Phases of Bosons or Fermions in confined optical lattices

TL;DR

This paper investigates the phase transitions of bosonic and fermionic atoms in confined optical lattices, calculating critical parameters for Mott insulator states and exploring observable phases like d-wave superconductivity through collective mode analysis.

Contribution

It provides a comprehensive analysis of phase diagrams and critical parameters for bosons and fermions in optical lattices using the Thomas-Fermi approximation, including novel phase discussions.

Findings

Critical radii and particle numbers for Mott insulator onset

Phase diagrams for 1D, 2D, and 3D lattices

Methods to observe phases like d-wave superconductivity

Abstract

Phases of Bose or Fermi atoms in optical lattices confined in harmonic traps are studied within the Thomas-Fermi approximation. Critical radii and particle number for onset of Mott insulator states are calculated and phase diagrams shown in 1D, and estimated for 2 and 3D. Methods to observe these and novel phases such as d-wave superconductivity is discussed. Specifically the collective modes are calculated.