BEC-BCS crossover, phase transitions and phase separation in polarized resonantly-paired superfluids

We study resonantly-paired s-wave superfluidity in a degenerate gas of two species (hyperfine states labeled by ↑, ↓) of fermionic atoms when the numbers N_↑ and N_↓ of the two species are unequal, i.e., the system is “polarized.” We find that the continuous crossover from the Bose-Einstein condensate (BEC) limit of tightly-bound diatomic molecules to the Bardeen-Cooper-Schrieffer (BCS) limit of weakly correlated Cooper pairs, studied extensively at equal populations, is interrupted by a variety of distinct phenomena under an imposed population difference ΔN ≡ N_↑ − N_↓. Our findings are summarized by a “polarization” (ΔN) versus Feshbach-resonance detuning (δ) zero-temperature phase diagram, which exhibits regions of phase separation, a periodic FFLO superfluid, a polarized normal Fermi gas and a polarized molecular superfluid consisting of a molecular condensate and a fully polarized Fermi gas. We describe numerous experimental signatures of such phases and the transitions between them, in particular focusing on their spatial structure in the inhomogeneous environment of an atomic trap.     

D-Dimensional Dirac Fermions BEC-BCS Crossover Thermodynamics

An effective relativistic continuum massive Proca Lagrangian action is used to account for the Lorentz vector condensation effects on the equation of state of the strongly interacting fermions system. The interior quantum fluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized Thomson problem counterterm background. The general analytical formulas for the d-dimensional thermodynamics are given near the unitary limit region. In the non-relativistic limit for d=3, the universal dimensionless coefficient ξ=4/9 and energy gap Δ/ε_f=5/18 are reasonably consistent with the existing theoretical and experimental results. In the unitary limit for d=2 and T=0, the universal coefficient can even approach the extreme occasion ξ=0 corresponding to the infinite effective fermion mass m^*=∞, which can be mapped to the strongly coupled two-dimensional electrons and is quite similar to the three-dimensional Bose-Einstein condensation of ideal boson gas. Instead, for d=1, the universal coefficient ξ is negative, implying the non-existence of phase transition from superfluidity to normal state. The solutions manifest the quantum Ising universal class characteristic of the strongly coupled unitary fermions gas.     

D-Dimensional Dirac Fermions BEC-BCS Crossover Thermodynamics

An effective relativistic continuum massive Proca Lagrangian action is used to account for the Lorentz vector condensation effects on the equation of state of the strongly interacting fermions system. The interior quantum fluctuation effects are incorporated as an external field approximation indirectly through a fictive generalized Thomson Problem counterterm background. The general analytical formulas for the d-dimensional thermodynamics are given near the unitary limit region. In the non-relativistic limit for d = 3, the universal dimensionless coefficient ξ = 4/9 and energy gap △/εf = 5/ 18 are reasonably consistent with the existing theoretical and experimental results. In the unitary limit for d = 2 and T = 0, the universal coefficient can even approach the extreme occasion ξ = 0 corresponding to the infinite effective fermion mass m* = ∞, which can be mapped to the strongly coupled two-dimensional electrons and is quite similar to the three-dimensional Bose-Einstein condensation of ideal boson gas. Instead, for d = 1, the universal coefficient ξ is negative, implying the non-existence of phase transition from superfluidity to normal state. The solutions manifest the quantum Ising universal class characteristic of the strongly coupled unitary fermions gas.     

Observation of the BEC-BCS crossover in a degenerate Fermi gas of lithium atoms

We observe characteristic atomic behaviors in the Bose-Einstein-condensation-Bardeen-Cooper-Schrieffer(BEC-BCS)crossover,by accurately tuning the magnetic field across the Feshbach resonance of lithium atoms.The magnetic field is calibrated by measuring the Zeeman shift of the optical transition.A non-monotonic anisotropic expansion is observed across the Feshbach resonance.The density distribution is explored in different interacting regimes,where a condensate of diatomic molecules forms in the BEC limit with the indication of a bimodal distribution.We also measure the three-body recombination atom loss in the BEC-BCS crossover,and find that the magnetic field of the maximum atom loss is in the BEC limit and gets closer to the Feshbach resonance when decreasing the atom temperature,which agrees with previous experiments and theoretical prediction.This work builds up a controllable platform for the study on the strongly interacting Fermi gas.     

The quantum pressure correction to the excitation spectrum of the trapped superfluid Fermi gases in a BEC-BCS crossover

Using quantum hydrodynamic approaches, we study the quantum pressure correction to the collective excitation spectrum of the interacting trapped superfluid Fermi gases in the BEC-BCS crossover. Based on a phenomenological equation of state, we derive hydrodynamic equations of the system in the whole BEC-BCS crossover regime. Beyond the Thomas--Fermi approximation, expressions of the frequency corrections of collective modes for both spherical and axial symmetric traps excited in the BEC-BCS crossover are given explicitly. The corrections of the eigenfrequencies due to the quantum pressure and their dependence on the inverse interaction strength, anisotropic parameter and particle numbers of the condensate are discussed in detail.     

超流费米气体相滑移时的密度分布

当前在冷原子和玻色爱因斯坦凝聚(BEC)领域的一个重要问题是在Feshbach共振附近的冷费米气体如何从BEC态演变到BCS(Bardeen Schrieffer Cooper)态.本文进一步研究在Feshbach共振附近超流态的相滑移现象.通过具体的数值计算，给出了费米气体在相滑移时的粒子数密度的分布，并对不同温度下的相滑移的大小进行了分析.结果表明，相滑移现象可以作为实验上判断系统是否处于超流态的一个可行的判据. 关键词： 超流费米气体 相滑移 Feshbach共振     

Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases

A strongly correlated Fermi system plays a fundamental role in very different areas of physics, from neutron stars, quark–gluon plasmas, to high temperature superconductors. Despite the broad applicability, it is notoriously difficult to be understood theoretically because of the absence of a small interaction parameter. Recent achievements of ultracold trapped Fermi atoms near a Feshbach resonance have ushered in enormous changes. The unprecedented control of interaction, geometry and purity in these novel systems has led to many exciting experimental results, which are to be urgently understood at both low and finite temperatures. Here we review the latest developments of virial expansion for a strongly correlated Fermi gas and their applications on ultracold trapped Fermi atoms. We show remarkable, quantitative agreements between virial predictions and various recent experimental measurements at about the Fermi degenerate temperature. For equations of state, we discuss a practical way of determining high-order virial coefficients and use it to calculate accurately the long-sought third-order virial coefficient, which is now verified firmly in experiments at ENS and MIT. We discuss also virial expansion of a new many-body parameter—Tan’s contact. We then turn to less widely discussed issues of dynamical properties. For dynamic structure factors, the virial prediction agrees well with the measurement at the Swinburne University of Technology. For single-particle spectral functions, we show that the expansion up to the second order accounts for the main feature of momentum-resolved rf-spectroscopy for a resonantly interacting Fermi gas, as recently reported by JILA. In the near future, more practical applications with virial expansion are possible, owing to the ever-growing power in computation.     

BCS-BEC渡越过程超流费米气体在线性变化势中的集体激发

基于超流流体力学方程组和标度理论,数值研究了Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein Condensate (BEC)渡越过程中超流费米气体在线性减小谐振子势下的集体激发.详细研究了包括谐振子势频率线性减小的速度,减小到的幅度以及势阱各向异性参数对集体激发的影响.通过频谱分析和数据拟合,分别研究了各向同性势和各向异性势下在最小振幅激发下所对应的模式,且数值计算得到的频率值在整个BCS-BEC渡越过程中与前期的理论结果符合得很好.该工作可以为后面超流费米气体集体激发的实验提供有益的理论参考     

Quasiparticle Spectrum of Quantum Degenerate Fermi Gas in the Presence of Self-Consistent Magnetization Field

In this paper, we develop a systematic and simple method to derive quasiparticle spectrum of the quantum degenerate Fermi gases within the framework of Hartree-Fock-Bogoliubov theory which turns a general nonlinear twobody interaction Hamiltonian into a bilinear Hamiltonian by introducing certain self-consistent mean fields. Applying the approach, we obtain the quasi-particle spectrum of the model describing the superfluid phase transition that arises when a Feshbach resonance pairing occurs in adiute Fermi gas in the presence of the magnetization fields m =U∑k and mk=U∑k.When the gap parameter △ is smaller than one or both of the magnetization fields, the spectrum manifests roton-type structure dramatically different from the spectrum in the absence of the magnetization fields.     

Feshbach共振下BCS-BEC渡越量子分析

考虑一个涵盖分子间相互作用的多体模型,给出一种半解析计算模型中费米原子对转化成玻色分子转化率的有效方法.这种方法主要使用独立交叉近似,并在平均场理论下推导出一个精确计算转化率的解析公式.对比分析证明,该解析公式的计算结果得到多体模型的数值分析的支持,并与Rice小组的⁶Li实验能够很好的吻合.     

Polarons in alkaline-earth-like atoms with multiple background Fermi surfaces

We study the impurity problem in a Fermi gas of ¹⁷³Yb atoms near an orbital Feshbach resonance (OFR), where a single moving particle in the ³P₀ state interacts with two background Fermi seas of particles in different nuclear states of the ground ¹S₀ manifold. By employing wave function ansatz to molecule and polaron states, we investigate various properties of the molecule, the attractive polaron, and the repulsive polaron states. In comparison to the case where only one Fermi sea is populated, we find that the presence of an additional Fermi sea acts as an energy shift between the two channels of the OFR. In addition, quantum fluctuations near the Fermi level can also induce sizable effects to various properties of the attractive and repulsive polarons.     

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.     

Attack-Induced Entanglement of Noninteracting Fermi Gas

The bipartite entanglement in Fermi gas without interaction is investigated when there ace three fermions in the system. The negativity and the yon Neumann entropy are employed to measure the entanglement of the system. The position of the third fermion can affect the entanglement between the first and the second fermions. The entanglement can be enhanced or suppressed when the third fermion changes its position. When the two fermions are at the same position or when their distance is more than 2.0/kF, the third fermion cannot affect them.     

The shear viscosity of a two component Fermi gas with unequal population at low temperatures

The shear viscosity of spin-polarized Fermi gas at low temperatures is calculated by using the Green’s functions method. In the BEC limit where a Feshbach resonance gives rise to tightly bound dimer molecules, the contributions of the interactions between dimer-atom and imer-dimer take into account to the viscous relaxation rate.     

四氯化碳费米共振的拉曼光谱研究

费米共振现象是一种广泛存在于分子振动光谱中的现象,特别是结构比较复杂的多原子分子.在多原子分子中当振动倍频或组合频位于某一基频附近,由于发生振动耦合,会出现两个新峰,峰的位置向两侧发生移动,二者谱线强度发生变化,把这种现象称为费米共振.费米共振现象不仅存在于红外光谱中,也存在于拉曼光谱中.文章中测量了CCl4的拉曼光谱,利用所得到的谱线峰位和用Originpro7.5软件程序获得积分强度,用费米共振的相关理论计算了C-Cl的a1对称伸缩振动频率v1与C-Cl2的f对称弯曲振动频率v4的组合频(v1 v4)与(某一未知基频)C-Cl的f对称伸缩振动频率v03的费米共振特征参数,进而计算出了耦合系数W和这一未知基频v03.该文对理解费米共振,了解分子振动频率,研究分子结构有很重要的参考价值.     

Diffusive Thermal Conductivity of Superfluid Fermi Gas in p-Wave State at Low Temperatures

The diffusive thermal conductivity tensor of p-wave superfluid at low temperatures is calculated by using the Boltzmann equation approach. We use the Sykes and Brooker procedure and show that K xx is equal to K yy and these are related to T-1 , also K zz is proporated to T-3 .     

BCS-BEC渡越过程中超流费米气体Efimovian膨胀的研究

基于耦合流体力学方程组,分别研究了各向同性和各向异性轴对称势阱下Bardeen-CooperSchrieffer–Bose-Einstein condensate(BCS-BEC)渡越过程中超流费米气体的Efimovian膨胀.当费米气体处于幺正极限,体系标度不变,气体膨胀尺寸展现出一系列平台结构,气体的演化由对数周期函数描述;当费米气体处于非幺正极限超流区域,体系标度不变性破缺,气体的演化偏离对数周期变化;另外我们还发现对于各向异性的费米气体,即使处于幺正极限,谐振子势的各向异性也会导致体系标度不变性破缺.     

Diffusive Thermal Conductivity of Superfluid Fermi Gas in p-Wave State at Low Temperatures

The diffusive thermal conductivity tensor of p-wave superfluid at low temperatures is calculated by using the Boltzmann equation approach. We use the Sykes and Brooker procedure and show that K_xx is equal to K_yy and these are related to T^-1, also K_zz is proporated to T^-3.     

基于准经典近似研究强磁场中高温费米气体的统计性质

基于准经典近似研究强磁场中高温费米气体的统计性质,给出系统的统计特征量的解析式,分析磁场和温度对统计性质的影响.结果显示,与低温情况比较,高温下的统计特征量不再振荡,与自由费米气体比较,磁场总是降低系统的总能,增加系统的化学势、热容量、熵、压强和稳定性;而且温度越高,磁场对总能及热容量的影响越弱,对化学势的影响越大.