Effective low-dimensional Hamiltonian for strongly interacting atoms in a transverse trap

We derive an effective low-dimensional Hamiltonian for strongly interacting ultracold atoms in a transverse trapping potential near a wide Feshbach resonance. The Hamiltonian includes crucial information about transverse excitations in an effective model with renormalized interaction between atoms and composite dressed molecules. We fix all the parameters in the Hamiltonian for both one- and two-dimensional cases.Comment: v2: 5 pages, 1 figure; expanded presentation of the formalis

Anharmonicity Induced Resonances for Ultracold Atoms and their Detection

When two atoms interact in the presence of an anharmonic potential, such as an optical lattice, the center of mass motion cannot be separated from the relative motion. In addition to generating a confinement-induced resonance (or shifting the position of an existing Feshbach resonance), the external potential changes the resonance picture qualitatively by introducing new resonances where molecular excited center of mass states cross the scattering threshold. We demonstrate the existence of these resonances, give their quantitative characterization in an optical superlattice, and propose an experimental scheme to detect them through controlled sweeping of the magnetic field.Comment: 6 pages, 5 figures; expanded presentatio

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

Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap

We present a solution of the three-fermion problem in a harmonic potential across a Feshbach resonance. We compare the spectrum with that of the two-body problem and show that it is energetically unfavorable for the three fermions to occupy one lattice site rather than two. We also demonstrate the existence of an energy level crossing in the ground state with a symmetry change of its wave function, suggesting the possibility of a phase transition for the corresponding many-body case.Comment: 5 pages, 6 figures, typos corrected, references adde

A general T-matrix approach applied to two-body and three-body problems in cold atomic gases

We propose a systematic T-matrix approach to solve few-body problems with s-wave contact interactions in ultracold atomic gases. The problem is generally reduced to a matrix equation expanded by a set of orthogonal molecular states, describing external center-of-mass motions of pairs of interacting particles; while each matrix element is guaranteed to be finite by a proper renormalization for internal relative motions. This approach is able to incorporate various scattering problems and the calculations of related physical quantities in a single framework, and also provides a physically transparent way to understand the mechanism of resonance scattering. For applications, we study two-body effective scattering in 2D-3D mixed dimensions, where the resonance position and width are determined with high precision from only a few number of matrix elements. We also study three fermions in a (rotating) harmonic trap, where exotic scattering properties in terms of mass ratios and angular momenta are uniquely identified in the framework of T-matrix.Comment: 14 pages, 4 figure

Cavitation of Electrons Bubbles in Liquid Helium Below saturation Pressure

We have used a Hartree-type electron-helium potential together with a density functional description of liquid $^4$He and $^3$He to study the explosion of electron bubbles submitted to a negative pressure. The critical pressure at which bubbles explode has been determined as a function of temperature. It has been found that this critical pressure is very close to the pressure at which liquid helium becomes globally unstable in the presence of electrons. It is shown that at high temperatures the capillary model overestimates the critical pressures. We have checked that a commonly used and rather simple electron-helium interaction yields results very similar to those obtained using the more accurate Hartree-type interaction. We have estimated that the crossover temperature for thermal to quantum nucleation of electron bubbles is very low, of the order of 6 mK for $^4$He.Comment: 22 pages, 9 figure

Coastal oceanography and sedimentology in New Zealand, 1967-91.

This paper reviews research that has taken place on physical oceanography and sedimentology on New Zealand's estuaries and the inner shelf since c. 1967. It includes estuarine sedimentation, tidal inlets, beach morphodynamics, nearshore and inner shelf sedimentation, tides and coastal currents, numerical modelling, short-period waves, tsunamis, and storm surges. An extensive reference list covering both published and unpublished material is included. Formal teaching and research programmes dealing with coastal landforms and the processes that shape them were only introduced to New Zealand universities in 1964; the history of the New Zealand Journal of Marine and Freshwater Research parallels and chronicles the development of physical coastal science in New Zealand, most of which has been accomplished in last 25 years