Related papers: Atoms and coatoms in three-generated lattices
We present an algorithm for the classification of triples of lattice polytopes with a given mixed volume $m$ in dimension 3. It is known that the classification can be reduced to the enumeration of so-called irreducible triples, the number…
We load atoms into every site of an optical lattice and selectively spin flip atoms in a sublattice consisting of every other site. These selected atoms are separated from their unselected neighbors by less than an optical wavelength. We…
In a numerical investigation, we demonstrate the existence and curious evolution of vortices in a ladder-type three-level nonlinear atomic vapor with linear, cubic, and quintic susceptibilities considered simultaneously with the dressing…
In solid materials, nontrivial topological states, electron correlations, and magnetism are central ingredients for realizing quantum properties, including unconventional superconductivity, charge and spin density waves, and quantum spin…
Two constructions of lattice packings of $ n $-dimensional cross-polytopes ($ \ell_1 $ balls) are described, the density of which exceeds that of any prior construction by a factor of at least $ 2^{\frac{n}{\ln n}(1 + o(1))} $ when $ n \to…
A coding lattice $\Lambda_c$ and a shaping lattice $\Lambda_s$ forms a nested lattice code $\mathcal{C}$ if $\Lambda_s \subseteq \Lambda_c$. Under some conditions, $\mathcal{C}$ is a finite cyclic group formed by rectangular encoding. This…
We predict the existence of spatially localized nontrivial vortex states of a Bose-Einstein condensate with repulsive atomic interaction confined by a three-dimensional optical lattice. Such vortex-like structures include planar vortices,…
We present a quantum interference approach to preserve coherence in the external states of an atom trapped in an optical lattice. We show that this is possible by suitably choosing the initial state of the atom. We demonstrate this in…
We map certain highly correlated electron systems on lattices with geometrical frustration in the motion of added particles or holes to the spatial defect-defect correlations of dimer models in different geometries. These models are studied…
Featuring excellent coherence and operated parallelly, ultracold atoms in optical lattices form a competitive candidate for quantum computation. For this, a massive number of parallel entangled atom pairs have been realized in…
Square lattice designs are often used in trials of new varieties of various agricultural crops. However, there are no square lattice designs for 36 varieties in blocks of size six for four or more replicates. Here we use three different…
We observe effects of collective atomic motion in a one-dimensional optical lattice coupled to an optomechanical system. In this hybrid atom-optomechanical system, the lattice light generates a coupling between the lattice atoms as well as…
A geometrical model for tri-nuclear molecules is presented. An analytical solution is obtained provided the nuclei, which are taken to be prolately deformed, are connected in line to each other. Furthermore, the tri-nuclear molecule is…
Mixtures of bosonic and fermionic atoms in optical lattices provide a promising arena to study strongly correlated systems. In experiments realizing such mixtures in the quantum degenerate regime the temperature is a key parameter. In this…
Geometrically frustrated systems with a large degeneracy of low energy states are of central interest in condensed-matter physics. The kagome net - a pattern of corner-sharing triangular plaquettes - presents a particularly high degree of…
We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the…
Strongly interacting fermions define the properties of complex matter at all densities, from atomic nuclei to modern solid state materials and neutron stars. Ultracold atomic Fermi gases have emerged as a pristine platform for the study of…
In this paper, we count all non-isomorphic lattices on $n$ elements, containing four reducible elements and having nullity three. This work is in respect of Birkhoff's open problem (which is NP-complete) of counting all finite lattices on…
We create a gray optical lattice structure using a blue detuned laser field coupling an atomic ground state of angular momentum J simultaneously to two excited states with angular momenta J and J-1. The atoms are cooled and trapped at…
Most experiments with ultracold atoms in optical lattices have contact interactions, and therefore operate at high densities of around one atom per site to observe the effect of strong interactions. Strong ranged interactions can be…