Weak measurements with a qubit meter

We derive schemes to measure the so-called weak values of quantum system observables by coupling of the system to a qubit meter system. We highlight, in particular, the meaning of the imaginary part of the weak values, and show how it can be measured directly on equal footing with the real part of the weak value. We present compact expressions for the weak value of single qubit observables and of product observables on qubit pairs. Experimental studies of the results are suggested with cold trapped ions.     

Nonperturbative theory of weak pre- and post-selected measurements

This paper starts with a brief review of the topic of strong and weak pre- and post-selected (PPS) quantum measurements, as well as weak values, and afterwards presents original work. In particular, we develop a nonperturbative theory of weak PPS measurements of an arbitrary system with an arbitrary meter, for arbitrary initial states of the system and the meter. New and simple analytical formulas are obtained for the average and the distribution of the meter pointer variable. These formulas hold to all orders in the weak value. In the case of a mixed preselected state, in addition to the standard weak value, an associated weak value is required to describe weak PPS measurements. In the linear regime, the theory provides the generalized Aharonov–Albert–Vaidman formula. Moreover, we reveal two new regimes of weak PPS measurements: the strongly-nonlinear regime and the inverted region (the regime with a very large weak value), where the system-dependent contribution to the pointer deflection decreases with increasing the measurement strength. The optimal conditions for weak PPS measurements are obtained in the strongly-nonlinear regime, where the magnitude of the average pointer deflection is equal or close to the maximum. This maximum is independent of the measurement strength, being typically of the order of the pointer uncertainty. In the optimal regime, the small parameter of the theory is comparable to the overlap of the pre- and post-selected states. We show that the amplification coefficient in the weak PPS measurements is generally a product of two qualitatively different factors. The effects of the free system and meter Hamiltonians are discussed. We also estimate the size of the ensemble required for a measurement and identify optimal and efficient meters for weak measurements. Exact solutions are obtained for a certain class of the measured observables. These solutions are used for numerical calculations, the results of which agree with the theory. Moreover, the theory is extended to allow for a completely general post-selection measurement. We also discuss time-symmetry properties of PPS measurements of any strength and the relation between PPS and standard (not post-selected) measurements.     

Strong entanglement criterion involving momentum weak values

In recent years weak values have been used to explore interesting quantum features in novel ways. In particular, the real part of the weak value of the momentum operator has been widely studied, mainly in connection with Bohmian trajectories. Here we focus on the imaginary part and its role in relation with the entanglement of a bipartite system. We establish an entanglement criterion based on weak momentum correlations, that allows to discern whether the entanglement is encoded in the amplitude and/or in the phase of the wave function. Our results throw light on the physical role of the real and imaginary parts of the weak values, and stress the relevance of the latter in the multi-particle scenario.     

QCD asymmetry and polarized hadron structure function measurement

It is shown that in hard processes with a single polarized particle contributions proportional to two-arguments distribution functions (parton correlation densities) can receive imaginary parts even from the Born subprocess. This results in large (not proportional to α_s) single asymmetries. Such an asymmetry is calculated in the process λN↑ → λX, which can serve as a good parton meter for the correlation densities.     

Steady-State Analysis of a Two-Mode Laser System with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

An inhomogeneously broadened two-mode laser system with cross-correlations between the real and imag- inary parts of quantum noise is considered. The Fokker-Planek equation of the system is derived by the phase-locking method. The steady-state probability distribution, the mean light intensity, the normalization autocorrelation function, and cross correlation function are calculated. The results indicate that： （i） The cross-correlation between the real and imaginary parts of quantum noise can cause the stationary probability distribution from one peak structure to two extrema structure when the laser system is operated above threshold; （ii） The cross-correlation between the real and imaginary parts of quantum noise enhance the light intensity fluctuation and decrease the laser output when the laser system is operated below or near threshold; （iii） The effect of the cross-correlation between the real and imaginary parts of quantum noise is very weak on the stationary properties when the laser system is operated far above threshold.     

Dielectrics with strong and weak processes of polarization relaxation

The relationships between electrical parameters of layers needed both for the transition from strong to weak relaxations and for when there are no extrema in the relation between frequency and the dielectric loss tangent and imaginary parts of dielectric permeability are determined using a model for a double-layered dielectric with the serial inclusion of strata. The literature data was analyzed, allowing us to discover heterogeneous materials with developing strong and weak relaxation polarization. Materials for which the mean time of relaxation for dielectric permeability and conductivity differ were found.     

基于离子交换条波导的生物溶液浓度传感研究

提出并实施了一种实验推定离子交换单模条波导折射率分布的新方法,给出扩散系数可用常量等效的离子交换条件,导出了条波导离子交换制备过程的两维扩散方程的一般解,拟合推定了离子交换条波导的折射率分布.多波长测试的折射率色散通过引入玻璃色散关系解决,样品测试中表征导模吸收损耗的传播常量虚部由KK变换确定.在此基础上,试制了光纤-条波导-光纤一体化传感器结构,验证实测了多种不同浓度的葡萄糖溶液,最低检测限为0.1 μM,实现了低浓度微量测试,验证了条波导传感机制的有效性.     

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当同时使用离子(或电子)回旋及中性束注入方式加热等离子体时,高能量粒子的能量分布函数一般应为尾部隆起(简称尾隆)分布。这种具有正能量梯度区域的分布函数更容易激发不稳定性,同时由于分布函数尾部隆起,在色散关系中引入了新的色散函数。主要研究了这种新色散函数的计算方法,结果表明:色散函数实部是关于原点对称的奇函数;而虚部则是关于纵轴对称的偶函数。色散函数的实部有2~4个极值点且极值点的位置与尾隆分布函数的能量梯度⊿有关、虚部有1~3个极值点但极值点位置与⊿无关。当其宗量趋于无穷大时,色散函数的值趋于零。当尾隆分布趋近于麦克斯韦分布时,用该方法计算的结果与色散函数表中给出的结果非常吻合。     

高能量粒子尾隆分布情况下的色散函数研究

当同时使用离子(或电子)回旋及中性束注入方式加热等离子体时,高能量粒子的能量分布函数一般应为尾部隆起(简称尾隆)分布。这种具有正能量梯度区域的分布函数更容易激发不稳定性,同时由于分布函数尾部隆起,在色散关系中引入了新的色散函数。主要研究了这种新色散函数的计算方法,结果表明：色散函数实部是关于原点对称的奇函数;而虚部则是关于纵轴对称的偶函数。色散函数的实部有2~4 个极值点且极值点的位置与尾隆分布函数的能量梯度Δ 有关、虚部有1~3 个极值点但极值点位置与Δ 无关。当其宗量趋于无穷大时,色散函数的值趋于零。当尾隆分布趋近于麦克斯韦分布时,用该方法计算的结果与色散函数表中给出的结果非常吻合。     

量热式激光能量计内外表面温差对测量结果的影响

从理论上研究了量热式激光能量计激光照射过程中和激光照射后内外表面温度时间关系．编制了计算机程序计算得到激光照射时间内以及激光停止照射后内外表面温度关系曲线．通过稳定的高温温度场加热试验件模拟激光照射量热式激光能量计内外表面温度的升温过程，通过迅速将试验件移离高温温度场模拟激光停止照射后量热式能量计内外表面温度的变化，并测量了量热式能量内外表面温度时间曲线．实验和理论研究结果相符，结果表明激光停止照射后，内外表面温度迅速趋近，由此引入的测量不确定度小于0．25％．     

Antiproton-deuteron annihilation at low energies

Recent experimental data obtained by the OBELIX collaboration on ˉpD and ˉp⁴ He total annihilation cross sections are analyzed. The combined analysis of these data with existing antiprotonic atom data allows, for the first time, the imaginary parts of the S-wave scattering lengths for the two nuclei to be extracted. The obtained values are: Im a^sc ₀= [−0.62 ± 0.02 stat) ± 0.04 (sys)] fm for ˉpD and Im a^sc ₀= [−0.36 ± 0.03 (stat)^+0.19 _−0.11 (sys)] fm for ˉp ⁴He. This analysis indicates an unexpected behaviour of the imaginary part of the ˉp-nucleus S-wave scattering length as a function of the atomic weight A: |Im a^sc ₀| (macr;pp) > |Im a^sc ₀| (ˉpD) > |Im a^sc ₀ (ˉp⁴ He). Received: 3 November 1999 / Revised version: 15 December 1999     

Crystal melting processes of propylene carbonate and 1,3-propanediol investigated by the reed-vibration mechanical spectroscopy for liquids

The melting of crystals is one of the most common and general phase transition phenomena.However, the mechanism of crystal melting is not well understood, and more experimental measurements and explorations are still needed.The mechanical spectra of propylene carbonate and 1,3-propanediol during the crystal melting processes are measured by the reed vibration mechanical spectroscopy for liquids(RMS-L) for the first time.The experimental results show that as the temperature increases, the real part of the complex Young modulus first decreases slowly, and then quickly drops to zero;meanwhile, its imaginary part increases slowly at first, then goes up and drops quickly to zero, showing a peak of internal friction.Preliminary analyses indicate that both the real and imaginary parts can present some characteristics of the melting process, such as the transition from the disconnected liquid regions to the connected liquid regions, that from the connected crystal regions to the disconnected crystal regions, and so on.In addition, the results show that the melting rate per unit volume of crystalline phase versus temperature satisfies the Arrhenius relation at the initial stage of melting, and deviates from this relation as the temperature increases to a certain value.Therefore, the RMS-L will provide an effective supplement for the further study of melting.     

Macroscopic response of the nuclear surface

The macroscopic surface response of a semi-infinite Fermi liquid is considered. On the basis of Landau's kinetic equation, a dispersion relation is derived for the free surface modes. In the limit of weak quasiparticle interaction we find a surface mode with a purely imaginary frequency. This mode is shown to be critically damped if the stiffness is given by the excess surface energy and the friction by the one-body wall formula. By assuming a correspondence with the quantum relation between dissipation rate and response function, the macroscopic surface response function is obtained. The results are applied to inelastic scattering of protons from nuclei. While the qualitative behavior of the nuclear response is reproduced by the semi-infinite model, the decrease with energy is too rapid.     

任意磁场位形下弱相对论等离子体的普遍色散关系

由相对论回旋动力论方程出发,推导出弱相对论非均匀等离子体的普遍色散关系。该色散关系可以适用于任意的磁场位形和任意有限频率。在色散关系中把带有速度平方项分母的奇异积分用等离子体漂移色散函数解析地表示出来,从而可以把这一结果用于较系统地解析或半解析地研究由弱相对论效应,磁场的梯度和曲率,回旋频移等共振驱动的各种微观不稳定性的性质。由于推导时考虑了温度各向异性的麦氏分布函数,因而可以直接推广并应用到损失锥非平衡分布的情况。文中还演示了它在低杂漂移不稳定性研究中的应用。由该色散关系出发,可以简捷并系统地得到Drake等人的结果。 关键词：     

The nuclear self-energy and related quantities in the semiclassical approximation

By using our recently developed semiclassical model for the imaginary part of the optical potential, we calculate here the polarization and correlation contributions to the real part via the dispersion relation. As underlying nonlocal mean-field potential, the semiclassical Hartree-Fock potential evaluated with the Gogny D1 effective interaction or the Perey-Buck potential is employed. With this full self-energy or second-order mass operator we calculate consistently depths, radial dependence and volume integrals of the single-particle potential, rearrangement energies and effective masses, the momentum distribution, mean free paths of a nucleon in a nucleus, and single-particle level densities. We obtain depths which are in excellent agreement with experiment including the Fermi anomaly: the effective mass exhibits a strong bump at the Fermi and the nuclear surface and the single-particle level density at the Fermi energy is enhanced by 65% yielding almost the correct average experimental value.     

从多波段图像中获取大气透过率的测量方法

提出了一种基于单帧多波段图像测量非气体吸收波段和弱气体吸收波段大气透过率的方法,可应用于相关光电工程中评估和修正大气衰减影响.首先,利用经过绝对辐射定标的图像采集设备获得辐射图像;其次,基于大气中图像退化光学模型与暗通道先验统计理论得到辐射图像暗通道对应的宽波段平均大气透过率;最后,结合特定波段消光系数和宽波段平均消光系数间的关系得到特定波段的大气透过率.实验对比分析表明:本文方法与能见度仪、激光雷达测量结果相关性较高,其中与能见度仪相比,相关系数在0.89和0.95之间,与激光雷达相比,相关系数在0.95和0.97之间;在1km近距离条件下与能见度仪、激光雷达测量结果平均相对偏差最高分别为9%和6%,在远距离条件下,与能见度仪测量结果相比,4km和6km平均相对偏差最高分别为15%和30%,与激光雷达测量结果相比,4km和6km平均相对偏差最高分别为9%和18%.     

Neutron ambient dose equivalent from 5 MeV/u 10,11B, 12,13C and 16,18O projectiles incident on a thick Al target

The neutron ambient dose equivalent has been measured from ¹⁰B, ¹¹B, ¹²C, ¹³C, ¹⁶O and ¹⁸O projectiles of energy 5 MeV/amu incident on a thick Al target at 0°, 30°, 60° and 90° with respect to the beam direction using a conventional dose equivalent meter. The calculated results obtained using previously reported empirical relations do not reproduce the experimental data. The results obtained from the PACE nuclear reaction code are closer to the experimental data as compared to the various empirical expressions. The ratio of the increase in the dose rates when the projectile is changed from the lighter to the heavier isotopes is fairly reproduced by most of the empirical formulations and the PACE code. A previously reported relation for the slope parameter is used to predict the directional distribution of the neutron dose for the projectiles used in this study. The calculated doses are lower than the experimental results in the forward directions but agree within the uncertainties at the backward directions. A new set of projectile-based parameters have been derived from the present experimental data which can be used in an empirical formulation.     

The Imaginary Parts of Two-Loop Self-Energy in ITF and RTF

The imaginary parts of φ⁴ two-loop self-energy are investigated in both imaginary and real time finite-temperature formalisms (ITF and RTF). The two results are showed to be different, their relation is obtained, and the physical interpretation is discussed respectively.     

Ultrasmall polarization rotation measurements via weak value amplification

We propose a framework to analyze weak measurements based on an angular version of the von Neumann measurement scheme, where the coupling between the system and the meter causes rotation of the measuring variable. We also discuss an experimental application of this theory in which measurements of weak optical activity and reflection-induced polarization rotation could be amplified in nearly two orders of magnitude. It can shed a new light on a great variety of physical chemistry, molecular biology and nanotechnology studies.     

Analytical properties of the mean field in many fermion systems

The importance of the dispersion relation linking the real and the imaginary parts of the mean field in many fermion systems is pointed out. General models are built for the imaginary part. The properties of the real part close to the Fermi level are discussed in relation with these models. Its analytical behaviour is determined by the analytical behaviour of the imaginary part in the same domain, but the numerical values can be strongly influenced by the large energy behaviour of the same quantity. The sensitivity upon the behaviour in the intermediate domain is described semiquantitatively. The nuclear matter case is briefly discussed. The generality of our results is pointed out.