the torsion part, for which the greatest common
divisor of plays a central role as well. In the case
where or we obtain a complete classification
for . Our results support the conjecture that
coincides with . This would lead to a complete
classification of , and is related to a conjecture about
-graphs.Comment: 27 pages; v2: minor update in 5.7; v3: some typos corrected, one
reference added, to appear in Ergodic Theory Dynam. System
C*-Algebras of algebraic dynamical systems and right LCM semigroups
We introduce algebraic dynamical systems, which consist of an action of a
right LCM semigroup by injective endomorphisms of a group. To each algebraic
dynamical system we associate a C*-algebra and describe it as a semigroup
C*-algebra. As part of our analysis of these C*-algebras we prove results for
right LCM semigroups. More precisely we discuss functoriality of the full
semigroup C*-algebra and compute its K-theory for a large class of semigroups.
We introduce the notion of a Nica-Toeplitz algebra of a product system over a
right LCM semigroup, and show that it provides a useful alternative to study
algebraic dynamical systems.Comment: 28 pages, to appear in Indiana Univ. Math.
On C*-algebras associated to right LCM semigroups
We initiate the study of the internal structure of C*-algebras associated to
a left cancellative semigroup in which any two principal right ideals are
either disjoint or intersect in another principal right ideal; these are
variously called right LCM semigroups or semigroups that satisfy Clifford's
condition. Our main findings are results about uniqueness of the full semigroup
C*-algebra. We build our analysis upon a rich interaction between the group of
units of the semigroup and the family of constructible right ideals. As an
application we identify algebraic conditions on S under which C*(S) is purely
infinite and simple.Comment: 31 page
Equilibrium states on right LCM semigroup C*-algebras
We determine the structure of equilibrium states for a natural dynamics on
the boundary quotient diagram of -algebras for a large class of right LCM
semigroups. The approach is based on abstract properties of the semigroup and
covers the previous case studies on ,
dilation matrices, self-similar actions, and Baumslag-Solitar monoids. At the
same time, it provides new results for large classes of right LCM semigroups,
including those associated to algebraic dynamical systems.Comment: 43 pages, to appear in Int. Math. Res. No
Imaging electric fields in the vicinity of cryogenic surfaces using Rydberg atoms
The ability to characterize static and time-dependent electric fields in situ
is an important prerequisite for quantum-optics experiments with atoms close to
surfaces. Especially in experiments which aim at coupling Rydberg atoms to the
near field of superconducting circuits, the identification and subsequent
elimination of sources of stray fields is crucial. We present a technique that
allows the determination of stray-electric-field distributions
at distances of less than from (cryogenic) surfaces using
coherent Rydberg-Stark spectroscopy in a pulsed supersonic beam of metastable
helium atoms. We demonstrate the
capabilities of this technique by characterizing the electric stray field
emanating from a structured superconducting surface. Exploiting coherent
population transfer with microwave radiation from a coplanar waveguide, the
same technique allows the characterization of the microwave-field distribution
above the surface.Comment: 6 pages, 4 figure
Measuring the dispersive frequency shift of a rectangular microwave cavity induced by an ensemble of Rydberg atoms
In recent years the interest in studying interactions of Rydberg atoms or
ensembles thereof with optical and microwave frequency fields has steadily
increased, both in the context of basic research and for potential applications
in quantum information processing. We present measurements of the dispersive
interaction between an ensemble of helium atoms in the 37s Rydberg state and a
single resonator mode by extracting the amplitude and phase change of a weak
microwave probe tone transmitted through the cavity. The results are in
quantitative agreement with predictions made on the basis of the dispersive
Tavis-Cummings Hamiltonian. We study this system with the goal of realizing a
hybrid between superconducting circuits and Rydberg atoms. We measure maximal
collective coupling strengths of 1 MHz, corresponding to 3*10^3 Rydberg atoms
coupled to the cavity. As expected, the dispersive shift is found to be
inversely proportional to the atom-cavity detuning and proportional to the
number of Rydberg atoms. This possibility of measuring the number of Rydberg
atoms in a nondestructive manner is relevant for quantitatively evaluating
scattering cross sections in experiments with Rydberg atoms
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