Phase diagrams and multistep condensations of spin-1 bosonic gases in optical lattices

TL;DR

This paper systematically explores the phase diagrams and multistep condensation phenomena of spin-1 bosonic gases in optical lattices under magnetic fields using bosonic dynamical mean-field theory, revealing complex magnetic orders and temperature-dependent behaviors.

Contribution

It provides the first comprehensive phase diagrams for both antiferromagnetic and ferromagnetic interactions, highlighting novel multistep condensation effects in strongly correlated spin-1 bosons.

Findings

Identification of competing magnetic orders including nematic, spin-singlet, and ferromagnetic phases.

Observation of a ferromagnetic-to-nematic-insulating phase transition at small quadratic Zeeman energy.

Discovery of abnormal multistep condensation where critical temperatures vary non-monotonically with magnetization.

Abstract

Motivated by recent experimental processes, we systemically investigate strongly correlated spin-1 ultracold bosons trapped in a three-dimensional optical lattice in the presence of an external magnetic field. Based on a recently developed bosonic dynamical mean-field theory (BDMFT), we map out complete phase diagrams of the system for both antiferromagnetic and ferromagnetic interactions, where various phases are found as a result of the interplay of spin-dependent interaction and quadratic Zeeman energy. For antiferromagnetic interactions, the system demonstrates competing magnetic orders, including nematic, spin-singlet and ferromagnetic insulating phase, depending on longitudinal magnetization, whereas, for ferromagnetic case, a ferromagnetic-to-nematic-insulating phase transition is observed for small quadratic Zeeman energy, and the insulating phase demonstrates the nematic order for large Zeeman energy. Interestingly, at low magnetic field and finite temperature, we find an abnormal multi-step condensation of the strongly correlated superfluid, i.e. the critical condensing temperature of the $m_F=-1$ component with antiferromagnetic interactions demonstrates an increase with longitudinal magnetization, while, for ferromagnetic case, the Zeeman component $m_F = 0$ demonstrates a local minimum for the critical condensing temperature, in contrast to weakly interacting cases.