二维带电自旋-1/2费米气体的磁性质

通过引入描述电荷-磁场和自旋-磁场相互作用竞争关系的自旋因子,研究了磁场和简谐势阱双重约束的二维带电自旋-1/2费米气体的磁性质.结果表明,当自旋因子很小时,系统显示出抗磁性,随着自旋因子的进一步增大,系统逐渐转变为顺磁性.自旋因子的临界值将磁化强度划分为抗磁性区和顺磁性区,临界值随磁场和温度的增大仅发生微小的改变.     

费米超流气体的非线性Landau-Zener 隧穿

在平均场近似下,通过对相平面和不动点的分析, 研究了非线性两能级系统中费米超流气体的Landau-Zener 隧穿现象. 研究发现,费米子间的相互作用能够显著地影响量子隧穿. 当相互作用参数c小于临界值c^*时,在绝热极限下隧穿仍然满足量子绝热定理, 而大于这一临界值时,量子绝热定理不再满足. 最后通过和线性情况比较,得到了c*时隧穿率与扫描速率间满足的指数关系.     

费米气体在光晶格中的自俘获现象及其周期调制

研究了一维光晶格中费米气体从BCS区过渡到unitarity区研究相图及周期调制现象. 通过调节散射长度与耠合系数对相图的影响, 发现在unitarity 区, 从约瑟夫振荡到振荡自俘获及振荡自俘获到自俘获, 存在耦合系数的临界值, 同时得到了临界耦合系数与散射长度的关系. 关键词： 费米气体 自俘获 周期调制     

费米超流气体在幺正极限区域的非线性Ramsey干涉

该文分别研究了在三种极限情况下费米超流气体在幺正极限区域的非线性Ramsey干涉图样的频率与系统参数之间的关系, 研究发现费米子间的相互作用以及双势阱间最低能量差对干涉图样的角频率有显著的影响. 通过数值模拟和理论分析, 得到了干涉图样的角频率和系统参数之间的关系, 发现数值和解析结果符合得很好.     

Thermodynamic properties of two-dimensional charged spin-1/2 Fermi gases

Based on the mean-field theory, we investigate the thermodynamic properties of the two-dimensional (2D) charged spin-1/2 Fermi gas. Landé factor g is introduced to measure the strength of the paramagnetic effect. There is a competition between diamagnetism and paramagnetism in the system. The larger the Landé factor, the smaller the entropy and specific heat. Diamagnetism tends to increase the entropy, while paramagnetism leads to the decrease of the entropy. We find that there exists a critical value of Landé factor for the transition point due to the competition. The entropy of the system increases with the magnetic field when g < 0.58. With the growth of paramagnetism, when g > 0.58, the entropy first decreases with the magnetic field, then reaches a minimum value, and finally increases again. Both the entropy and specific heat increase with the temperature, and no phase transition occurs. The specific heat tends to a constant value at the hightemperature limit, and it approaches to zero at very low temperatures, which have been proved by the analytical calculation.     

Francis Bitter and “Landau diamagnetism”

A forgotten paper by Francis Bitter on the diamagnetism of a quantum electron gas, published in 1930, is discussed. By an approximate method, later considered unsatisfactory, Bitter obtained a result qualitatively similar to the standard formula first established by Landau in the same year. Editor's note: This paper is intended as an historical note and is published in keeping with our policy of publishing such documentary material from time to time. 3 See, for example, the obituary in theNew York Times, July 27, 1967.     

强磁场中Fermi气体的稳定性及顺磁性

运用理论解析和数值模拟的方法,研究强磁场中Fermi气体在低温下的稳定性及顺磁性, 分析温度、磁场对稳定性及磁化率的影响.研究结果显示,强磁场引起系统稳定性的改变, 这种改变与温度有关,而温度对稳定性改变及磁化率的影响又与自由气体的化学势即粒子数密度有关. 当自由系统的化学势为偶数时,磁场弱化系统的稳定性,温度升高可降低系统的磁化率; 当自由系统的化学势为奇数时,磁场强化系统的稳定性,温度升高可增大系统的磁化率. 升高温度,可以弱化磁场对系统稳定性的影响;加强磁场,可以使得系统稳定性的改变发生振荡, 使系统磁化率的振荡中心下移.     

Fermi超流气体在unitarity区域和Bose-Einstein凝聚区域的自俘获现象研究米

在平均场理论和两模近似下,通过观察布居数差随时间的演化,以及布居数差的平均随非线性相互作用参数的变化,研究了对称双势阱以及势阱问高频调制时Fermi超流气体在unitarity区域和Bose-Einstein凝聚区域的自俘获现象．给出了出现自俘获现象的边界条件;发现高频调制在一定调制范围内使自俘获现象更容易实现．最后研究了初值对自俘获的影响,发现初值的绝对值︳s（O）︳的增加更有利于自俘获的实现．     

Fermi超流气体在unitarity区域和Bose-Einstein 凝聚区域的自俘获现象研究

在平均场理论和两模近似下,通过观察布居数差随时间的演化, 以及布居数差的平均随非线性相互作用参数的变化, 研究了对称双势阱以及势阱间高频调制时Fermi超流气体在unitarity区域和Bose-Einstein凝聚区域的自俘获现象. 给出了出现自俘获现象的边界条件;发现高频调制在一定调制范围内使自俘获现象更容易实现. 最后研究了初值对自俘获的影响, 发现初值的绝对值|s(0)|的增加更有利于自俘获的实现.     

匀强磁场与简谐势阱中的低维荷电自旋-1玻色气体

采用截断求和法和半经典近似,以二维理想玻色气体为例,研究了磁场和简谐势阱中低维荷电自旋-1玻色子的相变及磁性质．结果表明,电荷-磁场和自旋-磁场作用的竞争导致玻色-爱因斯坦凝聚临界温度随磁场的增大先略微上升后缓慢下降．截断求和法能够有效的改进半经典近似的不足．最后,讨论了磁化强度由抗磁性到顺磁性的转变及自旋因子临界值随磁场和温度的变化．     

Pseudogap phenomena in ultracold atomic Fermi gases

The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high Tc superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum sinmlator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high Tc superconductivity. One obstacle to the ultimate understand- ing of high Tc superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics comnnmity, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fuctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high Tc superconductivity.     

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.     

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．     

基于半经典近似研究费米气体的稳定性及顺磁性

基于半经典近似方法,给出重力场和强磁场共存下费米子的能谱.然后由泊松公式导出费米气体的热力学势函数.在此基础上,运用热力学关系式求解低温条件下系统的稳定性及磁化率的解析式,并通过数值模拟分析强磁场背景下重力场对稳定性及顺磁性的影响机制.     

Dark lump excitations in superfluid Fermi gases

We study the linear and nonlinear properties of two-dimensional matter-wave pulses in disk-shaped superfluid Fermi gases.A Kadomtsev-Petviashvili I(KPI) solitary wave has been realized for superfluid Fermi gases in the limited cases of Bardeen-Cooper-Schrieffer(BCS) regime,Bose-Einstein condensate(BEC) regime,and unitarity regime.Onelump solution as well as one-line soliton solutions for the KPI equation are obtained,and two-line soliton solutions with the same amplitude are also studied in the limited cases.The dependence of the lump propagating velocity and the sound speed of two-dimensional superfluid Fermi gases on the interaction parameter are investigated for the limited cases of BEC and unitarity.     

Spin-orbit coupling in Bose-Einstein condensate and degenerate Fermi gases

We review our recent experimental realization and investigation of a spin orbit （SO） coupled Bose Einstein condensate （BEC） and quantum degenerate Fermi gas. By using two counter-propagathlg Ranlan lasers and controlling the different frequency of two R,aman lasers to engineer the atom light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We, observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as halhnarks of SO coupling in a Fermi gas. To clearly reveal the, property of SO coupling Fermi gas, we also study the momentmn-resolved radio-frequency spectroscopy which characterizes the energy momentum dispersion and spin composition of the quantum states. We observe the change of errmion surfaces in different helieity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracoht Fermi gas.     

基于半经典近似研究费米气体的稳定性及顺磁性

基于半经典近似方法,给出重力场和强磁场共存下费米子的能谱.然后由泊松公式导出费米气体的热力学势函数.在此基础上,运用热力学关系式求解低温条件下系统的稳定性及磁化率的解析式,并通过数值模拟分析强磁场背景下重力场对稳定性及顺磁性的影响机制.     

强相互作用极化费米气体中涡旋束缚态的研究

涡旋态的研究对理解冷原子体系超流特性有很重要的价值. 文章在简要回顾涡旋态研究历史的基础上,介绍了文章作者近期在超冷极化费米气体中涡旋态的工作.通过应用平均场的方法,从理论上研究了强相互作用极化费米气中单个涡旋态的结构.发现在涡旋态核中,Andreev 束缚态的填充可引起一种量子相变.这就提供了一种新颖的探测Andreev 束缚态的方法,在冷原子物理中,可通过吸收成像方法来完成.进一步文章作者对涡旋态的核尺寸进行了研究,发现涡旋态的核尺寸随着体系极化程度的增加而变大.     

Rotating Fermi gases in an anharmonic trap

Motivated by recent experiments on rotating Bose-Einstein condensates, we investigate a rotating, polarized Fermi gas trapped in an anharmonic potential. We apply a semiclassical expansion of the density of states in order to determine how the thermodynamic properties depend on the rotation frequency. The accuracy of the semiclassical approximation is tested and shown to be sufficient for describing typical experiments. At zero temperature, rotating the gas above a given frequency Ω_DO leads to a ‘donut’-shaped cloud which is analogous to the hole found in two-dimensional Bose-Einstein condensates. The free expansion of the gas after suddenly turning off the trap is considered and characterized by the time and rotation frequency dependence of the aspect ratio. Temperature effects are also taken into account and both low- and high-temperature expansions are presented for the relevant thermodynamical quantities. In the high-temperature regime a virial theorem approach is used to study the delicate interplay between rotation and anharmonicity.     

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.