Standard Lattices Research Articles

Transition of laser cooling between standard and Raman optical lattices

Reduced-period optical lattices based on Raman transitions allow for sub-Doppler laser cooling. An important parameter of this Raman optical lattice is the frequency difference ${\ensuremath{\Delta}}_{\mathrm{d}}$ between two virtual energy levels involved in the atom-field interaction scheme. In this work, we use experimental time-of-flight data and quantum simulations to characterize laser cooling in the Raman lattice as a function of ${\ensuremath{\Delta}}_{\mathrm{d}}$. Two different domains of laser cooling are identified. For small ${\ensuremath{\Delta}}_{\mathrm{d}}$, atoms are cooled due to a well-known mechanism that also occurs in standard optical lattices. For large ${\ensuremath{\Delta}}_{\mathrm{d}}$, atoms are cooled based on Raman transitions. We study the transition between the two domains of laser cooling in detail.

Atomic structures of iron-based single-crystalline nanowires crystallized inside multi-walled carbon nanotubes as revealed by analytical electron microscopy

Atomic structures of single-crystalline iron-based nanowires crystallized inside multi-walled carbon nanotubes during pyrolysis on silicon substrates with ferrocene as a precursor were analyzed using high-resolution analytical transmission electron microscopy and electron diffraction. Standard crystal lattices, namely body-centered cubic (bcc) α-Fe, face-centered cubic (fcc) γ-Fe and orthorhombic cementite Fe 3C, were all found to form inside the nanotubes. A fraction of α-Fe nanowires, thermodynamically favorable at room temperature, was found to be dominant. Both bcc and fcc nanowires display a wide variety of lattice planes being parallel to the nanotube walls, with none of the orientations being preferable. The minor fraction of the nanowires had unidentified long-period crystal lattices with doubled or tripled periodicities as compared to those found in the standard cubic iron phases. The crystal matching of these unusual structures to stable orthorhombic Fe 3C or less stable iron carbides, e.g., Fe 5C 2, Fe 7C 3, failed. The non-conventional phases were tentatively assigned to rarely seen silicon-doped octahedral iron carbides. Both long-period and standard cementite nanowires exhibited well-defined transient zones in the vicinity of nanowire–tube shell interfaces, where perfectly ordered carbide lattice fringes disappeared. The results suggest the non-existence of metastable equilibrium in the nanoscale Fe–C system between carbide and graphite phases during iron crystallization inside graphitic tubular channels.

Laser cooling in an optical lattice that employs Raman transitions

We demonstrate laser cooling in an optical lattice that employs Raman transitions. Four laser beams with different frequencies form a one-dimensional lattice with a basic lattice period that is a factor of 2 less than in standard optical lattices. Rb atoms are cooled to $8\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{K}$. We measure the intensity- and detuning-dependence of the cooling mechanism. Our experimental results agree well with theoretical models.

Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics

Kinetically constrained lattice models of glasses introduced by Kob and Andersen (KA) are analyzed. It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality. But in the ergodic cases, the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations. The cooperativity is characterized by two length scales whose behavior controls finite-size effects: these are essential for interpreting simulations. In contrast to hypercubic lattices, on Bethe lattices KA models undergo a dynamical (jamming) phase transition at a critical density: this is characterized by diverging time and length scales and a discontinuous jump in the long-time limit of the density autocorrelation function. By analyzing generalized Bethe lattices (with loops) that interpolate between hypercubic lattices and standard Bethe lattices, the crossover between the dynamical transition that exists on these lattices and its absence in the hypercubic lattice limit is explored. Contact with earlier results are made via analysis of the related Fredrickson-Andersen models, followed by brief discussions of universality, of other approaches to glass transitions, and of some issues relevant for experiments.

Perfect pattern formation of neutral atoms in an addressable optical lattice

We propose a physical scheme for formation of an arbitrary pattern of neutral atoms in an addressable optical lattice. We focus specifically on the generation of a perfect optical lattice of simple orthorhombic structure with unit occupancy, as required for initialization of a neutral atom quantum computer. The scheme employs a compacting process that is accomplished by sequential application of two types of operations: a flip operator that changes the internal state of the atoms, and a shift operator that selectively moves the atoms in one internal state along the lattice principal axis. Realizations of these elementary operations and their physical limitations are analyzed. The complexity of the compacting scheme is analyzed and we show that this scales linearly with the number of lattice sites per row of the lattice. Neutral atoms trapped in an optical lattice constitute an attractive system for implementation of scalable quantum computation f1-3g, simulation of many-body systems f4g, and implementation of topological quantum computing f5-9g. In standard optical lattices, small lattice constants present a serious obstacle to implementing quantum compu- tation, since it is difficult to address individual qubits with an external field. An optical lattice with a large lattice constant is in principle addressable, and can allow for the quantum state manipulation of individual atoms by an optical field. High addressability and controllability and low decoherence make addressable lattices promising candidates for large- scale quantum computer implementation. The present work focuses on preparation of the initializa- tion of an addressable optical lattice for the purposes of quantum computing. The objective is a perfectly filled, regu- lar optical lattice, with each site occupied by a single atom in its motional ground state and in a specific internal state. We consider one-dimensional s1Dd, orthorhombic two- dimensional s2Dd, and three-dimensional s3Dd lattices. After loading and laser-cooling atoms in the optical lattice, half the sites have a single atom and half are vacant. In order to use this system for scalable quantum computation, a perfect lat- tice with each site occupied by a single atom is required. We propose here an efficient, feasible scheme forcompacting the optical lattice, i.e., for removing vacant sites to the edge of the lattice, thus creating a smaller lattice, but one more suit- able for quantum computation. The scheme presented here can as well be used to make arbitrary patterns of neutral atoms in an addressable optical lattice. These include lattices with fractional occupation, a specific translational and rotational lattice symmetry, a bro- ken symmetry, and heteroatomic patterns. Another important property of the scheme is that it can be applied recursively to reach any desired accuracy of the pattern formation. After a large number of elementary operations, the lattice can be cooled and imaged again. The remaining defects can be eliminated by repeating the compacting scheme. This recur- sion increases the total pattern formation time by the total duration of additional cooling and imaging cycles, but does not result in any increase in the scaling of the pattern forma- tion, i.e., the algorithmic complexity of the scheme is un- changed. The possibility of preparing any homoatomic or heteroatomic pattern of neutral atoms to an arbitrarily high degree of perfection makes this scheme attractive for initial- ization of quantum simulations of condensed phase systems, in addition to initialization of quantum computation.

Analysis of Seven NEPTUN-III (Tight-Lattice) Bottom-Flooding Experiments with RELAP5/MOD3.3/BETA

Seven tight-lattice NEPTUN-III bottom-flooding experiments are analyzed by using the frozen version of RELAP5, RELAP5/MOD3.3/BETA. This work is part of the Paul Scherrer Institute (PSI) contribution to the High Performance Light Water Reactor (HPLWR) European Union project and aims at assessing the capabilities of the code to model the reflooding phenomena in a tight hexagonal lattice (which was one of the core geometries considered at the time for an HPLWR) following a hypothetical loss-of-coolant accident scenario. Even though the latest version of the code has as a default the new PSI reflood model developed by the author, which was tested and assessed against reflooding data obtained at standard light water reactor lattices, this work shows that for tight lattices, the code underpredicts the peak clad temperatures measured during a series of reflooding experiments performed at the NEPTUN-III tight-lattice heater rod bundle facility. The reasons for these differences are discussed, and the (possible) changes needed in the framework of RELAP5/MOD3.3 for improving the modeling of reflooding in tight lattices are investigated.

Benchmark Calculations for Standard and DUPIC CANDU Fuel Lattices Compared with the MCNP-4B Code

Cell-code benchmark calculations have been performed for the standard CANDU and DUPIC CANDU fuel lattices compared with the MCNP-4B code. To consider the full isotopic composition and the temperature effect, new MCNP libraries have been generated from ENDF/B-VI release 3 and validated for typical benchmark problems. The lattice codes WIMS-AECL and HELIOS were then benchmarked by the MCNP code for the major physics parameters such as burnup reactivity, coolant void reactivity, fuel temperature coefficient, etc. The calculations have shown that the physics parameters estimated by the lattice codes are consistent with those by MCNP. However, there is a tendency that the error increases slightly when the fuel burnup is high. This study has shown that the WIMS-AECL produces reliable results for CANDU fuel analysis. However, it is recommended that the cross-section library be updated to be used for the high-burnup fuels even though the current results are generally acceptable. This study has also shown that the HELIOS code has the potential to be used for CANDU fuel lattice analysis in the future.

Some properties of the symmetric enveloping algebra of a subfactor, with applications to amenability and property $T$

We undertake here a more detailed study of the structure and basic properties of the symmetric enveloping algebra M\boxtimes_{e_N} M^{\mathrm{op}} associated to a subfactor N\subset M , as introduced in [Po5]. We prove a number of results relating the amenability properties of the standard invariant of N\subset M,{\mathcal G}_{N,M} , its graph \Gamma_{N,M} and the inclusion M\vee M^{\mathrm{op}} \subset M\boxtimes_{e_N}M^{\mathrm{op}} , notably showing that M\boxtimes_{e_N}M^{\mathrm{op}} is amenable relative to its subalgebra M\vee M^{\mathrm{op}} iff \Gamma_{N,M} (or equivalently {\mathcal G}_{N,M}) is amenable, i.e., \|\Gamma_{N,M}\|^2=[M:N] . We then prove that the hyperfiniteness of M\boxtimes_{e_N}M^{\mathrm{op}} is equivalent to M being hyperfinite and \Gamma_{N,M} being amenable. We derive from this a hereditarity property for the amenability of graphs of subfactors showing that if an inclusion of factors Q\subset P is embedded into an inclusion of hyperfinite factors N\subset M with amenable graph, then its graph \Gamma_{Q,P} follows amenable as well. Finally, we use the symmetric enveloping algebra to introduce a notion of property T for inclusions N\subset M , by requiring M\boxtimes_{e_N}M^{\mathrm{op}} to have the property T relative to M\vee M^{\mathrm{op}} . We prove that this property doesn't in fact depend on the inclusion N\subset M but only on its standard invariant \mathcal G_{N,M} , thus defining a notion of property T for abstract standard lattices \mathcal G .

Thermal Lattice-Boltzmann Models (TLBM) for Compressible Flows

The progress and challenges in thermal lattice-Boltzmann modeling are discussed. In particular, momentum and energy closures schemes are contrasted. Higher order symmetric (but no longer space filling) velocity lattices are constructed for both 2D and 3D flows and shown to have superior stability properties to the standard (but lower) symmetry lattices. While this decouples the velocity lattice from the spatial grid, the interpolation required following free-streaming is just 1D. The connection between fixed lattice vectors and temperature-dependent lattice vectors (obtained in the Gauss–Hermite quadrature approach) is discussed. Some (compressible) Rayleigh–Benard simulations on the 2D octagonal lattice are presented for extended BGK collision operators that allow for arbitrary Prandtl numbers.

Atom cooling and trapping by disorder

We demonstrate the possibility of three-dimensional cooling of neutral atoms by illuminating them with two counterpropagating laser beams of mutually orthogonal linear polarization, where one of the lasers is a speckle field, i.e. a highly disordered but stationary coherent light field. This configuration gives rise to atom cooling in the transverse plane via a Sisyphus cooling mechanism similar to the one known in standard two-dimensional optical lattices formed by several plane laser waves. However, striking differences occur in the spatial diffusion coefficients as well as in local properties of the trapped atoms.

Hubbard model ond−dimensional hypercubes: Exact solution for the two-electron case

The Hubbard model is exactly solved for two particles on $d\ensuremath{-}$dimensional hypercubes. It is shown that the spectrum can be separated into two parts: a trivial ($U$-independent) part resulting from symmetries of hypercubes and a nontrivial part expressed as a single-impurity problem on a set of finite chains of size ${d}^{\ensuremath{'}}+1$ ${(d}^{\ensuremath{'}}<~d).$ The exact expression for the one-particle Green's function is given. Finally, we discuss the extension of these results to standard hypercubic lattices with periodic boundary conditions.

Study of transport properties on percolating clusters growth upon very hot dimer deposition

Transport properties are investigated by means of Monte Carlo simulations on percolating clusters obtained depositing very hot dimers in two dimensions. The properties are discussed within the framework of the random walks arguments. The diffusion exponent d w and the spectral dimension d s exhibit finite size effects and their asymptotic values in the thermodynamic limit differ from both the corresponding to standard percolation and Euclidean lattices.

On the electrostatics of cubic crystals

The electrostatic potential in an ionic crystal is presented in terms of the zeroth-order MacDonald function by means of decomposition of the crystal lattice into sets of parallel lines with the periodic charge distribution with the zero net charge within a period. The method is applied to the calculation of the Madelung constants of a series of standard cubic lattices, doped fullerides and idealized Y-Ba-Cu-O crystals.

The space groups of axial crystals and quasicrystals

We compute all the three-dimensional quasicrystallographic space groups with n-fold axial point groups and standard lattices by a method that treats crystals and quasicrystals on an equal footing. We do not rely on projecting higher-dimensional crystallographic space groups, our results are valid for arbitrary n, and our analysis is elementary. We regard space groups as a scheme for classifying diffraction patterns to be carried out in three-dimensional reciprocal space. The familiar three-dimensional crystallographic space groups with axial point groups emerge simply and directly as special cases of the general n-fold three-dimensional quasicrystallophic treatment with n=3, 4, and 6

A probabilistic approach to the site-percolation problem: II. Standard lattices

A simple method, based on the use of conditional probabilites, to derive the particle cluster distribution is presented for the site-percolation problem on standard lattices. Two approximations to the behaviour of the obtained probability distribution in the thermodynamic limit are considered. The first one corresponds to the case of finite clusters, while the second one allows us to deal with the case of the existence of clusters spanning the lattice, and thus to investigate the onset of the percolating cluster. The extrema (maxima) of the corresponding distribution are analytically and numerically analyzed.

The critical index of the magnetic susceptibility of 3D Ising models

Series expansions for certain thermodynamic variables have been computed for various standard model lattices. The high-temperature series for the magnetic susceptibility of the Ising model of three-dimensional SC, BCC and FCC lattices allows estimates of the critical index gamma of each series to be made. Dramatic progress in this direction was made by the Pade Dlog method, and here a similar technique is introduced. Estimates of gamma from row sequences of generalised inverse vector-valued Pade approximants are made. The results point to the conclusion that gamma =1.2406+or-0.0017 is the critical index common to all three lattices.

Phase diagrams of the q-state potts model on Bethe lattices

We use a rigorous, recently developed, method of solution of spin models on Bethe lattices (Cayley trees). It allows us to detect all the phases of the ferromagnetic and antiferromagnetic q-state Potts models in a field (FPM and APM respectively). The phase diagrams of the FPM are characterized by three critical lines of first-order transitions. In the APM the ordered phases (which appear always for h > 0, and under certain conditions for h= 0 and/or h<0) are separated from the disordered one by phase boundaries characterized by second-order transitions, and are separated one from the other by critical lines characterized by first-order and second-order transitions. Several results are found, which hold true on standard lattices, too.

Series study of random percolation in three dimensions

New high-density series data for the mean number, percolation probability and 'susceptibility' of finite clusters are presented for bond and site percolation on four standard three-dimensional lattices. A Pade approximant analysis of both high- and low-density series makes particular use of the rather precise unbiased estimates of the percolation threshold, pc, obtained recently by Heermann and Stauffer (1981) for the simple cubic lattice. For this lattice the authors obtain the biased estimate gamma =1.73+or-0.03 for the site problem and a similar estimate but with larger uncertainties for the bond problem. Such a value is significantly larger than earlier series estimates. Assuming gamma to be universal they obtain precise, although biased, estimates of pc for both bond and site percolation on all four lattices. Using the bond estimates of pc they find an overall biased estimate of beta =0.454+or-0.008 for bond percolation on all three-dimensional lattices. (The corresponding site problem requires further study.) Scaling estimates of other critical exponents are alpha =-0.64+or-0.05, delta =4.81+or-0.14, Delta =2.18+or-0.04, nu =0.88+or-0.02 and nu =0.03+or-0.03.