Spinor ultracold gases in one dimension represent an interesting example of strongly correlated quantum fluids. They have a rich phase diagram and exhibit a variety of quantum phase transitions. We consider a one-dimensional spinor gas of bosons with a large spin $S$. A particular example is the gas of chromium atoms (S=3), where the dipolar collisions efficiently change the magnetization and make the system sensitive to the linear Zeeman effect. We argue that in one dimension the most interesting effects come from the pairing interaction. If this interaction is negative, it gives rise to a (quasi)condensate of singlet bosonic pairs with an algebraic order at zero temperature, and for $(2S+1)\gg 1$ the saddle point approximation leads to physically transparent results. Since in one dimension one needs a finite energy to destroy a pair, the spectrum of spin excitations has a gap. Hence, in the absence of magnetic field there is only one gapless mode corresponding to phase fluctuations of the pair quasicondensate. Once the magnetic field exceeds the gap another condensate emerges, namely the quasicondensate of unpaired bosons with spins aligned along the magnetic field. The spectrum then contains two gapless modes corresponding to the singlet-paired and spin-aligned unpaired bose-condensed particles, respectively. At T=0 the corresponding phase transition is of the commensurate-incommensurate type.
Spinor ultracold gases in one dimension represent an interesting example of strongly correlated quantum fluids. They have a rich phase diagram and exhibit a variety of quantum phase transitions. We consider a one-dimensional spinor gas of bosons with a large spin S. A particular example is the gas of chromium atoms (S=3), where the dipolar collisions efficiently change the magnetization and make the system sensitive to the linear Zeeman effect. We argue that in one dimension the most interesting effects come from the pairing interaction. If this interaction is negative, it gives rise to a (quasi)condensate of singlet bosonic pairs with an algebraic order at zero temperature, and for (2S+1)≫1 the saddle point approximation leads to physically transparent results. Since in one dimension one needs a finite energy to destroy a pair, the spectrum of spin excitations has a gap. Hence, in the absence of magnetic field there is only one gapless mode corresponding to phase fluctuations of the pair quasicondensate. Once the magnetic field exceeds the gap another condensate emerges, namely the quasicondensate of unpaired bosons with spins aligned along the magnetic field. The spectrum then contains two gapless modes corresponding to the singlet-paired and spin-aligned unpaired bose-condensed particles, respectively. At T=0 the corresponding phase transition is of the commensurate-incommensurate type.
Spinor ultracold gases in one dimension (1D) represent an interesting example of strongly correlated quantum fluids. They have a rich phase diagram and exhibit a variety of quantum phase transitions. We consider a 1D spinor gas of bosons with a large spin S . A particular example is the gas of chromium atoms ( S =3), where the dipolar collisions efficiently change the magnetization and make the system sensitive to the linear Zeeman effect. We argue that in 1D the most interesting effects come from the pairing interaction. If this interaction is negative, it gives rise to a (quasi)condensate of singlet bosonic pairs with an algebraic order at zero temperature, and for (2 S +1)≫1 the saddle point approximation leads to physically transparent results. Since in 1D one needs a finite energy to destroy a pair, the spectrum of spin excitations has a gap. Hence, in the absence of a magnetic field, there is only one gapless mode corresponding to phase fluctuations of the pair quasicondensate. Once the magnetic field exceeds the gap, another condensate emerges, namely the quasicondensate of unpaired bosons with spins aligned along the magnetic field. The spectrum then contains two gapless modes corresponding to the singlet-paired and spin-aligned unpaired Bose condensed particles, respectively. At T =0, the corresponding phase transition is of the commensurate–incommensurate type.
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 magnetism and quantum phase transitions in a one-dimensional system of integrable spin-1 bosons with strongly repulsive density-density interaction and antiferromagnetic spin-exchange interaction via the thermodynamic Bethe ansatz method. At zero temperature, the system exhibits three quantum phases: (i) a singlet phase of boson pairs when the external magnetic field H is less than the lower critical field Hc1; (ii) a ferromagnetic phase of atoms in the hyperfine state ∣F=1,mF=1⟩ when the external magnetic field exceeds the upper critical field Hc2; and (iii) a mixed phase of singlet pairs and unpaired atoms in the intermediate region Hc1<H<Hc2. At finite temperatures, the spin fluctuations affect the thermodynamics of the model through coupling the spin bound states to the dressed energy for the unpaired mF=1 bosons. However, such spin dynamics is suppressed by a sufficiently strong external field at low temperatures. Thus the singlet pairs and unpaired bosons may form a two-component Luttinger liquid in the strong coupling regime.
We investigate pairing and quantum phase transitions in the one-dimensional two-component Fermi atomic gas in an external field. The phase diagram, critical fields, magnetization, and local pairing correlation are obtained analytically via the exact thermodynamic Bethe ansatz solution. At zero temperature, bound pairs of fermions with opposite spin states form a singlet ground state when the external field H<Hc1. A completely ferromagnetic phase without pairing occurs when the external field H>Hc2. In the region Hc1<H<Hc2, we observe a mixed phase of matter in which paired and unpaired atoms coexist. The phase diagram is reminiscent of that of type II superconductors. For temperatures below the degenerate temperature and in the absence of an external field, the bound pairs of fermions form hard-core bosons obeying generalized exclusion statistics.
The coherence of a quantum system is one of the key signatures of many-body physics. While a three-dimensional Bose-Einstein condensate (BEC) exhibits true long-range coherence, a Bose gas confined in a one-dimensional (1D) potential displays quasi-long-range order. Experimentally, these coherence properties are typically probed via the momentum distribution, which corresponds to the Fourier transform of the one-body correlation function. In two-dimensional (2D) systems, for example, momentum distribution enables the observation of the Berezinskii-Kosterlitz-Thouless (BKT) transition from a thermal cloud to a superfluid. With trimodal distribution fitting, an intermediate quasicondensate phase is also revealed. In 1D systems, the momentum distribution of a quenched Tonks-Girardeau (TG) Bose gas can be mapped to that of a non-interacting Fermi gas at a specific evolution time, achieving the rapidity distribution. On the other hand, spin-orbit coupling (SOC) has emerged as one of the central topics in ultracold atomic physics. In additional to creating an artificial electric or magnetic field, researchers also observe negative-mass dynamics in a spin-orbit-coupled BEC by engineering the curvature of the band dispersion. This phenomenon is directly observable in the density distribution of the system. In 1D systems, SOC also introduces rich physical phenomena; while low-energy 1D quantum systems are conventionally described by Tomonaga-Luttinger liquid (TLL) theory, SOC notably alters the energy-momentum dispersion. This modification gives rise to unconventional Luttinger liquids whose properties are governed by the spin-orbit coupling strength.In this work, we first investigate the qualitative properties of a 1D Bose gas and demonstrate the temperature dependence of the momentum distribution, revealing how the thermal fluctuations destroy the quasi-long-range order. In the second part, we probe the effects of 1D SOC on a 1D Bose gas, focusing on how SOC modifies the energy-momentum dispersion and the resulting momentum distribution. We demonstrate that within a specific parameter regime, the momentum distribution and its associated coherence properties undergo distinct qualitative changes. The occupied higher momentum states induce phase fluctuations and destroy the coherence of the system, showing signals of the non-Luttinger liquid physics. We probe the coherence properties of a 1D system along these two parameter axes.
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.