Ultracold atoms in optical lattices

Bosonic atoms trapped in an optical lattice at very low temperatures, can be modeled by the Bose-Hubbard model. In this paper, we propose a slave-boson approach for dealing with the Bose-Hubbard model, which enables us to analytically describe the physics of this model at nonzero temperatures. With our approach the phase diagram for this model at nonzero temperatures can be quantified.Comment: 29 pages, 10 figure

Aggregation of ecological indicators for mapping aquatic nature quality : overview of existing methods and case studies

Indicators for aquatic nature quality are calculated using ecological monitoring data from individual sampling stations. For reporting purposes, these results need to be aggregated and scaled up to higher levels (catchment area, country). This report provides an overview of different existing spatial aggregation methods for this purpose, including an evaluation of their suitability for aquatic ecological indicators. So-called „model-based„ methods, consisting of some sort of „kriging¿ step followed by calculation of the arithmetic mean, appeared to be the most appropriate. Application of these methods to multimetric indicators of aquatic macroinvertebrates in two Dutch subcatchment areas confirmed their suitability. However, the methods that were used were based on aggregation (using kriging) over Euclidian (straight), distances. It is recommended to conduct further research on the suitability of interpolation through stream networks, i.e., through the waterways themselves

Quantum phases in a resonantly-interacting Bose-Fermi mixture

We consider a resonantly-interacting Bose-Fermi mixture of $^{40}$K and $^{87}$Rb atoms in an optical lattice. We show that by using a red-detuned optical lattice the mixture can be accurately described by a generalized Hubbard model for $^{40}$K and $^{87}$Rb atoms, and $^{40}$K-$^{87}$Rb molecules. The microscopic parameters of this model are fully determined by the details of the optical lattice and the interspecies Feshbach resonance in the absence of the lattice. We predict a quantum phase transition to occur in this system already at low atomic filling fraction, and present the phase diagram as a function of the temperature and the applied magnetic field.Comment: 4 pages, 3 figure

Modelling and experiments of self-reflectivity under femtosecond ablation conditions

We present a numerical model which describes the propagation of a single femtosecond laser pulse in a medium of which the optical properties dynamically change within the duration of the pulse. We use a Finite Difference Time Domain (FDTD) method to solve the Maxwell's equations coupled to equations describing the changes in the material properties. We use the model to simulate the self-reflectivity of strongly focused femtosecond laser pulses on silicon and gold under laser ablation condition. We compare the simulations to experimental results and find excellent agreement.Comment: 11 pages, 8 figure

Mean-field theory for Bose-Hubbard Model under a magnetic field

We consider the superfluid-insulator transition for cold bosons under an effective magnetic field. We investigate how the applied magnetic field affects the Mott transition within mean field theory and find that the critical hopping strength $(t/U)_c$, increases with the applied field. The increase in the critical hopping follows the bandwidth of the Hofstadter butterfly at the given value of the magnetic field. We also calculate the magnetization and superfluid density within mean field theory.Comment: 11 pages, 7 figures, published versio

Mott insulators in an optical lattice with high filling factors

We discuss the superfluid to Mott insulator transition of an atomic Bose gas in an optical lattice with high filling factors. We show that also in this multi-band situation, the long-wavelength physics is described by a single-band Bose-Hubbard model. We determine the many-body renormalization of the tunneling and interaction parameters in the effective Bose-Hubbard Hamiltonian, and consider the resulting model at nonzero temperatures. We show that in particular for a one or two-dimensional optical lattice, the Mott insulator phase is more difficult to realize than anticipated previously.Comment: 5 pages, 3 figures, title changed, major restructuring, resubmitted to PR