Charge and spin dynamics of interacting fermions in a one-dimensional harmonic trap

We study an atomic Fermi gas interacting through repulsive contact forces in a one-dimensional harmonic trap. Bethe-ansatz solutions lead to an inhomogeneous Tomonaga-Luttinger model for the low energy excitations. The equations of motion for charge and spin density waves are analyzed both near the trap center and near the trap edges. While the center shows conventional spin-charge separation, the edges cause a giant increase of the separation between these modes.     

Nonequilibrium spin dynamics in a trapped fermi gas with effective spin-orbit interactions

We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and nontrivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive nonequilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.     

Rapidly rotating fermions in an anisotropic trap

We consider a cold gas of non-interacting fermions in a two-dimensional harmonic trap with two different trapping frequencies w_x\omega_x ≤ w_y\omega_y, and discuss the effect of rotation on the density profile. Depending on the rotation frequency Ω, and the trap anisotropy w_y\omega_y/w_x\omega_x, the density profile assumes two qualitatively different shapes. For small anisotropy, the density consists of elliptical plateaus of constant density, corresponding to Landau levels and is well described by a two-dimensional local density approximation. For large anisotropy, the density profile is Gaussian in the strong confining direction and semicircular with prominent Friedel oscillations in the weak direction. In this regime, a one-dimensional local density approximation is well suited to describe the system. The crossover between the two regimes is smooth where the step structure between the Landau level edges turn into Friedel oscillations.     

Collective excitations of a 1D Bose–Einstein condensate in an anharmonic trap

We investigate the collective excitations of a one-dimension Bose–Einstein condensate trapped in an anharmonic potential by solving the time-dependent Tonks–Girardeau equation. The governing equations of motions for the low-energy excitations are obtained using variational approaches. The motion of a 1D BEC in a harmonic trap is just like the motion of one particle in a harmonic trap. And quartic distortion of the potential causes the blue-shift and red-shift on the excitation frequency while cube distortion only causes the red-shift.     

受限一维无自旋费米子系统的性质研究

本文借助于一维自旋1/2-XXZ模型的Bethe-ansatz精确解, 利用局域密度近似(LDA), 讨论了谐振势中一维无自旋费米子的密度分布, 得出了ρ-u相图(这里的ρ为无量纲的粒子数密度 变量u为相互作用强度)对相图的分析表明, 随着原子密度和近邻相互作用的变化, 系统出现五个不同的混合量子相通过对热力学硬度S_ρ的计算, 发现其可作为体系的序参量, 其奇异点可用以度量受限体系中量子相变的发生     

First and second sound in a two-dimensional harmonically trapped Bose gas across the Berezinskii–Kosterlitz–Thouless transition

We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau’s two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii–Kosterlitz–Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified one-dimensional hydrodynamic equations and discuss the sound-wave propagation along the weakly confined direction. Due to the universal jump of the superfluid density inherent to the BKT transition, we show that the first sound velocity exhibits a kink across the transition. These predictions might be readily examined in current experimental setups for 2D dilute Bose gases with a sufficiently large number of atoms, where the finite-size effect due to harmonic traps is relatively weak.     

Fermions in 3D optical lattices: cooling protocol to obtain antiferromagnetism

A major challenge in realizing antiferromagnetic and superfluid phases in optical lattices is the ability to cool fermions. We determine the equation of state for the 3D repulsive Fermi-Hubbard model as a function of the chemical potential, temperature, and repulsion using unbiased determinantal quantum Monte Carlo methods, and we then use the local density approximation to model a harmonic trap. We show that increasing repulsion leads to cooling but only in a trap, due to the redistribution of entropy from the center to the metallic wings. Thus, even when the average entropy per particle is larger than that required for antiferromagnetism in the homogeneous system, the trap enables the formation of an antiferromagnetic Mott phase.     

Landau dynamics of a grey soliton in a trapped condensate

It is shown that grey soliton dynamics in a one-dimensional trap can be treated within the framework of the local density approximation as Landau dynamics of a quasiparticle. A soliton of arbitrary amplitude moves in the trapping potential without deformation of its density profile as a particle of mass 2m. The dynamics in the local density approximation is shown to be consistent with the perturbation theory for dark solitons. Dynamics of a vortex ring in a trap is discussed qualitatively.     

冷原子物理中的一维少体问题

作为构成量子多体系统的基本单元,一维少体系统的研究不仅可以在理论上为多体系统的量子关联及动力学等性质提供更为基本的理解,也可以为实验上制备多体系统提供更加方便和功能更加全面的方法.本文回顾了冷原子物理中一维少体系统最新的实验和理论进展.首先介绍了少体实验中实现的谐振子势阱中确定原子数的精确制备,亚稳态势阱和双阱系统中原子的隧穿,以及强相互作用下等效自旋链的实验结果.然后深度解析了理论研究方面,特别是基于精确可解模型的一些重要结果,包括亚稳态势阱中相互作用原子的隧穿概率,以及相应实验上常见势阱的能谱分析、密度分布、隧穿动力学以及强相互作用极限下的有效自旋链模型等.     

Spin-orbital phase synchronization in the magnetic field-driven electron dynamics in a double-well potential

We study the dynamics of an electron confined in a one-dimensional double-well potential in the presence of driving external magnetic fields. The orbital motion of the electron is coupled to the spin dynamics by spin-orbit interaction of the Dresselhaus type. We derive an effective time-dependent model Hamiltonian for the orbital motion of the electron and obtain a condition for synchronization of the orbital and the spin dynamics. We find an analytical expression for the Arnold 'tongue' and propose an experimental scheme for realizing the proposed synchronization.     

Stochastic model for the dynamics of a spin-oscillator coupled system

We construct a stochastic model for the dynamics of a one-dimensional system consisting of bilinearly coupled harmonic oscillators and spins. The spin dynamics is defined as a Glauber model where the spins are effectively coupled through their interaction with the oscillators. To maintain internal thermal equilibrium in the composite system, which does not exhibit Onsager symmetry, we introduce a phenomenological retarded friction in the oscillator equation of motion and relate it to the spin correlation function through a fluctuation-dissipation theorem. The oscillator susceptibility is derived and the behavior of its poles as functions of wavevector and temperature is studied. The results are compared to those obtained by other authors who have studied similar systems, using irreversible thermodynamics. In contrast to ours, these treatments do not give an explicit result for the wavevector dependence of the poles.     

Collective modes of type-ⅡWeyl fermions with repulsive S-wave interaction

Three-dimensional type-ⅡWeyl fermions possess overtilted cone-like low-energy band dispersion.Unlike the closed ellipsoidal Fermi surface for type-ⅠWeyl fermions,the Fermi surface is an open hyperboloid for type-ⅡWeyl fermions.We evaluate the spin and density susceptibility of type-ⅡWeyl fermions with repulsive S-wave interaction by means of Green’s functions.We obtain the particle–hole continuum along the tilted momentum direction and perpendicular to the tilted momentum direction respectively.We find the zero sound mode in some repulsive interaction strengths by numerically solving the pole equations of the susceptibility within the random-phase approximation.     

Multiple-quantum dynamics of one-dimensional nuclear spin systems in solids

Multiple-quantum spin dynamics is studied using analytic and numerical methods for one-dimensional finite linear chains and rings of nuclear spins 1/2 coupled by dipole-dipole interactions. An approximation of dipole-dipole interaction between nearest neighbors having the same constants is used to obtain exact expressions for the intensities of the multiple-quantum coherences in the spin systems studied, which are initially in thermal equilibrium and whose evolution is described by a two-spin two-quantum Hamiltonian. An approximation of nearest neighbors with arbitrary dipole-dipole interaction constants is used to establish a simple relationship between the multiple-quantum dynamics and the dynamics of spin systems with an XY Hamiltonian. Numerical methods are developed to calculate the intensities of multiple-quantum coherences in multiple-quantum NMR spectroscopy. The integral of motion is obtained to expand the matrix of the two-spin two-quantum Hamiltonian into two independent blocks. Using the nearest-neighbor approximation the Hamiltonian is factorized according to different values of the projection operator of the total spin momentum on the direction of the external magnetic field. Results of calculations of the multiple-quantum dynamics in linear chains of seven and eight nuclear spins and a six-spin ring are presented. It is shown that the evolution of the intensities of the lowest-order multiple-quantum coherences in linear chains is accurately described allowing for dipole-dipole interaction of nearest and next-nearest neighbors only. Numerical calculations are used to compare the contributions of nearest and remote spins to the intensities of the multiple-quantum coherences.     

Fermions in anisotropic harmonic trap

We study a few properties of fermions in an anisotropic harmonic trap in absence as well as in presence of an optical lattice. The density of states (DOS) and specific heat of the fermions are studied for different anisotropies. Analytical expressions for the DOS in a strongly anisotropic harmonic trap are derived. For a particular combined potential, where the fermions are hopping in a 3D lattice under a 2D harmonic potential, the Drude weight of the fermionic system is evaluated. The Drude weight is found to be flat in a wide range of fermion concentrations where it is almost temperature independent.     

一维强相互作用极化费米子的相图

文章首先简要评述了目前强相互作用的极化冷费米原子体系的研究现状.在三维,人们对该体系基态存在着不同认识.为对这个问题有进一步了解,文章探讨了一维强相互作用极化费米气体.在均匀情况下,这是一个可积系统,可以得到该体系的一个严格相图.作者发现了一种非均匀的超流相在相空间占主导地位.在有外加束缚势的实验情况下,通过局域密度泛函近似,作者发现了两种新颖的相分离相.     

Expansion dynamics of a two-component quasi-one-dimensional Bose–Einstein condensate: Phase diagram,self-similar solutions,and dispersive shock waves

We investigate the expansion dynamics of a Bose–Einstein condensate that consists of two components and is initially confined in a quasi-one-dimensional trap. We classify the possible initial states of the two-component condensate by taking into account the nonuniformity of the distributions of its components and construct the corresponding phase diagram in the plane of nonlinear interaction constants. The differential equations that describe the condensate evolution are derived by assuming that the condensate density and velocity depend on the spatial coordinate quadratically and linearly, respectively, which reproduces the initial equilibrium distribution of the condensate in the trap in the Thomas–Fermi approximation. We have obtained self-similar solutions of these differential equations for several important special cases and write out asymptotic formulas describing the condensate motion on long time scales, when the condensate density becomes so low that the interaction between atoms may be neglected. The problem on the dynamics of immiscible components with the formation of dispersive shock waves is considered. We compare the numerical solutions of the Gross–Pitaevskii equations with their approximate analytical solutions and numerically study the situations where the analytical method being used admits no exact solutions.     

Attractive Fermi gases with unequal spin populations in highly elongated traps

We investigate two-component attractive Fermi gases with imbalanced spin populations in trapped one-dimensional configurations. The ground state properties are determined with the local density approximation, starting from the exact Bethe-ansatz equations for the homogeneous case. We predict that the atoms are distributed according to a two-shell structure: a partially polarized phase in the center of the trap and either a fully paired or a fully polarized phase in the wings. The partially polarized core is expected to be a superfluid of the Fulde-Ferrell-Larkin-Ovchinnikov type. The size of the cloud as well as the critical spin polarization needed to suppress the fully paired shell are calculated as a function of the coupling strength.