Localized modes in arrays of boson-fermion mixtures

TL;DR

This paper investigates localized modes in a one-dimensional boson-fermion mixture within an optical lattice, revealing unique properties such as bounds on atom numbers and the absence of certain solitons, with stability analysis included.

Contribution

It introduces a mean-field model reducing to a nonlinear Schrödinger equation with periodic potential and nonlinearity, analyzing localized modes and their stability in boson-fermion mixtures.

Findings

Existence of a lower atom number bound for localized modes.

Certain small amplitude gap solitons are absent near gap edges.

The lowest symmetric mode branch may be restricted or absent, unlike in pure bosonic systems.

Abstract

It is shown that the mean-field description of a boson-fermion mixture with a dominating fermionic component, loaded in a one-dimensional optical lattice, is reduced to the nonlinear Schr\"{o}dinger equation with a periodic potential and periodic nonlinearity. In such system there exist localized modes having peculiar properties. In particular, for some regions of parameters there exists a lower bound for a number of atoms necessary for creation of a mode, while for other domains small amplitude gap solitons are not available in vicinity of either of the gap edges. We found that the lowest branch of the symmetric solution may either exist only for a restricted range of energies in a gap or does not exist, unlike in pure bosonic condensates. The simplest bifurcations of the modes are shown and stability of the modes is verified numerically.