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arXiv:0904.4110 · Physical Review A

Phase diagrams for spin-1 bosons in an optical lattice

Ming-Chiang Chung, Sungkit Yip

Published Nov 19, 2009• 8 citations
arXivHTMLPDF

Abstract

In this paper, the phase diagrams of a polar spin-1 Bose gas in a three-dimensional optical lattice with linear and quadratic Zeeman effects both at zero and finite temperatures are obtained within mean-field theory. The phase diagrams can be regrouped to two different parameter regimes depending on the magnitude of the quadratic Zeeman effect $Q$. For large $Q$, only a first-order phase transition from the nematic (NM) phase to the fully magnetic (FM) phase is found, while in the case of small $Q$, a first-order phase transition from the nematic phase to the partially magnetic (PM) phase, plus a second-order phase transition from the PM phase to the FM phase is obtained. If a net magnetization in the system exists, the first-order phase transition causes a coexistence of two phases and phase separation: for large $Q$, NM and FM phases and for small $Q$, NM and PM phases. The phase diagrams in terms of net magnetization are also obtained.

DOI
10.1103/physreva.80.053615

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In this paper, the phase diagrams of a polar spin-1 Bose gas in a three-dimensional optical lattice with linear and quadratic Zeeman effects both at zero and finite temperatures are obtained within mean-field theory. The phase diagrams can be regrouped to two different parameter regimes depending on the magnitude of the quadratic Zeeman effect QQQ. For large QQQ, only a first-order phase transition from the nematic (NM) phase to the fully magnetic (FM) phase is found, while in the case of small QQQ, a first-order phase transition from the nematic phase to the partially magnetic (PM) phase, plus a second-order phase transition from the PM phase to the FM phase is obtained. If a net magnetization in the system exists, the first-order phase transition causes a coexistence of two phases and phase separation: for large QQQ, NM and FM phases and for small QQQ, NM and PM phases. The phase diagrams in terms of net magnetization are also obtained.
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.
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We analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons in the presence of an external magnetic field, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. In particular at zero temperature, we determine both the Mott and the superfluid phases for the competition between the anti-ferromagnetic interaction and the linear Zeeman effect within the validity range of the Ginzburg-Landau theory. Moreover, we find that the phase transition between the superfluid and Mott insulator phases is of second order and that the transitions between the respective superfluid phases for anti-ferromagnetic interaction can be both of first and second order.
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We investigate strongly correlated spin-1 ultracold gases with antiferromagnetic interactions in a three-dimensional optical lattice in the presence of an external magnetic field, based on bosonic dynamical mean-field theory. Due to the interplay of spin-dependent and quadratic Zeeman interactions, the system demonstrates competing magnetic orders, including nematic, spin-singlet and ferromagnetic insulating phases, depending on longitudinal magnetization. The dependence of first-order superfluid-insulator transition on external magnetic fields is explored. Interestingly, at low magnetic field, we find an abnormal multi-step condensation of the strongly correlated superfluid, i.e. the critical condensing temperature of the mF=−1m_F=-1mF​=−1 component demonstrates an abnormal increase with longitudinal magnetization, in contrast to weakly interacting cases.