弱相互作用玻色气体的涡旋解

在柱坐标系中,求出了绝对零度情况下近理想玻色气体涡旋态的波函数和能量的近似解析形式．     

Beyond the Tonks-Girardeau gas: strongly correlated regime in quasi-one-dimensional Bose gases

We consider a homogeneous 1D Bose gas with contact interactions and a large attractive coupling constant. This system can be realized in tight waveguides by exploiting a confinement induced resonance of the effective 1D scattering amplitude. By using the diffusion Monte Carlo method we show that, for small densities, the gaslike state is well described by a gas of hard rods. The critical density for cluster formation is estimated using the variational Monte Carlo method. The behavior of the correlation functions and of the frequency of the lowest breathing mode for harmonically trapped systems shows that the gas is more strongly correlated than in the Tonks-Girardeau regime.     

Phase transition of trapped interacting Bose gases

We review some recent theoretical work on the phase transition of interacting Bose gases in the presence of external trapping potentials. A general framework for the study of such questions is presented which is based on the application of perturbative momentum-shell renormalization group methods to the trapped gas in the uncondensed phase. After giving an overview of this approach, we first establish its validity by comparing to previous results for homogeneous and harmonically trapped gases. Using this theoretical framework, we then examine various aspects of how external potentials influence the physics of condensation. (i) By studying the case of general power-law potentials and complemented by arguments from variational perturbation theory, it is quantitatively worked out how a growing inhomogeneity of the trapping potential diminishes nonperturbative effects at the transition. (ii) It is shown how by superimposing a weak periodic potentials on the homogeneous system, the characteristic nonperturbative momentum scale of critical interacting Bose gases can be probed. (iii) For a gas in a random potential, it is studied how condensation is affected by the combined influence of disorder effects and particle interactions.     

Ferromagnetic to antiferromagnetic transition of one-dimensional spinor Bose gases with spin-orbit coupling

The effect of the interatomic dipole-dipole interaction on the single-photon transmission spectrum is investigated theoretically in the single-mode optical waveguide containing a pair of dipole interaction two-level atoms and the incident photon, respectively. The results show that the interatomic dipole-dipole interaction can induce a remarkable change in the photon-atom on-resonance frequency in the single-photon transmission spectrum compared with the nonexistence of the interatomic dipole-dipole interaction. As a consequence, the original zero transmission probability at the original photon-atom resonant frequency increases to one directly thanks to the appropriately-chosen dipole-dipole interaction strength. Consequently, this characteristic reveals that the interatomic dipole-dipole interaction treated as an important internal physical mechanism can perform as a functional quantum switching to manipulate the photon’s transmission in the optical waveguide. The corresponding interpretations responsible for this phenomenon are presented.     

Dynamics and thermodynamics of the low-temperature strongly interacting Bose gas

We measure the zero-temperature equation of state of a homogeneous Bose gas of (7)Li atoms by analyzing the in situ density distributions of trapped samples. For increasing repulsive interactions our data show a clear departure from mean-field theory and provide a quantitative test of the many-body corrections first predicted in 1957 by Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957).]. We further probe the dynamic response of the Bose gas to a varying interaction strength and compare it to simple theoretical models. We deduce a lower bound for the value of the universal constant ξ > 0.44(8) that would characterize the universal Bose gas at the unitary limit.     

Density profiles of strongly interacting trapped fermi gases

We study density profiles in trapped fermionic gases, near Feshbach resonances, at all T< or =Tc and in the near Bose-Einstein condensation and unitary regimes. For the latter, we characterize and quantify the generally neglected contribution from noncondensed Cooper pairs. As a consequence of these pairs, our profiles are rather well fit to a Thomas-Fermi (TF) functional form, and equally well fit to experimental data. Our work lends support to the notion that TF fits can be used in an experimental context to obtain information about the temperature.     

Condensate statistics in one-dimensional interacting Bose gases: exact results

Recently, a quantum Monte Carlo method alternative to the path integral Monte Carlo method was developed for solving the N-boson problem; it is based on the stochastic evolution of classical fields. Here we apply it to obtain exact results for the occupation statistics of the condensate mode in a weakly interacting trapped one-dimensional Bose gas. The temperature is varied across the critical region down to temperatures lower than the trap level spacing. We also derive the condensate statistics in the Bogoliubov theory: this reproduces the exact results at low temperature and explains the suppression of odd numbers of noncondensed particles at T approximately 0.     

Critical temperature of interacting Bose gases in two and three dimensions

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.     

Ground-state properties of interacting two-component Bose gases in a one-dimensional harmonic trap

We study ground-state properties of interacting two-component boson gases in a one-dimensional harmonic trap by using the exact numerical diagonalization method. Based on numerical solutions of many-body Hamiltonians, we calculate the ground-state density distributions in the whole interaction regime for different atomic number ratio, intra- and inter-atomic interactions. For the case with equal intra- and inter-atomic interactions, our results clearly display the evolution of density distributions from a Bose condensate distribution to a Fermi-like distribution with the increase of the repulsive interaction. Particularly, we compare our result in the strong interaction regime to the exact result in the infinitely repulsive limit which can be obtained by a generalized Bose-Fermi mapping. We also discuss the general case with different intra- and inter-atomic interactions and show the rich configurations of the density profiles.     

Exact ground states of rotating Bose gases close to a Feshbach resonance

We study the ground states of rotating Bose gases when interactions are affected by a nearby Feshbach resonance. We show that exact ground states at high angular momentum can be found analytically for a general model for the resonant interactions. We identify parameter regimes where the exact ground states are exotic fractional quantum Hall states, the excitations of which obey nonabelian exchange statistics.     

Superfluid-insulator transition of strongly interacting fermi gases in optical lattices

We study a quantum phase transition between fermion superfluid (SF) and band insulator (BI) of fermions in optical lattices. The destruction of the band insulator is driven by the energy gain in promoting fermions from valance band to various conducting bands to form Cooper pairs. We show that the transition must take place in lattice height Vo/ER between 2.23 and 4.14. The latter is the prediction of mean-field theory while the former is the value for opening a band gap. As one moves across resonance to the molecule side, the SF-BI transition evolves into the SF-Mott-insulator transition of bosonic molecules. We shall also present the global phase diagram for SF-insulator transition for the BCS-BEC family.     

Ground-state properties of Fermi gases in the strongly interacting regime

The ground-state energies and pairing gaps in dilute superfluid Fermi gases have now been calculated with the quantum Monte Carlo method without detailed knowledge of their wave functions. However, such knowledge is essential to predict other properties of these gases such as density matrices and pair distribution functions. We present a new and simple method to optimize the wave functions of quantum fluids using the Green's function Monte Carlo method. It is used to calculate the pair distribution functions and potential energies of Fermi gases over the entire regime from atomic Bardeen-Cooper-Schrieffer superfluid to molecular Bose-Einstein condensation, spanned as the interaction strength is varied.     

玻色气体的磁性

物质磁性一直是凝聚态物理研究的重要课题.以往对磁性的探索主要是以费米子（局域或巡游的电子）为研究对象.由于传统的玻色系统液氦没有自旋,不表现磁性,玻色系统的磁性很少被关注.碱金属原子气体玻色-爱因斯坦凝聚的实现,在开辟了冷原子物理研究领域的同时,也打开了研究玻色系统磁性的大门.这是因为碱金属原子通常具有超精细结构,是旋量玻色气体,能够展示磁性.文章通过对比费米气体的相关结果,介绍了旋量玻色气体磁性的研究概况和最新进展,特别是铁磁性玻色气体的磁性相变以及在低温下铁磁性凝聚体的动力学特征.     

Shear viscosity and spin sum rules in strongly interacting Fermi gases

Fermi gases with short-range interactions are ubiquitous in ultracold atomic systems. In the absence of spin-flipping processes the number of atoms in each spin species is conserved separately, and we discuss the associated Ward identities. For contact interactions the spin conductivity spectral function σ_s(ω) has universal power-law tails at high frequency. We derive the spin f-sum rule and show that it is not affected by these tails in d < 4 dimensions. Likewise the shear viscosity spectral function η(ω) has universal tails; in contrast they modify the viscosity sum rule in a characteristic way.     

Decoherence-driven cooling of a degenerate spinor Bose gas

We investigate the relationship between the coherence of a partially Bose-condensed spinor gas and its temperature. We observe cooling of the normal component driven by decoherence as well as the effect of temperature on decoherence rates.     

玻色气体的磁性

物质磁性一直是凝聚态物理研究的重要课题.以往对磁性的探索主要是以费米子(局域或巡游的电子)为研究对象.由于传统的玻色系统液氦没有自旋,不表现磁性,玻色系统的磁性很少被关注.碱金属原子气体玻色-爱因斯坦凝聚的实现,在开辟了冷原子物理研究领域的同时,也打开了研究玻色系统磁性的大门.这是因为碱金属原子通常具有超精细结构,是旋量玻色气体,能够展示磁性.文章通过对比费米气体的相关结果,介绍了旋量玻色气体磁性的研究概况和最新进展,特别是铁磁性玻色气体的磁性相变以及在低温下铁磁性凝聚体的动力学特征.     

Dilute Fermi gas in quasi-one-dimensional traps: from weakly interacting fermions via hard core bosons to a weakly interacting Bose gas

We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size l(perpendicular). In the dilute limit (nl(perpendicular)<1, where n is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length aF. When l(perpendicular)/aF goes from -infinity to +infinity, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at aF approximately +/-nl2(perpendicular). In conclusion, we discuss experimental implications of these results.     

Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

The Lieb–Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low-dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal M-particle correlation functions, momentum distribution, and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb–Liniger model, we analytically calculate the two-point correlation function, the large moment tail of the momentum distribution, and the static structure factor of the model in terms of the fractional statistical parameter α = 1-2/γ, where γ is the dimensionless interaction strength. We also discuss the Tan's adiabatic relation and other universal relations for the strongly repulsive Lieb–Liniger model in terms of the fractional statistical parameter.     

强相互作用费米气体在谐振子势中的干涉演化

通过数值求解超流序参量方程,研究了强相互作用费米气体从光晶格中释放后的干涉条纹在谐振子势中的演化．发现对于强相互作用的费米气体,膨胀时弹性碰撞使得干涉条纹模糊．为了消除原子间的弹性碰撞而获得近弹道膨胀,实验上采用了快速磁场扫描技术．数值模拟了强相互作用费米气体在膨胀前的快速磁场扫描过程,得到了清晰的干涉条纹,且发现干涉条纹在谐振子势中做长时间周期振荡．计算了在不同超流区域所形成的干涉条纹,与实验观测到的一致．