Scattering Models for Ultracold Atoms

Abstract

We present a review of scattering models that can be used to describe the low-energy behavior of identical bosonic atoms. In the simplest models, the only degrees of freedom are atoms in the same spin state. More elaborate models have other degrees of freedom, such as atoms in other spin states or diatomic molecules. The parameters of the scattering models are specified by giving the S-wave phase shifts for scattering of atoms in the spin state of primary interest. The models are formulated as local quantum field theories and the renormalization of their coupling constants is determined. Some of the parameters can be constrained by renormalizability or by the absence of negative-norm states. The Green's functions that describe the evolution of two-atom states are determined analytically. They are used to determine the T-matrix elements for atom-atom scattering and the binding energies of diatomic molecules. The scattering models all exhibit universal behavior as the scattering length in a specific spin state becomes large.

60 pages, 6 figures, minor corrections

References in corpus (21)

• Universality in Few-body Systems with Large Scattering Length
• Production of cold molecules via magnetically tunable Feshbach resonances
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• Renormalization of the Three-Body System with Short-Range Interactions
• Effective Field Theory for Short-Range Forces
• The Three-Boson System with Short-Range Interactions
• More Effective Field Theory for Nonrelativistic Scattering
• Universal Properties of the Four-Body System with Large Scattering Length
• The Four-Boson System with Short-Range Interactions
• Resonance Superfluidity: Renormalization of Resonance Scattering Theory
• A renormalisation-group treatment of two-body scattering
• Non-perturbative regularization and renormalization: simple examples from non-relativistic quantum mechanics
• An effective field theory for coupled-channel scattering
• The Delta-Delta Intermediate State in 1S0 Nucleon-Nucleon Scattering From Effective Field Theory
• Wilsonian RG and Redundant Operators in Nonrelativistic Effective Field Theory
• Anomalous dimensions determine the power counting -- Wilsonian RG analysis of nuclear EFT --
• Simple Theoretical Models for Resonant Cold Atom Interactions
• Renormalization of $NN$ scattering: contact potential
• Generalised Point Interactions for the Radial Schrodinger Equation via Unitary Dilations
• More about the Wilsonian analysis on the pionless NEFT

Cited by in corpus (59)

• BCS-BEC crossover induced by a synthetic non-Abelian gauge field
• Structure and compositeness of hadron resonances
• Heavy Hadrons in Nuclear Matter
• Exact Relations for a Strongly-interacting Fermi Gas near a Feshbach Resonance
• Structure of Near-Threshold s-Wave Resonances
• Structure of near-threshold quasi-bound states
• Direct detection of dark matter in universal bound states
• Directional detection of dark matter in universal bound states
• Current response, structure factor and hydrodynamic quantities of a two- and three-dimensional Fermi gas from the operator-product expansion
• Using Line Shapes to Discriminate between Binding Mechanisms for the X(3872)
• Renormalization in the Three-body Problem with Resonant P-wave Interactions
• The three-boson system at next-to-leading order in an effective field theory for systems with a large scattering length
• Impossibility of the Efimov effect for p-wave interactions
• Generalized weak-binding relations of compositeness in effective field theory
• The double thresholds distort the lineshapes of the $P_{\psi s}^{\Lambda }(4338{)}^0$ resonance
• Bose-Fermi dualities for arbitrary one-dimensional quantum systems in the universal low energy regime
• Universal Two-body Physics in Dark Matter near an S-wave Resonance
• Rashbons: Properties and their significance
• Construction of a local barK N-pi Sigma-pi Lambda potential and composition of the Lambda(1405)
• Naturalness in Nuclear Effective Field Theories
• Universal duality transformations in interacting one-dimensional quantum systems
• Zero-Range Effective Field Theory for Resonant Wino Dark Matter II. Coulomb Resummation
• Three-body repulsive forces among identical bosons in one dimension
• Zero-Range Effective Field Theory for Resonant Wino Dark Matter I. Framework
• Mobile impurity in a Fermi sea from the functional renormalization group analytically continued to real time
• Narrow resonances and short-range interactions
• Weinberg's Compositeness
• Quark mass dependence of H-dibaryon in $\Lambda \Lambda$ scattering
• Effective theory and universal relations for Fermi gases near a $d$-wave interaction resonance
• Compositeness of $T_{cc}$ and $X(3872)$ by considering decay and coupled-channels effects
• Effective field theory of interactions on the lattice
• Stability of low-dimensional multicomponent Bose gases
• Effective field theory and the scattering process for magnons in the ferromagnet, antiferromagnet, and ferrimagnet
• Few-body states of bosons interacting with a heavy quantum impurity
• Nonrelativistic Effective Field Theory with a Resonance Field
• Universal physics of three bosons with isospin
• The Operator Product Expansion Beyond Leading Order for Two-Component Fermions
• High-momentum tail and universal relations of a Fermi gas near a Raman-dressed Feshbach resonance
• Examining coupled-channel effects in radiative charmonium transitions
• Mobile magnetic impurities in a Fermi superfluid: a route to designer molecules
• Compositeness of hadrons, nuclei, and atomic systems
• Quantum field theory for multipolar composite bosons with mass defect and relativistic corrections
• Universal relations and normal-state properties of a Fermi gas with laser-dressed mixed-partial-wave interactions
• Effective range expansion with a long-range force
• Spectrum of a family of spin-orbit coupled Hamiltonians with singular perturbation
• Modeling atom-atom interactions at low energy by Jost-Kohn potentials
• Floquet-Engineering of Feshbach Resonances in Ultracold Gases
• Feshbach Resonance in a Synthetic Non-Abelian Gauge Field
• Quark mass dependence of H-dibaryon
• Corrections to reaction-diffusion dynamics above the upper critical dimension
• Efimov Trimers near the Zero-crossing of a Feshbach Resonance
• Structure of exotic hadrons by a weak-binding relation with finite-range correction
• Role of the effective range in the weak-binding relation
• Compositeness of Hadrons and Near-Threshold Dynamics
• Fluctuation-induced first-order superfluid transition in unitary $\mathrm{SU}(N)$ Fermi gases
• Low-energy atomic scattering: s-wave relation between the interaction potential and the phase shift
• Model-independent determination of the compositeness of near-threshold quasibound states
• Resonant Floquet Scattering of Ultracold Atoms
• Compositeness of Near Threshold Quasi-Bound States