Pfaffian-like ground states for bosonic atoms and molecules in one-dimensional optical lattices

TL;DR

This paper investigates the ground states of bosonic atoms and molecules in one-dimensional optical lattices, demonstrating the emergence of Pfaffian-like states near the superfluid-Mott insulator transition and their potential for topological quantum computing.

Contribution

It provides the first evidence that Pfaffian-like states can be realized in realistic 1D systems and explores their non-Abelian anyonic excitations.

Findings

Ground state corresponds to Pfaffian-like state near phase transition

Supports non-Abelian anyonic excitations

Clarifies creation of exotic states in 1D systems

Abstract

We study ground states and elementary excitations of a system of bosonic atoms and diatomic Feshbach molecules trapped in a one-dimensional optical lattice using exact diagonalization and variational Monte Carlo methods. We primarily study the case of an average filling of one boson per site. In agreement with bosonization theory, we show that the ground state of the system in the thermodynamic limit corresponds to the Pfaffian-like state when the system is tuned towards the superfluid-to-Mott insulator quantum phase transition. Our study clarifies the possibility of the creation of exotic Pfaffian-like states in realistic one-dimensional systems. We also present preliminary evidence that such states support non-Abelian anyonic excitations that have potential application for fault-tolerant topological quantum computation.