济宁市1999—2000学年度第一学期期末统一考试高三数学试题

本试卷分第Ⅰ卷 (选择题 )和第Ⅱ卷 (非选择题 )两部分 .共 150分 .考试时间 12 0分钟 .第Ⅰ卷(选择题 ,共 60分 )参考公式三角函数的积化和差公式 :ｓｉｎαｃｏｓβ =12 [ｓｉｎ(α β) ｓｉｎ(α - β) ] ,ｃｏｓαｓｉｎβ =12 [ｓｉｎ(α β) -ｓｉｎ(α - β) ] ,ｃｏｓαｃｏｓβ =12 [ｃｏｓ(α β) ｃｏｓ(α - β) ] ,ｓｉｎαｓｉｎβ =- 12 [ｃｏｓ(α β) -ｃｏｓ(α - β) ] ;正棱台、圆台的侧面积公式 :Ｓ台侧 =12 (ｃ′ ｃ)ｌ ,其中ｃ′ ,ｃ分别表示上、下底面周长 ,ｌ表示斜高或母线长 ;台体的体积公式 :Ｖ台体 =13…     

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.     

An Enriched ^40K Source for Atomic Cooling

We have developed an enriched ⁴⁰K source used in ⁴⁰K--⁸⁷Rb atomic mixture cooling experiment. The enriched ⁴⁰K source is a home-made dispenser which releases ⁴⁰K atoms by the redox reaction between ⁴⁰K enriched KCl and calcium. It is efficient and easy to be made and used. We collect 10⁷ ～10^{8 40}K atoms in collection magneto-optical trap. With this dispenser, we perform a quantum degenerate Fermi gas experiment.     

基于非对称场流分离技术分离表征小米淀粉

基于非对称场流分离技术耦合多角度激光光散射检测器和示差折光检测器,建立了分离表征小米淀粉的方法。研究了进样量、交叉流流速、半衰期（t_1/2）、载液离子强度和pH值对小米淀粉分离效果的影响;考察了该方法的重现性;探究了小米淀粉分子结构。结果表明,在进样体积为50 μL、进样质量浓度为0.50 g/L、交叉流流速为1.2 mL/min、t_1/2=3 min、载液为10 mmol/L pH 7.00 NaNO₃（含3 mmol/L NaN₃）的条件下,小米淀粉分离效果最佳。该方法具有良好的重现性,得到的小米淀粉的回转半径相对标准偏差为3.4%、摩尔质量相对标准偏差为7.0%。     

电磁诱导透明介质中探测场量子噪声特性的实验研究

利用平衡零拍探测测量电磁诱导透明(EIT)介质中探测场的正交振幅和正交相位噪声谱。在平衡零拍探测系统中通过调节压电陶瓷来改变本振光的光程从而改变本振光与探测光的相对相位,进而测量不同相位对应的探测光的噪声分量。实验中电磁诱导透明介质中探测光与耦合光耦合导致探测光噪声的增大,发现在耦合光不同失谐下对探测光不同正交分量引入的额外噪声是不同的,同时得到了探测光噪声与耦合光功率及分析频率的关系。     

摄像机镜头畸变的一种非量测校正方法

为了减少噪声对摄像机镜头畸变的校正结果带来的影响,提出了一种校正摄像机镜头畸变的非量测方法.先找出由直线畸变而成的曲线,再用直线段连接每条曲线的两个端点形成一些闭合曲线.把它们的面积平方和定义为畸变测度,并用遗传算法搜索畸变测度的最小值.以此得到畸变参量.计算表明,该畸变测度具有较好的抗噪声能力,而遗传算法能避免收敛于局部极小值,减少了矫正图像的均方根误差.实验表明,对多幅图像分别和联合校正,相应矫正图像之间的均方根误差较小,计算和实验郜表明该校正方法具有良好的稳健性.     

利用PPKTP晶体产生真空压缩态及其Wigner准概率分布函数的量子重构

通过光学腔内置周期极化磷酸氧钛晶体的连续光学参量振荡器,以532nm光场为抽运场,产生1064nm的真空压缩态光场,利用平衡零拍探测技术得到3.41dB的实测压缩度,并采用量子层析技术重构出真空压缩态光场在相空间的Wigner准概率分布函数. 关键词： 真空压缩态光场 光学参量振荡器 量子层析 Wigner准概率分布函数     

Evaporative cooling of 87Rb atoms into Bose-Einstein condensate in an optical dipole trap

We create a Bose-Einstein condensate(BEC) of 87Rb atoms by runaway evaporative cooling in an optical trap.Two crossed infrared laser beams with a wavelength of 1064 nm are used to form an optical dipole trap.After precooling the atom samples in a quadrupole-Ioffe configuration(QUIC) trap under 1.5 μK by radio-frequency(RF) evaporative cooling,the samples are transferred into the center of the glass cell,then loaded into the optical dipole trap with 800 ms.The pure condensate with up to 1.5×105 atoms is obtained over 1.17 s by lowering the power of the trap beams.     

Experimental Observation of Spin-Exchange in Ultracold Fermi Gases

We experimentally study the spin exchange collision in ultracold~(40) K Fermi gases. The quadratic Zeeman shift,trap potential and temperature of atomic cloud will influence on the spin changing dynamics. Dependences of the spin components populations on the external bias magnetic field, the optical trap depth and the temperature of atomic cloud are experimentally investigated. The spin exchange from the initial states to the final state are observed for different initial states. This work shows an interesting process of reaching equilibrium by redistribution among the spin states with the spin exchange collision in an ultracold large-spin Fermi gas.     

大深度任意剖面形状光栅的模式理论和RTCM递推算法 *

采用模式理论和反射透射系数阵 (简记为RTCM)的递推算法 ,计算了任意偏振态的平面波从任意方向入射到大深度任意剖面形状的光栅中的衍射 .该方法物理概念清楚 ,算法简洁 ,计算速度快 ,算法稳定收敛 .把这种算法与R -矩阵算法和增强透射矩阵算法在计算准确度、计算稳定性和计算速度方面进行了比较 .