理想费米气体在n维势阱中的空间分布与有效囚禁范围（英文）

在Thomas-Fermi半经典近似适用条件下,求得了理想费米气体在n维广义幂律势阱中的态密度,进而研究了粒子数密度的空间分布,内能,热容量的空间变化以及等效化学势的一级近似.定义了绝对零度下的特征长度,求出了理想费米气体在n维广义幂律势阱中的有效囚禁范围.利用两个例子,揭示了理想费米气体的有效囚禁范围与外势形式,粒子数,粒子质量以及势场圆频率的依赖关系.     

囚禁弱相互作用玻色气体的势场优化准则

根据Thomas-Fermi近似,在基于最小动量态上玻色-爱因斯坦凝聚的前提下,研究了囚禁弱相互作用玻色气体势场的最优化问题.导出了指数吸引势阱中有效势场和粒子数极限判据,粒子数给定时,可由此判据求出所需势场强度;势场强度给定时,可由此判据求出粒子数极限.根据吸引相互作用系统的稳定性以及求出的排斥相互作用的最大粒子数极限,结合有效势场判据,分别给出了囚禁吸引和排斥相互作用玻色气体时,势场强度的最佳取值范围. 关键词： 玻色-爱因斯坦凝聚 弱相互作用 粒子数极限 势场强度     

原子激射器的空间有效增益范围

求出了γ维空间中理想玻色气体的态密度,采用Thomas-Fermi近似,导出了γ维广义幂律势阱中粒子数密度的空间分布.在此基础上,求出了原子激射器的空间有效增益范围(即γ维势阱中玻色-爱因斯坦凝聚的空间有效范围),并对其产生影响的相关因素进行了讨论.     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC).导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响.以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合.     

谐振子势阱囚禁玻色气体的玻色-爱因斯坦凝聚

基于Thomas-Fermi半经典近似方法研究了谐振子势阱约束下任意维理想玻色气体的玻色-爱因斯坦凝聚(BEC)．导出了玻色气体的BEC转变温度、基态粒子占据比例、内能和热容量等物理量的解析表达式,讨论了空间维度和谐振子势阱的影响．以二维和三维玻色系统为例,数值计算了上述热力学量,并与解析结果进行了对比,二者获得了较好的吻合．     

量子Generalized Reed-Solomon码

构造出了一族量子纠错码,这族码具有参数［［n,n-2k,k+1］］_q,是q维量子系统上的码,q是任意素数的幂.这族码的最小距离达到了理论上限,因此,以码距来说,它是最优的.证明了当2≤n≤q或者q²-q+2≤n≤q²时,码都是存在的. 关键词： 量子Generalized Reed-Solomon码 量子MDS码 量子纠错码 量子信息     

低维俘获原子的玻色-爱因斯坦凝聚中的有限粒子数效应

基于Thomas-Fermi近似,通过对配分函数的高温展开确定了体系的有效态密度，得到了在忽略相互作用下，低维受俘获原子玻色爱因斯坦凝聚的临界温度,并计算出了临界温度附近体系的比热容随温度的变化行为.研究结果表明：二维情况下，体系的比热容c正比于T²;而在一维情况下，c随温度呈线性增加. 关键词： 玻色-爱因斯坦凝聚 有限粒子数 低维束缚势 Thomas-Fermi近似     

强度应力干涉下多态多系统的可靠性研究

基于多元随机分析以及统计物理,建立了在系统强度与应力干涉下具有初始失效的多个状态以及多个相依子系统的可靠性模型. 在条件序列统计量的定义下推导了系统随机强度向量的概率密度函数;考虑各个子系统内零部件间的相干性,给出了不同结构的系统可靠性评估,将任意干涉系统可靠性表示为所有(n－i+1)/n(1≤i≤n)型冗余系统可靠性的线性组合. 为验证模型的有效性,基于二维Pareto分布给出了一个工程上的实例分析. 关键词： 干涉系统 可靠性 应力强度 条件序列统计     

数值方法研究谐振子势阱和磁场中的带电荷玻色气体

采用数值方法研究了谐振子势阱囚禁带电荷理想玻色气体在磁场中的热力学行为.数值计算结果表明,相变温度随着外加磁场的增加而减小,磁化强度和磁化率与系统温度和外加磁场有关.数值方法修正了托马斯-费米近似,同时极大地提高了计算的效率和精度.     

双δ激光脉冲作用下Paul阱中单离子的规则与混沌运动

考虑赝势近似下囚禁于Paul阱中的单离子与双δ脉冲型周期势相互作用系统的规则与混沌运动.应用积分方程方法得到系统的经典运动精确解,通过数值方法作出相空间轨道图和平均能量的时间演化曲线.结合分析与数值结果,发现两个有趣的结论.即在离子与单δ脉冲作用出现共振失稳的情形,在双δ脉冲作用下却出现了稳定的规则运动;离子随着双δ脉冲中两个脉冲之间的时间间隔减小而由规则运动转为混沌运动,其平均能量扩散的快慢与混沌运动的混乱程度相关.还研究了系统的共振失稳,发现通过 关键词： 双δ脉冲 囚禁离子 精确解 混沌     

Splitting between quadrupole modes of dilute quantum gas in a two-dimensional anisotropic trap

We consider quadrupole excitations of quasi-two-dimensional interacting quantum gas in an anisotropic harmonic oscillator potential at zero temperature. Using the time-dependent variational approach, we calculate a few low-lying collective excitation frequencies of a two-dimensional anisotropic Bose gas. Within the energy weighted sum-rule approach, we derive a general dispersion relation of two quadrupole excitations of a two-dimensional deformed trapped quantum gas. This dispersion relation is valid for both statistics. We show that the quadrupole excitation frequencies obtained from both methods are exactly the same. Using this general dispersion relation, we also calculate the quadrupole frequencies of a two-dimensional unpolarized Fermi gas in an anisotropic trap. For both cases, we obtain analytic expressions for the quadrupole frequencies and the splitting between them for arbitrary value of trap deformation. This splitting decreases with increasing interaction strength for both statistics. For a two-dimensional anisotropic Fermi gas, the two quadrupole frequencies and the splitting between them become independent of the particle number within the Thomas-Fermi approach. Received 21 September 2001 and Received in final form 9 December 2001     

三维简谐势阱中玻色-爱因斯坦凝聚的边界效应

在定义特征长度的基础上,应用Euler–MacLaurin公式,研究了理想玻色气体在三维简谐势阱中玻色-爱因斯坦凝聚的边界效应.结果表明:粒子的凝聚分数由于有限尺度和有限粒子数效应而减小,修正的凝聚分数和凝聚温度由于边界效应存在一个极大值,选择优化的最佳势阱参数,可以有效提高凝聚分数和凝聚温度;热容量的跃变存在边界效应和粒子数效应,选择合理的势阱参数时,热容量的跃变存在一个极小值.导出了简谐势阱中有限理想玻色气体的状态方程,揭示了压强的各向异性(或各向同性)取决于简谐势频率的各向异性(或各向同性).     

Josephson oscillation of a superfluid Fermi gas

Using the complete numerical solution of a time-dependent three-dimensional mean-field model we study the Josephson oscillation of a superfluid Fermi gas (SFG) at zero temperature formed in a combined axially-symmetric harmonic plus one-dimensional periodic optical-lattice (OL) potentials after displacing the harmonic trap along the axial OL axis. We study the dependence of Josephson frequency on the strength of the OL potential. The Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti et al. [Science 293, 843 (2001)] for a Bose-Einstein condensate and of the experiment of Pezzè et al. [Phys. Rev. Lett. 93, 120401 (2004)] for an ideal Fermi gas. We demonstrate a breakdown of Josephson oscillation in the SFG for a large displacement of the harmonic trap. These features of Josephson oscillation of a SFG can be tested experimentally.     

Crossover from Quantum to Boltzmann Statistics for Free Particles in a Single Harmonic Trap

With invoking analytical formulae in number theory and numerical calculations, we calculate the number of microstates in microcanonical ensemble for free particles in a single harmonic trap which in whole space defines a thermodynamic system but not a spatially homogeneous one. Once the number of excitation quanta m is larger than the square of the particle number N ² as m⪰O(N ²) when N≫1, the number of microcanonical microstates for an ideal, harmonically trapped Bose or Fermi gas gradually converge to the Boltzmann microcanonical microstates for the classical particles with a proper consideration of the indistinguishability.     

Optical probing of Eu ions confined in an RF trap

The Eu ions confined in an RF quadrupole trap, has been optically detected. Using a tunable dye laser which is pumped by a Nd-YAG pulsed laser system, the resonance ⁹S₄^9S_4–6p _3/2, J = 5 transition of the Eu ions have been excited and the resulting fluorescence to the metastable ⁹D_4-6^9D_{4-6} state has been detected. In preparation to determine the ground-state hyperfine splitting of the odd isotopes we found the optimum trapping operating point. We have also observed a number of instabilities inside the region of the stability for an ideal trap. These non-linear resonances arise from higher-order contributions to the ideal quadrupole potential.     

Critical temperature of Bose-Einstein condensation for weakly interacting bose gas in a potential trap

It has been a long history to study Bose-Einstein condensation (BEC) of weakly in-teracting Bose gas, and several theoretical models have been developed to research uni-form and weakly interacting Bose gas. Ref. [1] summarized all of these models and the corresponding results, which gave a derivation of critical temperature from ideal case 1/30Tc c n,?T = α (1) with a wide spread of parameter c from 0.7 to 2.33, where α is the scattering length of s wave and n is atom number density. Due…     

Collective excitations of a degenerate Fermi vapour in a magnetic trap

We evaluate the small-amplitude excitations of a spin-polarized vapour of Fermi atoms confined inside a harmonic trap. The dispersion law is obtained for the vapour in the collisional regime inside a spherical trap of frequency , with n the number of radial nodes and the orbital angular momentum. The low-energy excitations are also treated in the case of an axially symmetric harmonic confinement. The collisionless regime is discussed with main reference to a Landau-Boltzmann equation for the Wigner distribution function: this equation is solved within a variational approach allowing an account of non-linearities. A comparative discussion of the eigenmodes of oscillation for confined Fermi and Bose vapours is presented in an Appendix. Received 23 February 1999 and Received in final form 21 April 1999     

The universal sound velocity formula for the strongly interacting unitary Fermi gas

Due to the scale invariance,the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas.For example,the virial theorem between pressure and energy density of the ideal gas P=2E/3V is still satisfied by the unitary Fermi gas.This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation.For comparison,the sound velocities for the ideal Boltzmann,Bose and Fermi gas are also given.Quite interestingly,the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.     

Quantum information entropies of ultracold atomic gases in a harmonic trap

The position and momentum space information entropies of weakly interacting trapped atomic Bose–Einstein condensates and spin-polarized trapped atomic Fermi gases at absolute zero temperature are evaluated. We find that sum of the position and momentum space information entropies of these quantum systems containing N atoms confined in a D( ≤ 3)-dimensional harmonic trap has a universal form as S_t^(D) = N(a D - b lnN) S_\mathrm{t}^{(D)} = N(a D - b \ln N) , where a ≃ 2.332 and b = 2 for interacting bosonic systems and a ≃ 1.982 and b = 1 for ideal fermionic systems. These results obey the entropic uncertainty relation given by Beckner, Bialynicki-Birula and Myceilski.