Feshbach Resonance in Optical Lattices and the Quantum Ising Model

TL;DR

This paper explores the phase diagram and quantum phase transitions of two-species bosons in optical lattices, revealing a connection to the quantum Ising model and providing insights into Feshbach resonances.

Contribution

It demonstrates the emergence of a quantum Ising transition within the Mott phase of two-species bosons, supported by exact diagonalization and Landau theory.

Findings

Identification of superfluid and Mott phases in the phase diagram

Quantum Ising transition within the second Mott lobe

Confirmation of the transition in homonuclear cases

Abstract

Motivated by experiments on heteronuclear Feshbach resonances in Bose mixtures, we investigate s-wave pairing of two species of bosons in an optical lattice. The zero temperature phase diagram supports a rich array of superfluid and Mott phases and a network of quantum critical points. This topology reveals an underlying structure that is succinctly captured by a two-component Landau theory. Within the second Mott lobe we establish a quantum phase transition described by the paradigmatic longitudinal and transverse field Ising model. This is confirmed by exact diagonalization of the 1D bosonic Hamiltonian. We also find this transition in the homonuclear case.