Related papers: Finite atomic lattices and their monomial ideals
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
In this lecture I give a brief review of low-dimensional few-body problems recently encountered in attempting a quantitative description of ultracold atoms and molecules confined in 2D and 1D optical lattices. Multi-channel nature of these…
We consider the problem of reconstructing a nanocrystal at atomic resolution from electron microscopy images taken at a few tilt angles. A popular reconstruction approach called discrete tomography confines the atom locations to a coarse…
Precise knowledge of optical lattice depths is important for a number of areas of atomic physics, most notably in quantum simulation, atom interferometry and for the accurate determination of transition matrix elements. In such experiments,…
We give a new proof of the fact that any finite quadratic module can be decomposed into indecomposable ones. For any indecomposable finite quadratic module, we construct a lattice, and a positive definite lattice, both of which are of the…
Two-dimensional atomic arrays exhibit a number of intriguing quantum optical phenomena, including subradiance, nearly perfect reflection of radiation and long-lived topological edge states. Studies of emission and scattering of photons in…
Structures involving a lattice and join-endomorphisms on it are ubiquitous in computer science. We study the cardinality of the set $\mathcal{E}(L)$ of all join-endomorphisms of a given finite lattice $L$. In particular, we show for…
We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals.
Noise correlation analysis is a detection tool for spatial structures and spatial correlations in the in-trap density distribution of ultracold atoms. In this book chapter, we discuss the implementation, properties and limitations of the…
We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on ${\cal N}=1$ and ${\cal N}=4$ super Yang-Mills in four dimensions. Brief reviews of the corresponding…
We present a coherent filtering scheme which dramatically reduces the site occupation number defects for atoms in an optical lattice, by transferring a chosen number of atoms to a different internal state via adiabatic passage. With the…
We characterize the isomorphism types of principal ideals of the Turing degrees below 0' that are lattices as the lattices with a Sigma-0-3 presentation, by showing that each Sigma-0-3 presentable bounded upper semilattice is isomorphic to…
Clean metallic superlattice systems composed of alternating layers of superconducting and normal materials are considered, particularly aspects of the proximity effect as it affects the critical temperature. A simple model is used to…
We create low-entropy states of neutral atoms by utilizing a conceptually new optical-lattice technique that relies on a high-precision, high-bandwidth synthesis of light polarization. Polarization-synthesized optical lattices provide two…
Motivated by the behavior of the trace pairing over tame cyclic number fields, we introduce the notion of tame lattices. Given an arbitrary non-trivial lattice $\mathcal{L}$ we construct a parametric family of full-rank sub-lattices…
We provide an analytical description of the dynamics of an atom in an optical lattice using the method of perturbative adiabatic expansion. A precise understanding of the lattice-atom interaction is essential to taking full advantage of the…
We study Euclidean lattice formulations of non-gauge supersymmetric models with up to four supercharges in various dimensions. We formulate the conditions under which the interacting lattice theory can exactly preserve one or more nilpotent…
We define and study the canonical complex of a finite semidistributive lattice $L$. It is the simplicial complex on the join or meet irreducible elements of $L$ which encodes each interval of $L$ by recording the canonical join…
We construct a family of independent sets for finite, atomic, and graded lattices, extending the well-known cryptomorphism between geometric lattices and matroids. This construction leads to an embedding theorem into geometric lattices that…
Ultracold atoms in optical lattices are a powerful tool for quantum simulation, precise measurement, and quantum computation. A fundamental problem in applying this quantum system is how to manipulate the higher bands or orbitals in Bloch…