Quantum phases of atomic boson-fermion mixtures in optical lattices

TL;DR

This paper investigates the zero-temperature phase diagram of a one-dimensional boson-fermion mixture in an optical lattice, identifying various quantum phases through numerical solutions of the Bose-Fermi-Hubbard model.

Contribution

It provides a detailed numerical analysis of the phase diagram, revealing new insulating phases and characterizing their properties in a boson-fermion mixture.

Findings

Identification of multiple quantum phases including Mott-insulator and double-insulator phases.

Discovery of a phase with crystalline diagonal long-range order.

Observation of spatial separation of species in one insulating phase.

Abstract

The zero-temperature phase diagram of a binary mixture of bosonic and fermionic atoms in an one-dimensional optical lattice is studied in the framework of the Bose-Fermi-Hubbard model. By exact numerical solution of the associated eigenvalue problems, ground state observables and the response to an external phase twist are evaluated. The stiffnesses under phase variations provide measures for the boson superfluid fraction and the fermionic Drude weight. Several distinct quantum phases are identified as function of the strength of the repulsive boson-boson and the boson-fermion interaction. Besides the bosonic Mott-insulator phase, two other insulating phases are found, where both the bosonic superfluid fraction and the fermionic Drude weight vanish simultaneously. One of these double-insulator phases exhibits a crystalline diagonal long-range order, while the other is characterized by spatial separation of the two species.