Soluble models of strongly interacting ultracold gas mixtures in tight waveguides

A Fermi-Bose mapping method is used to determine the exact ground states of several models of mixtures of strongly interacting ultracold gases in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D spin-aligned Fermi gas with infinitely strong zero-range attractions). We detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and boson-fermion (BF) interactions. Exact results are given for density profiles in a harmonic trap, single-particle density matrices, momentum distributions, and density-density correlations. Since the ground state is highly degenerate, we analyze the splitting of the ground manifold for large but finite BB and BF repulsions.     

One-dimensional interacting anyon gas: low-energy properties and Haldane exclusion statistics

The low-energy properties of the one-dimensional anyon gas with a delta-function interaction are discussed in the context of its Bethe ansatz solution. It is found that the anyonic statistical parameter and the dynamical coupling constant induce Haldane exclusion statistics interpolating between bosons and fermions. Moreover, the anyonic parameter may trigger statistics beyond Fermi statistics for which the exclusion parameter alpha is greater than one. The Tonks-Girardeau and the weak coupling limits are discussed in detail. The results support the universal role of alpha in the dispersion relations.     

Bosonization, pairing, and superconductivity of the fermionic Tonks-Girardeau gas

We determine some exact static and time-dependent properties of the fermionic Tonks-Girardeau (FTG) gas, a spin-aligned one-dimensional Fermi gas with infinitely strongly attractive zero-range odd-wave interactions. We show that its two-particle reduced density matrix exhibits superconductive off-diagonal long-range order, and on a ring an FTG gas with an even number of atoms has a highly degenerate ground state with quantization of Coriolis rotational flux and high sensitivity to rotation and to external fields and accelerations. For a gas initially under harmonic confinement, we show that during an expansion the momentum distribution undergoes a "dynamical bosonization," approaching that of an ideal Bose gas without violating the Pauli exclusion principle.     

Composite-fermionization of the mixture composed of Tonks gas and Fermi gas

This paper investigates the ground-state properties of the mixture composed of the strongly interacting Tonks-Girardeau gas and spin polarized Fermi gas confined in one-dimensional harmonic traps, where the interaction between the Bose atoms and Fermi atoms is tunable. With a generalized Bose-Fermi transformation the mixture is mapped into a two-component Fermi gas. The homogeneous Fermi gas is exactly solvable by the Bethe-ansatz method and the ground state energy density can be obtained. Combining the ground-state energy function of the homogeneous system with local density approximation it obtains the ground-state density distributions of inhomogeneous mixture. It is shown that with the increase in boson-fermion interaction, the system exhibits composite-fermionization crossover.     

Nonequilibrium dynamics of Tonks-Girardeau gases on optical lattices

We summarize in the present work exact results obtained for Tonks-Girardeau gases on one-dimensional optical lattices both for the ground state and nonequilibrium dynamics. On the theoretical side, impenetrable bosons offer the opportunity to study strongly interacting systems in one-dimensional lattices exactly, by means of the Jordan-Wigner transformation, and hence contribute to the topic of strong correlations at the center of interest in both condensed matter physics and quantum gases. This motivation is further enhanced by recent experimental realizations of such systems with ultracold atoms. After having shown their universal properties in equilibrium, we concentrate on their nonequilibrium dynamics. It will be shown that, starting from a pure Fock state, quasi-long-range correlations develop dynamically and lead to the formation of quasicondensates with a momentum determined by the underlying lattice. We expect this effect to be relevant for atom lasers with full control of the wavelength. Then, we will show that the free evolution of an initially confined Tonks-Girardeau gas leads to a momentum distribution that approaches at long times that of the equivalent fermionic system, giving rise to a bosonic gas with a Fermi edge, and hence a fermionization that can only be obtained out of equilibrium. Remarkably, although the momentum distribution function of the Tonks-Girardeau gas becomes equal to the one of the fermions, no loss in coherence is observed in the system, as reflected by a large occupation of eigenstates of the one-particle density matrix.     

Interacting fermions in highly elongated harmonic traps

Quasi-one-dimensional two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated harmonic traps are determined within the local density approximation. For strong attractive effective interactions the existence of a molecular Tonks-Girardeau gas is predicted. The frequency of the lowest breathing mode is calculated as a function of the coupling strength for both attractive and repulsive interactions.     

Ground and excited states of spinor fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model

The ground and excited states of a one-dimensional (1D) spin-1/2 Fermi gas (SFG) with both attractive zero-range odd-wave interactions and repulsive zero-range even-wave interactions are mapped exactly to a 1D Lieb-Liniger-Heisenberg (LLH) model with delta-function repulsions depending on isotropic Heisenberg spin-spin interactions, such that the complete SFG and LLH energy spectra are identical. The ground state in the ferromagnetic phase is given exactly by the Lieb-Liniger (LL) Bethe ansatz, and that in the antiferromagnetic phase by a variational method combining Bethe ansatz solutions of the LL and 1D Heisenberg models. There are excitation branches corresponding to LL type I and II phonons and spin waves, the latter behaving quadratically for small wave numbers in the ferromagnetic phase and linearly in the antiferromagnetic phase.     

Dynamical role of anyonic excitation statistics in rapidly rotating bose gases

We show that for rotating harmonically trapped Bose gases in a fractional quantum Hall state, the anyonic excitation statistics in the rotating gas can effectively play a dynamical role. For particular values of the two-dimensional coupling constant g=-2pih2(2k-1)/m, where k is a positive integer, the system becomes a noninteracting gas of anyons, with exactly obtainable solutions satisfying Bogomol'nyi self-dual order parameter equations. Attractive Bose gases under rapid rotation thus can be stabilized in the thermodynamic limit due to the anyonic statistics of their quasiparticle excitations.     

Temperature dependence of volume and surface symmetry energy coefficients of nuclei

The thermal evolution of the energies and free energies of a set of spherical and near-spherical nuclei spanning the whole periodic table are calculated in the subtracted finite-temperature Thomas–Fermi framework with the zero-range Skyrme-type KDE0 and the finite-range modified Seyler–Blanchard interaction. The calculated energies are subjected to a global fit in the spirit of the liquid-drop model. The extracted parameters in this model reflect the temperature dependence of the volume symmetry and surface symmetry coefficients of finite nuclei, in addition to that of the volume and surface energy coefficients. The temperature dependence of the surface symmetry energy is found to be very substantial whereas that of the volume symmetry energy turns out to be comparatively mild.     

The dynamics of quantum discord and entanglement of two atoms coupled to two spatially separate cavities in cavity QED

We demonstrate that a kind of highly excited state of strongly attractive Hubbard model, named of Fermi super-Tonks-Girardeau state, can be realized in the spin-1/2 Fermi optical lattice system by a sudden switch of interaction from the strongly repulsive regime to the strongly attractive regime. In contrast to the ground state of the attractive Hubbard model, such a state is the lowest scattering state with no pairing between attractive fermions. With the aid of Bethe-ansatz method, we calculate energies of both the Fermi Tonks-Girardeau gas and the Fermi super-Tonks-Girardeau state of spin-1/2 ultracold fermions and show that both energies approach to the same limit as the strength of the interaction goes to infinity. By exactly solving the quench dynamics of the Hubbard model, we demonstrate that the Fermi super-Tonks-Girardeau state can be transferred from the initial repulsive ground state very efficiently. This allows the experimental study of properties of Fermi super-Tonks-Girardeau gas in optical lattices.     

Degeneracies in trapped two-component fermi gases

We report on previously unobserved intersystem degeneracies in two-component equal-mass Fermi gases with interspecies zero-range interactions under isotropic harmonic confinement. Over the past 10 years, two-component Fermi gases consisting of n_{1} spin-up and n_{2} spin-down atoms with interspecies zero-range interactions have become a paradigm for modeling condensed matter systems, nuclear matter, and neutron matter. We show that the eigenenergies of the (n_{1}+1,n_{2}-1) system are degenerate with the eigenenergies of the (n_{1},n_{2}) system for any s-wave scattering length a_{s}, including infinitely large, positive, and negative a_{s}. The existence of the intersystem degeneracies is demonstrated explicitly for few-body systems with n_{1}+n_{2}=4, 5, and 6. The degeneracies and associated symmetries are explained within a group theoretical framework.     

理想气体中的内势能

本文证明在无壁空间或无束缚力约束空间中,压力是气体以物态存在的束缚力.证明了热力学压力不仅是动量交换的统计平均值的量度,而且也是分子或原子空间位置分布(密度)的表征.理想气体在有限空间中的统计构形空间,具有逸散势-pV.这种系统构形空间内的各能级粒子具有相应的动量空间分布,其统计构形空间具有无序势TS.热力学平衡态具有处处相等p、T和总势能TS-pV.理想气体的二种势能具有对称性,总势能等于零;但其相应的无序势和逸散势都不等于零.     

Exponentially decaying correlations in a gas of strongly interacting spin-polarized 1D fermions with zero-range interactions

We consider the single-particle correlations and momentum distributions in a gas of strongly interacting, spinless 1D fermions with zero-range interactions. This system represents a fermionic version of the Tonks-Girardeau gas of impenetrable bosons as it can be mapped to a system of noninteracting 1D bosons. We use this duality to show that the T = 0, single-particle correlations exhibit an exponential decay with distance. This strongly interacting system is experimentally accessible using ultracold atoms and has a Lorentzian momentum distribution at large momenta whose width is given by the linear density.     

超冷费米气体的膨胀动力学研究新进展

多体系统的非平衡动力学演化是当前物理学中最具挑战性的问题之一.超冷量子费米原子气体具有较强的可控性,是研究多体非平衡动力学的理想系统,可以用来模拟和理解大爆炸后的早期宇宙、重离子碰撞中产生的夸克-胶子以及核物理等动力学.一般多体系统演化是非常复杂的,往往需要利用对称性来研究.利用Feshbach共振可以制备标度不变的费米原子气体:无相互作用和幺正费米量子气体.当远离平衡态时,可利用普适的指数和函数来刻画,其动力学可以通过对系统的时空演化进行标度变换来识别.本文主要介绍近年来强相互作用超冷费米气体的膨胀动力学研究进展,包括原子气体的各向异性展开、标度动力学和Efimovian膨胀动力学.     

Energy spectrum of fermionized bosonic atoms in optical lattices

We investigate the energy spectrum of fermionized bosonic atoms, which behave very much like spinless noninteracting fermions, in optical lattices by means of the perturbation expansion and the retarded Green's function method. The results show that the energy spectrum splits into two energy bands with single-occupation; the fermionized bosonic atom occupies nonvanishing energy state and left hole has a vanishing energy at any given momentum, and the system is in Mott-insulating state with a energy gap.Using the characteristic of energy spectra we obtained a criterion with which one can judge whether the Tonks-Girardeau (TG) gas is achieved or not.     

Experimental Observation of Spin-Exchange in Ultracold Fermi Gases

We experimentally study the spin exchange collision in ultracold~(40) K Fermi gases. The quadratic Zeeman shift,trap potential and temperature of atomic cloud will influence on the spin changing dynamics. Dependences of the spin components populations on the external bias magnetic field, the optical trap depth and the temperature of atomic cloud are experimentally investigated. The spin exchange from the initial states to the final state are observed for different initial states. This work shows an interesting process of reaching equilibrium by redistribution among the spin states with the spin exchange collision in an ultracold large-spin Fermi gas.     

The quantum geometry of spin and statistics

Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin–statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose–Fermi case we classify the corresponding possibilities for anyonic spin and statistics. We incorporate the underlying extended concept of symmetry into quantum field theory in a generalised path integral formulation capable of handling general braid statistics. For bosons and fermions the different path integrals and Feynman rules naturally emerge without introducing Grassmann variables. We also consider the anyonic example of quons and obtain the path integral counterpart to the usual canonical approach.     

Bosons in cigar-shaped traps: Thomas-Fermi regime, Tonks-Girardeau regime, and in between.

We present a quantitative analysis of the experimental accessibility of the Tonks-Girardeau gas in present-day experiments with cigar-trapped alkalis. For this purpose we derive, using a Bethe ansatz generated local equation of state, a set of hydrostatic equations describing one-dimensional, delta-interacting Bose gases trapped in a harmonic potential. The resulting solutions cover the entire range of atomic densities.     

自旋-轨道耦合作用下双组分量子气体中的动力学结构因子与求和规则

在自旋-轨道耦合作用下,双组分量子气体中密度涨落和自旋涨落的动力学结构因子满足不同形式的求和规则.特别是动力学结构因子的一阶矩一般不具有空间反演对称性.针对两个特定的模型——Raman耦合作用下的无相互作用费米气体与弱相互作用玻色气体,分别计算了在不同参数条件下密度涨落和自旋涨落的动力学结构因子,并讨论了实验上观测其一阶矩偏离空间反演对称所需达到的能谱分辨率.     

Phase separation in the trapped spinor gases with anisotropic spin-spin interaction

We investigate the effect of the anisotropic spin-spin interaction on the ground state density distribution of the one dimensional spin-1 bosonic gases within a modified Gross-Pitaevskii theory both in the weakly interaction regime and in the Tonks-Girardeau (TG) regime. We find that for ferromagnetic spinor gas the phase separation occurs even for weak anisotropy of the spin-spin interaction, which becomes more and more obvious and the component of m_F=0 diminishes as the anisotropy increases. However, no phase separation is found for anti-ferromagnetic spinor gas in both regimes.