An uncertainty relation for joint position-momentum measurements

It is shown that the lower bound in the uncertainty relation for joint position-momentum measurements is twice as large as that in the usual Heisenberg uncertainty principle for separate measurements.     

Heisenberg's uncertainty principle

Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and momentum distributions in any quantum state; for the inaccuracies of any joint measurement of these quantities; and for the inaccuracy of a measurement of one of the quantities and the ensuing disturbance in the distribution of the other quantity. Whilst conceptually distinct, these three kinds of uncertainty relations are shown to be closely related formally. Finally, we survey models and experimental implementations of joint measurements of position and momentum and comment briefly on the status of experimental tests of the uncertainty principle.     

蒙特卡罗方法评定峰值检波器标定不确定度北大核心CSCD

针对高功率微波(HPM)脉冲测试用峰值检波器标定不确定度评估中测量函数非显式,直接测量量与被测量间概率分布传递困难等问题,研究建立了蒙特卡罗分析方法(MCM),利用有限带宽S参数网络时域响应计算原理建立了检波器标定系统的时域仿真模型,模型包含标定系统各微波器件S参数、检波电压、监测峰值功率等直接测量量,以及微波脉冲反射、叠加及传输延迟等物理过程。根据MCM原理对模型中各直接测量量引入特定分布的随机误差,通过重复计算,获得了检波器标定曲线的不确定度及其概率分布。     

Use of diffuse reflections in tunable diode laser absorption spectroscopy: implications of laser speckle for gas absorption measurements

The use of diffusely scattering materials as a means of eliminating interference fringes has been investigated. Their use introduces laser speckle that can contribute a random, rather than periodic, uncertainty to gas measurements. We have established a method for quantifying the uncertainty due to speckle and investigated ways of reducing it. We characterised the speckle at 823 nm allowing the use of low-cost CCD cameras. We have tested the principle of the model by making gas absorption measurements on the 1650-nm methane absorption line using wavelength-modulation spectroscopy, for which preliminary results are presented. PACS 42.62.Fi; 42.25.Hz; 42.30.Ms     

Non-incremental interferometric displacement measurement using a laser Doppler sensor with phase coding

The inspection of fast rotating objects with rough surfaces is an important task in the emerging field of process control. However, this is challenging since fast and non-contact inspection techniques with a measurement uncertainty in the nanometer range are often required. We present a novel optical sensor allowing non-incremental interferometric displacement measurement of moving solid state objects with rough surfaces. It features three wavelength coded interference fringe systems which are superposed slightly tilted. The displacement is determined by evaluating the phase shift between the resulting scattered light signals. Experimentally, a measurement uncertainty of 660 nm was obtained. This displacement uncertainty is independent of the lateral object velocity in principle. Due to this unique feature, the sensor can be utilized advantageously for precise displacement and vibration measurements of high speed objects as demonstrated by vibration measurements at a turbo pump shaft rotating with 48 000 rpm.     

Preparation-limited predictions in Einstein-Podolsky-Rosen experiments

It is shown that unavoidable uncertainties arising from the experimental conditions in which systems are prepared for Einstein-Podolsky-Rosen experiments severely limit the possibilities for prediction. In the example originally proposed by EPR, time measurements are necessary for precise position predictions. If the preparation is designed to make the timing errors negligible, the parameters chosen for the preparation fix minimum uncertainties in the predictions leaving the observer no choice in the matter. In the case of correlated spin measurements, the preparation leaves the observer no control over the effect of the detector on the particles; the uncertainty of the previous condition of any one particle is so large that no (classical) prediction of the response of another detector is possible. Thus, there are as yet no proposed experiments which satisfy the conditions required by EPR—i.e., precise predictions which violate the uncertainty principle.     

Limiting temporal and spectral resolution in spectroscopy and microscopy of coherent Raman scattering with chirped ultrashort laser pulses

Chirped ultrashort light pulses offer new options for coherent nonlinear spectroscopy and microscopy. We show here that the temporal resolution of spectroscopy and microscopy based on coherent anti-Stokes Raman scattering (CARS) can be smoothly tuned within a broad range, with upper and lower bounds of this range controlled by the pump and probe pulse durations. The spectral resolution of CARS spectroscopy and microscopy is analyzed as a function of the duration and chirp of the pump pulses. Pulses with a periodic phase modulation can provide the limiting spectral resolution of the CARS technique, corresponding to the lower bound of uncertainty in spectral measurements, dictated by the uncertainty principle.     

Path integrals, the ABL rule and the three-box paradox

The three-box problem is analysed in terms of virtual pathways, interference between which is destroyed by a number of intermediate measurements. The Aharonov-Bergmann-Lebowitz (ABL) rule is shown to be a particular case of Feynman's recipe for assigning probabilities to exclusive alternatives. The ‘paradoxical’ features of the three box case arise in an attempt to attribute, in contradiction to the uncertainty principle, properties pertaining to different ensembles produced by different intermediate measurements to the same particle. The effect can be mimicked by a classical system, provided an observation is made to perturb the system in a non-local manner.     

Effects of Hawking Radiation on the Entropic Uncertainty in a Schwarzschild Space‐Time

The Heisenberg uncertainty principle describes a basic restriction on an observer's ability of precisely predicting the measurement of a pair of noncommuting observables, and virtually is at the core of quantum mechanics. Herein, the aim is to study the entropic uncertainty relation (EUR) under the background of a Schwarzschild black hole and its control. Explicitly, dynamical features of the measuring uncertainty via entropy are developed in a practical model where a stationary particle interacts with its surrounding environment while another particle—serving as a quantum memory reservoir—undergoes free fall in the vicinity of the event horizon of the Schwarzschild space‐time. It shows higher Hawking temperatures would give rise to an inflation of the entropic uncertainty on the measured particle. This is suggestive of the fact the measurement uncertainty is strongly correlated with degree of mixing present in the evolving particles. Additionally, based on information flow theory, a physical interpretation for the observed dynamical behaviors related with the entropic uncertainty in such a genuine scenario is provided. Finally, an efficient strategy is proposed to reduce the uncertainty by non‐tracing‐preserved operations. Therefore, our explorations may improve the understanding of the dynamic entropic uncertainty in a curved space‐time, and illustrate predictions of quantum measurements in relativistic quantum information sciences.     

浅析量子力学中的不确定性原理

德国物理学家海森伯在1927年提出的不确定性原理,包括两力学量间的不确定性原理和能量与时间的不确定性原理,它的提出意味着量子力学不仅有了完整的数学形式,而且有了合理的理论解释.本文尝试通过对不确定性原理的创立背景、过程、应用等来对这一原理做简要介绍,特别强调了科学讨论在科学发展中的作用.     

Photoassociation of cold Ca atoms

We present the first measurement of a photoassociative spectrum of an alkaline earth element near the dissociation limit. The observed spectrum of Ca2 formed from cold atoms shows the regular vibrational series with the characteristic spacing of the 1/R3 asymptotic potential. The interpretation is in principle simplified compared to previous measurements on alkali metals by the nondegenerate ground state and the missing hyperfine structure of 40Ca. As an example, we derive the natural decay rate of the excited atomic 4p 1P1 state from the positions of the observed vibrational and rotational resonances with reduced uncertainty compared to previous measurements.     

Entropic formulation of uncertainty relations for successive measurements

An entropic formulation of uncertainty relations is obtained for the case of successive measurements. The lower bound on the overall uncertainty, that is obtained for the case of successive measurements, is shown to be larger than the recently derived Deutsch-Partovi lower bound on the overall uncertainty in the case of distinct measurements.     

Uncertainty and complementarity in axiomatic quantum mechanics

In this work an investigation of the uncertainty principle and the complementarity principle is carried through. A study of the physical content of these principles and their representation in the conventional Hilbert space formulation of quantum mechanics forms a natural starting point for this analysis. Thereafter is presented more general axiomatic framework for quantum mechanics, namely, a probability function formulation of the theory. In this general framework two extra axioms are stated, reflecting the ideas of the uncertainty principle and the complementarity principle, respectively. The quantal features of these axioms are explicated. The sufficiency of the state system guarantees that the observables satisfying the uncertainty principle are unbounded and noncompatible. The complementarity principle implies a non-Boolean proposition structure for the theory. Moreover, nonconstant complementary observables are always noncompatible. The uncertainty principle and the complementarity principle, as formulated in this work, are mutually independent. Some order is thus brought into the confused discussion about the interrelations of these two important principles. A comparison of the present formulations of the uncertainty principle and the complementarity principle with the Jauch formulation of the superposition principle is also given. The mutual independence of the three fundamental principles of the quantum theory is hereby revealed.     

Incorporation of generalized uncertainty principle into Lifshitz field theories

In this paper, we will incorporate the generalized uncertainty principle into field theories with Lifshitz scaling. We will first construct both bosonic and fermionic theories with Lifshitz scaling based on generalized uncertainty principle. After that we will incorporate the generalized uncertainty principle into a non-abelian gauge theory with Lifshitz scaling. We will observe that even though the action for this theory is non-local, it is invariant under local gauge transformations. We will also perform the stochastic quantization of this Lifshitz fermionic theory based generalized uncertainty principle.     

DONAR: a computer processing system to extend ultrasonic pulse-echo testing

A dedicated general purpose digital computer has been built on the principle of a sampled-data system to run an ultrasonic subsystem under programmed control. A most significant application is the ability to extract a signal from an interfering background. As illustrated in the paper, a 1 mm diameter transducer was used to measure the diameter of a 2.5 mm OD plastics tube with 0.4 mm wall thickness. Echoes from all four surfaces were displayed and the measurements indicated an uncertainty of less than 0.1 mm.     

Quantum theory and Einstein's general relativity

We discuss the meaning and prove the accordance of general relativity, wave mechanics, and the quantization of Einstein's gravitation equations themselves. Firstly, we have the problem of the influence of gravitational fields on the de Broglie waves, which influence is in accordance with Eeinstein's weak principle of equivalence and the limitation of measurements given by Heisenberg's uncertainty relations. Secondly, the quantization of the gravitational fields is a quantization of geometry. However, classical and quantum gravitation have the same physical meaning according to limitations of measurements given by Einstein's strong principle of equivalence and the Heisenberg uncertainties for the mechanics of test bodies.     

Spatial imaging of the H2(+) vibrational wave function at the quantum limit

We experimentally obtained a direct image of the nuclear wave functions of H(2)(+) by dissociating the molecule via electron attachment and determining the vibrational state using the cold target recoil ion momentum spectroscopy technique. Our experiment visualizes the nodal structure of different vibrational states. We compare our results to the widely used reflection approximation and to quantum simulations and discuss the limits of position measurements in molecules imposed by the uncertainty principle.     

干涉法测量气体低压下声速的实验研究

介绍了干涉法测量气体声速的试验原理和变程干涉声速测量的实验系统,使用本套测量系统测得的气体声速的精度可达5×10-4。根据热力学原理,分析了气体声速与理想气体比定压热容之间的物理关系。在本套实验系统上测得了一批高精度的新环保制冷剂的气相声速数据,并可进一步确定其理想气体比定压热容.     

六面顶压机上常温高压超声测量的样品组装设计

 简要介绍了高压超声测试技术中样品组装的设计原则。设计了一套新的样品组装,并测量了纯Al和纯Cu在常温下的等温状态方程。实验结果表明,新的组装能够实现较理想的准静水压加载,同时也能够测试出良好的超声信号。分析了六面顶压机上常温超声测量的主要误差来源。