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arXiv:1711.05470 · Scientific Reports

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

Xiaolei Zan, Jing Liu, Jinsen Han, Jianhua Wu, Yongqiang Li

Published Jun 8, 2018• 6 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41598-018-27503-0

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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.
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.
Since the experimental realization of Bose-Einstein condensation in 1995, the field of ultracold atoms has expanded rapidly, and has become an important arena for exploring diverse quantum many-body physics, as highlighted by the experimental observation of quantum phase transitions in the system of bosons in a periodic potential, which is described by the Bose-Hubbard model.Recently, ultracold atoms with spin degrees of freedom are actively studied because the coupling between the internal spin degrees of freedom and the spatial degrees of freedom can give rise to novel and interesting physics.A minimal model for studying such physics is the spin-1 Bose-Hubbard model, which describes spin-1 bosons in a periodic potential.The model has a spin-dependent interaction, which can be ferromagnetic or antiferromagnetic, and it is known that although the ferromagnetic model resembles the spinless counterpart, the antiferromagnetic model exhibits totally different features, which make the model much more intensively studied compared with the ferromagnetic one.However, the presence of an external magnetic field can change the situation, because the positive quadratic Zeeman energy competes with the ferromagnetic interaction, which can give rise to rich phases.In this thesis, we explore the ground-state and nonzero-temperature phase diagrams of the spin-1 Bose-Hubbard model under an external magnetic field.To analyze the model, we use an approximation method called the decoupling approximation, or equivalently, the Gutzwiller variational ansatz.It is shown that, in addition to the Mott insulator phase, the model possesses two superfluid phases.Moreover, for large values of a spin-dependent interaction, the phase transitions between the two superfluid phases can be discontinuous.Such discontinuous phase transitions are shown to survive at nonzero but sufficiently low temperature.The discontinuous phase transitions are in clear contrast to the mean-field theory of weakly interacting spin-1 bosons without a lattice, which predicts that the corresponding phase transition is continuous, signifying the importance of the effect of strong interactions on the interplay between the spatial and spinor degrees of freedom. 4.1.2The grand Hamiltonian . . . . . . . . .
We investigate strongly correlated spin-1 ultracold bosons with antiferromagnetic interactions in a cubic optical lattice, based on bosonic dynamical mean-field theory. Rich phase diagrams of the system are mapped out at both zero and finite temperature, and in particular the existence of a spin-singlet condensate is established. Interestingly, at finite temperature, we find that the superfluid can be heated into a Mott insulator with even (odd) filling via a first- (second-) order phase transition, analogous to the Pomeranchuk effect in 3He^{3}\mathrm{He}3He. Moreover, for typical experimental setups, we estimate the critical temperature (entropy) for different ordered phases and our results suggest that direct experimental observation of these phases is promising.
We investigate spin-order of ultracold bosons in an optical lattice by means of dynamical mean-field theory. A rich phase diagram with anisotropic magnetic order is found, both for the ground state and at finite temperatures. Within the Mott insulator, a ferromagnetic to antiferromagnetic transition can be tuned using a spin-dependent optical lattice. In addition we find a supersolid phase, in which superfluidity coexists with antiferromagnetic spin order. We present detailed phase diagrams at finite temperature for the experimentally realized heteronuclear 87Rb-41K^{87}\text{R}\text{b-}^{41}\text{K}87Rb-41K mixture in a three-dimensional optical lattice.
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.
We derive the ground-state phase diagram of antiferromagnetic spin-1 bosons trapped in a square optical lattice in the limit of large negative quadratic Zeeman interaction, i.e., a limit where only two spin components σ=↑,↓\sigma=\uparrow, \downarrowσ=↑,↓ are involved. The system thus reduces to an interacting binary Bose gas. Our quantum Monte Carlo simulations reveal a phase transition from a x−yx-yx−y ferromagnetic-order to a spin insulator without symmetry breaking, inside the Mott insulating phase with two particles per site. This 3D-XY transition is characterized by the establishment of a finite local magnetic moment along the zzz-axis and by counterflow superfluidity inside the Mott phase. When increasing the spin-spin interaction amplitude U2U_2U2​, this transition merges with the Mott-superfluid transition and becomes first-order. We derive the phase diagram of the spin-charge separation with respect to U2U_2U2​ parameter.