Effective single-band models for strongly interacting fermions in an optical lattice

To test effective Hamiltonians for strongly interacting fermions in an optical lattice, we numerically find the energy spectrum for two fermions interacting across a Feshbach resonance in a double well potential. From the spectrum, we determine the range of detunings for which the system can be described by an effective lattice model, and how the model parameters are related to the experimental parameters. We find that for a range of strong interactions the system is well described by an effective $t-J$ model, and the effective superexchange term, $J$, can be smoothly tuned through zero on either side of unitarity. Right at and around unitarity, an effective one-band general Hubbard model is appropriate, with a finite and small on-site energy, due to a lattice-induced anharmonic coupling between atoms at the scattering threshold and a weakly bound Feshbach molecule in an excited center of mass state.Comment: 7 pages, 7 figures; minor typos correcte

Characterization by NMR of Reactants and Products of Hydrofluoroether Isomers, CF3(CF2)3OCH3 and (CF3)2C(F)CF2OCH3, Reacting with Isopropyl Alcohol

The 3M Company product Novec™ 71IPA DL, a mixture of methoxyperfluorobutane, methoxyperfluoroisobutane and 4.5 wt.% isopropyl alcohol, has been found to be very stable at ambient temperature, producing fluoride at the rate of ~1 ppm/year. Our earlier kinetic and theoretical studies have identified the reaction mechanism. This paper identifies the 1H and 19F NMR chemical shifts, multiplicities, and coupling constants of reactants and the major products that result from aging the mixture in sealed Pyrex NMR tubes for periods up to 1.8 years at temperatures from 26 °C to 102 °C. Chemical shifts and coupling constants of fluorine and hydrogen atoms on the hydrofluoroethers and isopropyl alcohol are traced through the reactions to their values in the products – esters, isopropylmethyl ether, and HF. These spectral positions, multiplicities, and coupling constants are presented in table format and as figures to clarify the transformations observed as the samples age

Bound Chains of Tilted Dipoles in Layered Systems

Ultracold polar molecules in multilayered systems have been experimentally realized very recently. While experiments study these systems almost exclusively through their chemical reactivity, the outlook for creating and manipulating exotic few- and many-body physics in dipolar systems is fascinating. Here we concentrate on few-body states in a multilayered setup. We exploit the geometry of the interlayer potential to calculate the two- and three-body chains with one molecule in each layer. The focus is on dipoles that are aligned at some angle with respect to the layer planes by means of an external eletric field. The binding energy and the spatial structure of the bound states are studied in several different ways using analytical approaches. The results are compared to stochastic variational calculations and very good agreement is found. We conclude that approximations based on harmonic oscillator potentials are accurate even for tilted dipoles when the geometry of the potential landscape is taken into account.Comment: 10 pages, 6 figures. Submitted to Few-body Systems special issue on Critical Stability, revised versio