Stirring trapped atoms into fractional quantum Hall puddles

We theoretically explore the generation of few-body analogs of fractional quantum Hall states. We consider an array of identical few-atom clusters (n=2,3,4), each cluster trapped at the node of an optical lattice. By temporally varying the amplitude and phase of the trapping lasers, one can introduce a rotating deformation at each site. We analyze protocols for coherently transferring ground state clusters into highly correlated states, producing theoretical fidelities in excess of 99%.Comment: 4 pages, 3 figures (13 subfigures) -- v2: published versio

Explanation of 100-fold reduction of spectral shifts for hydrogen on helium films

We show that helium film-mediated hydrogen-hydrogen interactions account for a two orders of magnitude discrepancy between previous theory and recent experiments on cold collision shifts in spin-polarized hydrogen adsorbed on a helium film. These attractive interactions also explain the anomalous dependence of the cold collision frequency shifts on the $^3$He covering of the film. Our findings suggest that the gas will become mechanically unstable before reaching the Kosterlitz-Thouless transition unless the experiment is performed in a drastically different regime, for example with a much different helium film geometry.Comment: 4+ pages, 1 figure (3 subfigures), revtex

Many-body physics in the radio frequency spectrum of lattice bosons

We calculate the radio-frequency spectrum of a trapped cloud of cold bosonic atoms in an optical lattice. Using random phase and local density approximations we produce both trap averaged and spatially resolved spectra, identifying simple features in the spectra that reveal information about both superfluidity and correlations. Our approach is exact in the deep Mott limit and in the deep superfluid when the hopping rates for the two internal spin states are equal. It contains final state interactions, obeys the Ward identities (and the associated conservation laws), and satisfies the $f$-sum rule. Motivated by earlier work by Sun, Lannert, and Vishveshwara [Phys. Rev. A \textbf{79}, 043422 (2009)], we also discuss the features which arise in a spin-dependent optical lattice.Comment: 6 pages, 4 figures, 13 subfigure

Local versus global equilibration near the bosonic Mott-superfluid transition

We study the response of trapped two dimensional cold bosons to time dependent lattices. We find that in lattice ramps from 11 (superfluid, $\hbar/U_{\text{i}} = 3$ms, $\hbar/J_{\text{i}} = 45$ms) to 16 recoils (Mott, $\hbar/U_{\text{f}} = 2$ms, $\hbar/J_{\text{f}} = 130$ms) the local number fluctuations remains at their equilibrium values if ramps are slower than 3 ms. Global transport, however, is much slower (1s), especially in the presence of Mott shells. This separation of timescales has practical implications for cold atom experiments and cooling protocols.Comment: 4 pages, 4 figs. 6 subfigure

High temperature thermodynamics of fermionic alkaline earth atoms in optical lattices

We calculate experimentally relevant properties of trapped fermionic alkaline earth atoms in an optical lattice, modeled by the SU(N) Hubbard model. Our calculation is accurate when the temperature is much larger than the tunneling rate, similar to current regimes in ultracold atom experiments. In addition to exploring the Mott insulator-metal crossover, we calculate final temperatures achieved by the standard experimental protocol of adiabatically ramping from a non-interacting gas, as a function of initial gas temperature and final state lattice parameters. Of particular experimental interest, we find that increasing $N$ gives substantially \textit{colder} Mott insulators, up to more than a factor of five for relevant parameters. This cooling happens for all $N$, fixing the initial entropy, or for all N \lsim 20 (the exact value depends on dimensionality), fixing the initial temperature.Comment: 4+ pages main text, 2 figures. 3 pages supplementary information, 2 figures. v2: added citatio

On-site correlations in optical lattices: band mixing to coupled quantum Hall puddles

We extend the standard Bose-Hubbard model to capture arbitrarily strong on-site correlations. In addition to being important for quantitatively modeling experiments, for example, with Rubidium atoms, these correlations must be included to describe more exotic situations. Two such examples are when the interactions are made large via a Feshbach resonance, or when each site rotates rapidly, making a coupled array of quantum Hall puddles. Remarkably, even the mean field approximation to our model includes all on-site correlations. We describe how these on-site correlations manifest themselves in the system's global properties: modifying the phase diagram and depleting the condensate.Comment: 4 pages, 4 figure

Development of Simplified Models of Water Quality in Lignite Mining Areas

The development of complex decision support model systems for the analysis of regional water policies for regions with intense socio-economic development effecting and being affected by the water resources system is of increasing importance. One of the most illustrative examples are regions with open-pit lignite mining. Such model systems have to be based on appropriate submodels e.g. for water quality processes. The paper describes submodel for groundwater and surface water quality with special regard to open-pit lignite mining regions. We consider the discharge of acid ferruginous water into rivers as having the most important impact on water quality in open-pit lignite mining areas. One goal of the model system is the choice of the necessary degree of purification for mine water treatment plants, taking into account self-purification in rivers and remaining pits as well as the water quality demand of down-stream water users. Based on comprehensive water quality models, the development of which is described in the paper, the possibilities for the derivation of reduced models are described. Those model have been elaborated for groundwater, as the source of pollution, mine water treatment plants as control units, river sections with an intake of acid ferruginous water, and remaining pits, which can also serve as effective control units. Related with each other, these models form the complex system model, a system of differential equations. They were numerically solved. The computer program is included in the paper