Dynamical crystal creation with polar molecules or Rydberg atoms in optical lattices

We investigate the dynamical formation of crystalline states with systems of polar molecules or Rydberg atoms loaded into a deep optical lattice. External fields in these systems can be used to couple the atoms or molecules between two internal states: one that is weakly interacting and one that exhibits a strong dipole-dipole interaction. By appropriate time variation of the external fields we show that it is possible to produce crystalline states of the strongly interacting states with high filling fractions chosen via the parameters of the coupling.We study the coherent dynamics of this process in one dimension (1D) using a modified form of the time-evolving block decimation (TEBD) algorithm, and obtain crystalline states for system sizes and parameters corresponding to realistic experimental configurations. For polar molecules these crystalline states will be long-lived, assisting in a characterization of the state via the measurement of correlation functions. We also show that as the coupling strength increases in the model, the crystalline order is broken. This is characterized in 1D by a change in density-density correlation functions, which decay to a constant in the crystalline regime, but show different regions of exponential and algebraic decay for larger coupling strengths

On the IR behaviour of the Landau-gauge ghost propagator

We examine analytically the ghost propagator Dyson-Schwinger Equation (DSE) in the deep IR regime and prove that a finite ghost dressing function at vanishing momentum is an alternative solution (solution II) to the usually assumed divergent one (solution I). We furthermore find that the Slavnov-Taylor identities discriminate between these two classes of solutions and strongly support the solution II. The latter turns out to be also preferred by lattice simulations within numerical uncertainties.Comment: 15 pages, Axodraw neede

A Ghost Story: Ghosts and Gluons in the IR regime of QCD

We discuss the different methods to obtain reliable informations about the deep infra-red behaviour of the gluon and ghost Green functions in QCD. We argue that a clever combination of analytical inputs and numerical ones is necessary. We illustrate this statement about the distinction between two classes of solutions of the ghost propagator Dyson-Schwinger equation (GPDSE). We conclude that the solution II ("decoupling") with a finite renormalised ghost dressing function at zero momentum is strongly favored by lattice QCD, We derive a method to solve numerically the GPDSE using lattice inputs concerning the gluon propagator. We derive an analytical small momentum expansion of the Ghost dressing function. We prove from the large cut-off behaviour of the ghost propagator renormalisation constant, $\widetilde Z_3$, that the bare ghost dressing function is infinite at the infinite cut-off limit.Comment: 12 pages 6 figure

On the Density of Coprime m-tuples over Holomorphy Rings

Let $\mathbb F_q$ be a finite field, $F/\mathbb F_q$ be a function field of genus $g$ having full constant field $\mathbb F_q$, $\mathcal S$ a set of places of $F$ and $H$ the holomorphy ring of $\mathcal S$. In this paper we compute the density of coprime $m$-tuples of elements of $H$. As a side result, we obtain that whenever the complement of $\mathcal S$ is finite, the computation of the density can be reduced to the computation of the $L$-polynomial of the function field. In the rational function field case, classical results for the density of coprime $m$-tuples of polynomials are obtained as corollaries.Comment: To appear in International Journal of Number Theor

Energy Dependence of Scattering Ground State Polar Molecules

We explore the total cross section of ground state polar molecules in an electric field at various energies, focusing on RbCs and RbK. An external electric field polarizes the molecules and induces strong dipolar interactions leading to non-zero partial waves contributing to the scattering even as the collision energy goes to zero. This results in the need to compute scattering problems with many different values of total M to converge the total cross section. An accurate and efficient approximate total cross section is introduced and used to study the low field temperature dependence. To understand the scattering of the polar molecules we compare a semi-classical cross section with quantum unitarity limit. This comparison leads to the ability to characterize the scattering based on the value of the electric field and the collision energy.Comment: Accepted PRA, 10 pages, 5 figure

Instanton traces in lattice gluon correlation functions

Strong coupling constant computed in Landau gauge and MOM renormalization scheme from lattice two and three gluon Green Functions exhibits an unexpected behavior in the deep IR, showing a maximum value around $1 {\rm GeV}$. We analise this coupling below this maximum within a semiclassical approach, were gluon degrees of freedom at very low energies are described in terms of the classical solutions of the lagrangian, namely instantons. We provide some new results concerning the relationship between instantons and the low energy dynamics of QCD, by analising gluon two- and three-point Green functions separately and with the help of a cooling procedure to eliminate short range correlations.Comment: 4 pages, talk given at XXXX Rencontres de Moriond on QCD and Hadronic Interactions, La Thuile (Italy

Ground state cooling of atoms in optical lattices

We propose two schemes for cooling bosonic and fermionic atoms that are trapped in a deep optical lattice. The first scheme is a quantum algorithm based on particle number filtering and state dependent lattice shifts. The second protocol alternates filtering with a redistribution of particles by means of quantum tunnelling. We provide a complete theoretical analysis of both schemes and characterize the cooling efficiency in terms of the entropy. Our schemes do not require addressing of single lattice sites and use a novel method, which is based on coherent laser control, to perform very fast filtering.Comment: 12 pages, 7 figure