轨道Feshbach共振附近类碱土金属原子的杂质态问题

近年来,碱土金属原子和类碱土金属原子体系的研究成为冷原子物理的研究热点之一.特别是最近在~(173)Yb原子中发现的轨道Feshbach共振,使得研究有强相互作用的碱土金属和类碱土金属原子系统成为可能,极大扩展了此类原子体系的研究范围.本文介绍了~(173)Yb费米气体在轨道Feshbach共振附近的杂质态问题.在此问题中,位于~3P0态的杂质原子与处于基态的背景费米海相互作用,并在费米海表面产生分子态或极化子态.本文使用试探波函数的研究方法,首先对分子态和吸引极化子态进行介绍,并重点描述了分子态与吸引极化子态间的转变.其次归纳总结了排斥极化子态的相关性质,如有效质量、衰变率等.然后考虑双费米面情况,介绍在闭通道中引入另外一个费米面对系统产生的影响.最后简要介绍二维~(173)Yb费米气体中的杂质态问题.     

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     

Energy Spectrum of a Degenerate Fermi Gas at the BEC-BCS Crossover

A theoretical study of the BCS-BEC crossover is presented. Starting from a two-channel Boson-Fermion resonance model, the BCS-Bogoiubov mean-field method and the Green＇s function method are adopted. The result shows that we can end up with a BCS-type theory but with a composite order parameter. Calculation shows that the Bose condensate of BCS Cooper pairs is proportional to the molecular BEC of Bose molecules. The resonance superfluid phase is indicated by the energy spectrum with an obvious interpretation of the transition mechanism.     

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.     

Non-universal Fermi polaron in quasi two-dimensional quantum gases

We consider an impurity problem in a quasi-two-dimensional Fermi gas, where a spin-down impurity is immersed in a Fermi sea of N spin-up atoms. Using a variational approach and an effective two-channel model, we obtain the energy for a wide range of interaction strength and for various different mass ratios between the impurity and the background fermion in the context of heteronuclear mixture. We demonstrate that in a quasi-two-dimensional Fermi gas there exists a transition of the ground state from polaron in the weakly interacting region to molecule in the strongly interacting region. The critical interaction strength of the polaron-molecule transition is non-universal and depends on the particle density of the background Fermi sea. We also investigate the excited repulsive polaron state, and find similar non-universal behavior.     

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.     

Repulsive Polarons in One-Dimensional Fermi Gases

Using the variational method, we study the properties of a spin-down impurity immersed in a onedimensional(1 D) spin-up Fermi sea. With repulsive interactions between them, the impurity is dressed up by surrounding particles in Fermi sea and forms a polaron. We clearly calculate the binding energy, effective mass, momentum distribution, Tan contact, and pair correlation. Even in strong repulsive regimes, the results can agree with the exact Bethe Ansatz results. The repulsive polaron energy E+ is below Fermi energy EF and no negative effective masses are found in whole interaction regimes, unequal masses polarons are also calculated. We show a clear momentum distribution and calculate the Tan contact from three different aspects. Furthermore, we explore the particle-hole excitation and find that the hole terms in Fermi sea have a great influence on the polaron energy and contact in repulsive regime. These results show that the variational method can still be used effectively in 1 D repulsive polaron system.     

Polaron and molecular states of a spin–orbit coupled impurity in a spinless Fermi sea

We investigate the polaron and molecular states of a fermionic atom with one-dimensional spin–orbit coupling(SOC)coupled to a three-dimensional spinless Fermi sea. Because of the interplay among the SOC, Raman coupling and spinselected interatomic interactions, the polaron state induced by the spin–orbit coupled impurity exhibits quite unique features. We find that the energy dispersion of the polaron generally has a double-minimum structure, which results in a finite center-of-mass(c.m.) momentum in the ground state, different from the zero-momentum polarons where SOC are introduced into the majority atoms. By further tuning the parameters such as the atomic interaction strength, a discontinuous transition between the polarons with different c.m. momenta may occur, signaled by the singular behavior of the quasiparticle residue and effective mass of the polaron. Meanwhile, the molecular state as well as the polaron-to-molecule transition is also strongly affected by the Raman coupling and the effective Zeeman field, which are introduced by the lasers generating SOC on the impurity atom. We also discuss the effects of a more general spin-dependent interaction and mass ratio. These results would be beneficial for the study of impurity physics brought by SOC.     

费米原子对的玻色-爱因斯坦凝聚

通过磁场可以用原子散射的Feshbach共振来调节原子间的相互作用，使之成为排斥或吸引，以及改变作用的强度，运用这个方法可以使费米原子形成分子，也可以在多体作用下形成费米原子配对，在温度够低的条件下可以得到分子的BEC以及原子配对的凝聚体，这些现象在实验室中的实现是2004年物理学的重要成就之一，本文对此给予简短的评述。     

Polaron, molecule and pairing in one-dimensional spin-1/2 Fermi gas with an attractive Delta-function interaction

Using solutions of the discrete Bethe ansatz equations, we study in detail the quantum impurity problem of a spin-down fermion immersed into a fully ploarized spin-up Fermi sea with weak attraction. We prove that this impurity fermion in the one-dimensional (1D) fermionic medium behaves like a polaron for weak attraction. However, as the attraction grows, the spin-down fermion binds with one spin-up fermion from the fully-polarized medium to form a tightly bound molecule. Thus it is seen that the system undergos a crossover from a mean field polaron-like nature into a mixture of excess fermions and a bosonic molecule as the attraction changes from weak attraction into strong attraction. This polaron-molecule crossover is universal in 1D many-body systems of interacting fermions. In a thermodynamic limit, we further study the relationship between the Fredholm equations for the 1D spin-1/2 Fermi gas with weakly repulsive and attractive delta-function interactions.     

Superexchange-mediated magnetization dynamics with ultracold alkaline-earth atoms in an optical lattice

Superexchange and inter-orbital spin-exchange interactions are key ingredients for understanding(orbital) quantum magnetism in strongly correlated systems and have been realized in ultracold atomic gases.Here we study the spin dynamics of ultracold alkaline-earth atoms in an optical lattice when the two exchange interactions coexist.In the superexchange interaction dominating regime,we find that the time-resolved spin imbalance shows a remarkable modulated oscillation,which can be attributed to the interplay between local and nonlocal quantum mechanical exchange mechanisms.Moreover,the filling of the long-lived excited atoms affects the collapse and revival of the magnetization dynamics.These observations can be realized in state-dependent optical lattices combined with the state-of-the-art advances in optical lattice clock spectroscopy.     

Radio-frequency spectroscopy of weakly bound molecules in ultracold Fermi gas

We create weakly bound Feshbach molecules in ultracold Fermi gas40K by sweeping a magnetic field across a broad Feshbach resonance point 202.2 G with a rate of 20 ms/G and perform the dissociation process using radio-frequency(RF) technology. From RF spectroscopy, we obtain the binding energy of the weakly bound molecules in the vicinity of Feshbach resonance. Our measurement also shows that the number of atoms generated from the dissociation process is different at various magnetic fields with the same RF amplitude, which gives us a deeper understanding of weakly bound Feshbach molecules.     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.     

实际费米气体的低温性质

实际气体粒子间都存在弱的相互作用,利用赝势法求出无外势时实际费米气体的能谱,导出了低温低密度下实际费米气体的化学势、压强、熵、内能和定容热容等物理量的解析表达式,探讨了粒子间相互作用对系统低温性质的影响．     

Influence of pressure effect on Fermi resonance in binary solution

The Fermi resonance behaviours of the two groups of binary solutions --- pyridine and methanol, benzene and carbon tetrachloride, under different pressures are investigated according to their Raman spectra. The effect of pressure on Fermi resonance in binary solution differs significantly from that in pure liquid. In a binary solution, with the intermolecular distance shortening, the intermolecular interaction potential increases, the shift rates of the Raman spectral lines increase, the spectral line splitting occurs ahead of that in pure liquid, and the wavenumber separation Δ₀ between the unperturbed harmonic levels shifts more quickly, too. The Fermi resonance parameters, the coupling coefficient W and the intensity ratio R of the two Raman bands, decrease rapidly with pressure increasing, and the pressure at which Fermi resonance phenomenon disappears is much lower than that in pure liquid, especially in the solution whose molecules are of the same polarity. This article is valuable in the identification and the assignment of spectral lines under high pressure, as well as the study of high pressure effect, intermolecular interaction, and solvent effects in different cases, etc.     

幺正极限附近费米气体反常激发模式的涡旋

在幺正极限附近研究了处于旋转外势中费米气体的量子化涡旋动力学. 选取适当的试探波函数并利用含时变分法, 得到了小振幅涡旋运动方程及描述其反常激发模式的解. 详细讨论了在幺正极限附近的反常模式产生的条件. 结果显示系统囚禁外势的临界转动频率在幺正极限附近随粒子间相互作用参数的增加而变大, 而涡旋进动的周期则随着粒子间相互作用参数的增加而减小. 关键词： 费米气体 涡旋 幺正极限     

二元溶液中基频拉曼散射系数随浓度变化对费米共振的影响

在二硫化碳(CS₂)和苯(C₆H₆)的二元溶液中,随着相对体积浓度而变化,C₆H₆的基频ν_１(992 cm-1) 的拉曼散射系数随浓度减小而增加,而CS₂的基频ν₁(656 cm-1)的拉曼散射系数则随浓度增加而增加。文章测量了这二元溶液相对不同体积浓度的拉曼光谱。结果表明,尽管CS₂和C₆H₆的基频ν₁的强度都随着浓度变化而发生较大变化,但C₆H₆的基频ν₁对其参与的ν₁+ν₆～ν₈费米共振几乎没有影响,而CS₂的基频ν₁强度的变化不仅对ν₁～2ν₂费米共振产生较大影响,还使基频ν₂发生变化。文章给出了实验结果,并用Bertran费米共振理论和群论给予了解释。     

磁场中非广延相对论费米系统的统计性质

基于广义外势中的非广延统计理论,运用理论解析与数值模拟方法,研究磁场中非广延极端相对论费米气体的热力学性质,给出总能、热容量、化学势的解析式,分析非广延参数、极端相对论效应、磁场及温度对系统热力学性质的影响机理.研究显示,非广延参数不仅对热力学性质有直接的影响,而且也影响着磁场的物理效应. 随温度的升高,非广延参数及磁场对热力学性质的影响均被放大.极端相对论效应对化学势及热容量有特别显著的影响.     

硬球势中相对论费米气体的热力学性质

用量子统计与数值模拟相结合的方法,在广义外势中相对论费米系统的热力学量的基础上,研究硬球势中相对论费米气体的热力学性质.得到了考虑相对论效应时系统的内能和热容量的解析表达式,分析了相对论效应对内能和热容量的影响.研究表明:与非相对论比较,相对论费米气体的内能和热容量更高;相对论特征量越大,热容量的转折温度越低;随着温度的升高,特征量越大,内能就越大.