Feshbach Molecules in a One-dimensional Optical Lattice

We present the theory of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. Using a two-channel description of the resonance, we derive analytic results for the scattering states inside the continuum band and the discrete bound states outside the band. We identify a Fano resonance profile, and the survival probability of a molecule when swept through the Bloch band of scattering states by varying an applied magnetic field. We discuss how these results may be used to investigate the importance of the structured nature of the continuum in experiments.Comment: 4 pages, 3 figure

Two-channel Feshbach physics in a structured continuum

We analyze the scattering and bound state physics of a pair of atoms in a one-dimensional optical lattice interacting via a narrow Feshbach resonance. The lattice provides a structured continuum allowing for the existence of bound dimer states both below and above the continuum bands, with pairs above the continuum stabilized by either repulsive interactions or their center of mass motion. Inside the band the Feshbach coupling to a closed channel bound state leads to a Fano resonance profile for the transmission, which may be mapped out by RF- or photodissociative spectroscopy. We generalize the scattering length concept to the one-dimensional lattice, where a scattering length may be defined at both the lower and the upper continuum thresholds. As a function of the applied magnetic field the scattering length at either band edge exhibits the usual Feshbach divergence when a bound state enters or exits the continuum. Near the scattering length divergences the binding energy and wavefunction of the weakly bound dimer state acquires a universal form reminiscent of those of free-space Feshbach molecules. We give numerical examples of our analytic results for a specific Feshbach resonance, which has been studied experimentally.Comment: 18 pages, 9 embedded figure

Scattering and binding of different atomic species in a one-dimensional optical lattice

The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average discrete coordinates applies and makes the problem analytically tractable, and we present a number of new results and features compared to the case of identical atoms.Comment: 5 pages, 4 figure

Theory of Feshbach molecule formation in a dilute gas during a magnetic field ramp

Starting with coupled atom-molecule Boltzmann equations, we develop a simplified model to understand molecule formation observed in recent experiments. Our theory predicts several key features: (1) the effective adiabatic rate constant is proportional to density; (2) in an adiabatic ramp, the dependence of molecular fraction on magnetic field resembles an error function whose width and centroid are related to the temperature; (3) the molecular production efficiency is a universal function of the initial phase space density, the specific form of which we derive for a classical gas. Our predictions show qualitative agreement with the data from [Hodby et al, Phys. Rev. Lett. {\bf{94}}, 120402 (2005)] without the use of adjustable parameters

Statistical mechanics of a Feshbach coupled Bose-Fermi gas in an optical lattice

We consider an atomic Fermi gas confined in a uniform optical lattice potential, where the atoms can pair into molecules via a magnetic field controlled narrow Feshbach resonance. The phase diagram of the resulting atom-molecule mixture in chemical and thermal equilibrium is determined numerically in the absence of interactions under the constraint of particle conservation. In the limiting cases of vanishing or large lattice depth we derive simple analytical results for important thermodynamic quantities. One such quantity is the dissociation energy, defined as the detuning of the molecular energy spectrum with respect to the atomic one for which half of the atoms have been converted into dimers. Importantly we find that the dissociation energy has a non-monotonic dependence on lattice depth.Comment: 9 pages, 5 figure

A Giant Sand Injection Complex: The Upper Jurassic Hareelv Formation of East Greenland

A major intrusive sandstone complex of Late Jurassic age is spectacularly exposed in Jameson land, East Greenland. It is probably the largest in the World, and covers an area of 55x70 km with a thickness of 200–400 m, and forms the Upper Oxfordian–Volgian Hareelv Formation. The complex consists of black basinal mudstones and highly irregular sandstone bodies, dykes and sills. The sand was derived from collapse of the front of sandy shelf-margin wedges, which triggered hyperconcentrated to concentrated density flows, and deposited massive sands further down the slope, at the base-of-slope and in the basin. The sand of some flows was loaded into the slope muds while elsewhere it flowed in steep-sided gullies formed by retrogressive slumping of the slope muds. All sand bodies were liquefied subsequent to burial and the sand was intruded into the surrounding black compacted muds and mudstones. Intrusion took place repeatedly over a long time interval, in environments ranging from very shallow to relatively deep burial, and the primary sediment structures of the sands were generally lost during these processes. It is rarely possible to determine the degree of post-burial remobilization but it ranges from rather small-scale modifications to wholesale liquefaction and out-of-place intrusion of the sand over many tens of metres. Sandstone dykes and sills occur ubiquitously and were emplaced by all combinations of stoping and dilation. The intrusive sand bodies range in dimensions from centimetres to many hundreds of metres. Deposition took place during the most important Mesozoic rift event in East Greenland and the pervasive remobilization and liquefaction of all sand bodies in the Hareelv Formation is interpreted as having been caused mainly by cyclic earthquake shocks. Additional important factors were slope shear stress, build up of pore pressure due to loading, slumping, upwards movement of pore waters expelled from the compacting muds, and also possibly of biogenic and thermogenic gas. The Hareelv Formation is an excellent field analogue for deeply buried hydrocarbon reservoirs, which have been modified by remobilization and injection of the sands

Angular momentum exchange between coherent light and matter fields

Full, three dimensional, time-dependent simulations are presented demonstrating the quantized transfer of angular momentum to a Bose-Einstein condensate from a laser carrying orbital angular momentum in a Laguerre-Gaussian mode. The process is described in terms of coherent Bragg scattering of atoms from a chiral optical lattice. The transfer efficiency and the angular momentum content of the output coupled vortex state are analyzed and compared with a recent experiment.Comment: 4 pages, 4 figure