The effect of localization on interference. I. Calculated intensities for a feasible optical experiment

A simple geometry utilizing a laser-excited atomic beam as light source, and a nearby oscillating mirror, would permit the observation of a two-channel optical interference effect involving photons which can be localized predominantly in one channel by coincidence observations of the recoiling source atom. A sacrifice of the optimum conditions for photon interference is necessary even when photon localization in one channel is accomplished by an observation of the recoil atom. This necessity arises because the width of the slit defining the atomic beam, and with it the important optical source dimension, must be comparable to the optical wavelength to obtain the small uncertainty in initial total momentum needed for significant localization. Quantum mechanical calculations of the coincidence intensity and singles intensity as a function of mirror position are made for a source width of five quarter wavelengths and are compared to a classical optics calculation of the singles intensity. The coincidence intensity calculation, as expected, predicts a smaller interference effect than classical optics due to the photon localization. The singles intensity calculation also predicts the same reduction in the classical interference effect, as a consequence of the orthoganality of the final atom states.     

Timeless Configuration Space and the Emergence of Classical Behavior

The inherent difficulty in talking about quantum decoherence in the context of quantum cosmology is that decoherence requires subsystems, and cosmology is the study of the whole Universe. Consistent histories gave a possible answer to this conundrum, by phrasing decoherence as loss of interference between alternative histories of closed systems. When one can apply Boolean logic to a set of histories, it is deemed ‘consistent’. However, the vast majority of the sets of histories that are merely consistent are blatantly nonclassical in other respects, and further constraints than just consistency need to be invoked. In this paper, I attempt to give an alternative answer to the issues faced by consistent histories, by exploring a timeless interpretation of quantum mechanics of closed systems. This is done solely in terms of path integrals in non-relativistic, timeless, configuration space. What prompts a fresh look at such foundational problems in this context is the advent of multiple gravitational models in which Lorentz symmetry is not fundamental, but only emergent. And what allows this approach to overcome previous barriers to a timeless, conditional probabilities interpretation of quantum mechanics is the new notion of records—made possible by an inherent asymmetry of configuration space. I outline and explore consequences of this approach for foundational issues of quantum mechanics, such as the natural emergence of the Born rule, conservation of probabilities, and the Sleeping Beauty paradox.     

Analog of Formula of Total Probability for Quantum Observables Represented by Positive Operator Valued Measures

We represent Born’s rule as an analog of the formula of total probability (FTP): the classical formula is perturbed by an additive interference term. In this note we consider practically the most general case: generalized quantum observables given by positive operator valued measures and measurement feedback on states described by atomic instruments. This representation of Born’s rule clarifies the probabilistic structure of quantum mechanics (QM). The probabilistic counterpart of QM can be treated as the probability update machinery based on the special generalization of classical FTP. This is the essence of the Växjö interpretation of QM: statistical realist contextual and local interpretation. We analyze the origin of the additional interference term in quantum FTP by considering the contextual structure of the two slit experiment which was emphasized by R. Feynman.     

Many-body effect in the coincidence L3 and M3 photoelectron spectroscopy spectra of Cu metal

The coincidence L₃ and M₃ photoelectron spectroscopy (PES) main lines of Cu metal are calculated by a many-body theory. There is no peak-energy shift between the singles PES main line and the coincidence one. The asymmetric narrowing of the coincidence PES main line on the low kinetic energy (KE) side is very small. This is in accord with recent experimental findings. In Cu metal, the shakeup satellite intensity is small and the main-line satellite separation energy is much larger than the core–hole lifetime width. The interference via the final-state interaction is negligible. In the PES main line, the imaginary part of the self-energy by shakeup excitations, which is very small compared to the core–hole lifetime width, decreases very slowly in linear with photoelectron KE. The branching ratio of Auger decay of a single hole state then increases very slowly in linear with photoelectron KE so that the deviation of the coincidence PES main line from the singles one is very small. The 939 eV structure seen only in the coincidence L₃ PES spectrum of Cu metal is attributed to the enhancement of the inelastic peak of a smaller energy loss due to electrons of a smaller average emission depth measured in coincidence with the elastic Auger peak. The structure will not be enhanced in the singles PES spectrum. The background subtraction in the coincidence spectrum cannot be the same as that in the singles one. Such consideration is necessary before we can conclude about the asymmetric narrowing on the low KE side. A unique capability of APECS by which one can determine the photoelectron KE dependent part of the imaginary part of the self-energy is pointed out.     

两个独立全光纤多通道光子纠缠源的Hong-Ou-Mandel干涉

独立光子源的干涉是实现复杂量子体系应用(比如多光子纠缠态产生和量子隐形传态等)的核心技术.利用100 GHz密集波分复用技术,实现了1.55μm全光纤多通道独立纠缠光子源的Hong-Ou-Mandel干涉,在不去除暗符合(随机符合计数)的情况下,可见度为53.2%±8.4%,去除暗符合可见度可达到82.9%±5.3%.给出了关于色散位移光纤中基于自发四波混频过程产生的单光子光谱纯度严格的理论描述,模拟了抽运脉冲宽度和滤波器带宽对单光子光谱纯度的影响,并给出了理论上的最佳条件(最佳的抽运脉冲宽度为8 ps,高斯滤波器带宽为40 GHz及以下).在测量Hong-Ou-Mandel干涉之前,先测量了液氮冷却状态下的色散位移光纤关联光子源的符合和随机符合比率,在抽运功率为23μW的情况下,最大比率可以达到131.Hong-Ou-Mandel干涉在高精度光学测量、测量装置无关的量子密钥分配等应用中扮演着极为重要的角色.     

Playing with Planets,by Gerard 't Hooft

Open channels exist between the rows or planes of atoms in a crystal. In experiments with carefully defined beams of energetic ions it is possible to inject particles into these channels. There they travel with relative ease, being reflected back and forth between the channel walls by a correlated series of atomic collisions. The main types of experiment on this phenomenon are summarized and the classical theory is developed. Classical treatment is not adequate for light particles, such as electrons or positrons because their de Broglie wavelength is greater and a wave mechanical version is outlined in a form which is also suitable for describing protons. This confirms that for heavy particles classical theory can explain any experiments performed so far, but it is just possible that the interpretation of more precise proton experiments may require wave mechanics.     

Afshar’s Experiment Does Not Show a Violation of Complementarity

A recent experiment performed by S. Afshar [first reported by M. Chown, New Sci. 183:30, 2004] is analyzed. It was claimed that this experiment could be interpreted as a demonstration of a violation of the principle of complementarity in quantum mechanics. Instead, it is shown here that it can be understood in terms of classical wave optics and the standard interpretation of quantum mechanics. Its performance is quantified and it is concluded that the experiment is suboptimal in the sense that it does not fully exhaust the limits imposed by quantum mechanics.     

双量子点Aharonov-Bohm干涉系统输运性质的大偏离分析

由于电子的多体关联和量子相干性的联合作用, 双量子点Aharonov-Bohm 干涉系统中的电子输运过程隐含 内在的快、慢两条通道, 且通道之间的有效耦合强度可以通过磁通调控. 但是, 这一非平庸的内在性质, 在通常的稳态输运电流中不能得以反映. 本文利用在研究非平衡动力学相变中所发展的大偏离方法, 对该输运系统中的电子动力学路径做大偏离统计分析. 结果显示, 以上内在性质将诱导出路径空间中清晰的动力学相变行为.     

没有薛定谔猫态

新近有个超导量子干涉器件的实验,使澄清量子力学基本解释有了可能.分析此实验和相关实验之后,作出断言,抽象量子态没有信息,且波函数是个尚待观察者要去做的实验的几率幅.故用常用术语将量子态或波函数过分具体化,恐怕要招致误解.因而从本质上讲,薛定谔猫态是不存在的.     

Quantum Correlations Evolution Asymmetry in Quantum Channels

It was demonstrated that the entanglement evolution of a specially designed quantum state in the bistochastic channel is asymmetric. In this work, we generalize the study of the quantum correlations, including entanglement and quantum discord, evolution asymmetry to various quantum channels. We found that the asymmetry of entanglement and quantum discord only occurs in some special quantum channels, and the behavior of the entanglement evolution may be quite different from the behavior of the quantum discord evolution. To quantum entanglement, in some channels it decreases monotonously with the increase of the quantum channel intensity. In some other channels, when we increase the intensity of the quantum channel, it decreases at first, then keeps zero for some time, and then rises up. To quantum discord, the evolution becomes more complex and you may find that it evolutes unsmoothly at some points. These results illustrate the strong dependence of the quantum correlations evolution on the property of the quantum channels.     

用于符合测量的多通道符合计数器

符合测量在量子光学实验中有着重要的应用,它可以用于测量纠缠光子对和单光子干涉等实验。在使用过程中,经常用到三通道或更多通道的符合测量,这种情况下简单的门电路无法满足使用要求,而现场可编程门阵列(FPGA)为实现低成本、小体积的多通道符合计数系统提供了解决方案。同时,基于FPGA的多通道符合计数系统还可以提供ns精度的符合分辨时间,避免本底光噪声对探测器的影响,从而有效抑制偶然符合,进一步提高了多通道符合计数系统的性能。本文介绍了基于FPGA的多通道符合计数器,并实验测量了单光子探测器信号的符合计数。     

Many-body effect in Auger-photoelectron coincidence spectroscopy spectra

When the shakeup/down excitations are not negligible in the core-level electron ionization, the photoelectron spectral peak measured in coincidence with a selected singles (noncoincidence) Auger-electron spectral peak does not necessarily coincide with the singles one. We discuss how the interference between the core-hole decay of a fully relaxed core-hole state and that of an incompletely relaxed one via the interaction between the final states created by the respective core-hole decays, affects the kinetic energy shift and asymmetrical lineshape change of the coincidence photoelectron spectrum compared to the singles one. When the final-state interaction is considerable, the interference reduces much the energy shift and the asymmetrical lineshape change. By the Auger-photoelectron coincidence spectroscopy (APECS) we can study the interference effect which does not manifest in the singles photoelectron spectrum. We discuss also the interference effect when the core-hole decay rates of both the fully relaxed core-hole state and the incompletely relaxed one depend critically on the changes in both the Auger-electron kinetic energy and the final-state potential. The effect is fairly independent of the changes.     

Reinterpretation of Quantum Mechanics Based on the Statistical Interpretation

I attempt to develop further the statistical interpretation of quantum mechanics proposed by Einstein and developed by Popper, Ballentine, etc. Two ideas are proposed in the present paper. One is to interpret momentum as a property of an ensemble of similarly prepared systems which is not satisfied by any one member of the ensemble of systems. Momentum is regarded as a statistical parameter like temperature in statistical mechanics. The other is the holistic assumption that a probability distribution is determined as a whole as most likely to be realized. This is the same as the chief assumption in statistical mechanics, and maximum likelihood in classical statistics. These ideas enable us to understand statistically (1) the formalism of quantum mechanics, (2) Heisenberg's uncertainty relations, and (3) the origin of quantum equations. They also explain violation of Bell's inequality and the interference of probabilities.     

The physics of the Einstein-Podolsky-Rosen paradox

The Einstein-Podolsky-Rosen paradox as formulated in their original paper is critically examined. Their argument that quantum mechanics is incomplete is shown to be unsatisfactory on two important grounds. (i) The gedanken experiment proposed by Einstein, Podolsky, and Rosen is physically unrealizable, and consequently their argument is invalid as it stands. (ii) The basic assumptions of their argument are equivalent to the assumption that quantum mechanical systems are in fact describable by unique eigenfunctions of the operators corresponding to physical observables, independent of any observation or measurement. Following an argument due to Furry, it is shown that this interpretation of quantum mechanics must lead to some physical predictions at variance with those of conventional quantum mechanics. A decisive experiment has been performed by Freedman and Clauser, which rules out this interpretation, and imposes severe restrictions on any alternative theory which incorporates the Einstein, Podolsky, and Rosen concept of physical reality.     

Challenges to Bohr’s Wave-Particle Complementarity Principle

Contrary to Bohr’s complementarity principle, in 1995 Rabinowitz proposed that by using entangled particles from the source it would be possible to determine which slit a particle goes through while still preserving the interference pattern in the Young’s two slit experiment. In 2000, Kim et al. used spontaneous parametric down conversion to prepare entangled photons as their source, and almost achieved this. In 2012, Menzel et al. experimentally succeeded in doing this. When the source emits entangled particle pairs, the traversed slit is inferred from measurement of the entangled particle’s location by using triangulation. The violation of complementarity breaches the prevailing probabilistic interpretation of quantum mechanics, and benefits Bohm’s pilot-wave theory.     

Generation of a Quadphoton via Seventh‐Order Nonlinear Susceptibility

With a wide range of potential applications, the generation of nonclassical multiphoton and number states has attracted renewed interest recently. Here, a correlated quadphoton with seventh‐order nonlinear susceptibility is reported in which all four photons are simultaneously created via an eight‐wave mixing (EWM) process in an atomic medium. The efficiency of the pure EWM process is low, which results from the small order of magnitude of the seventh‐order nonlinear susceptibility (the quadphoton correlation with four periods corresponding to 8 channels and 12 resonance positions). But the EWM process has a strong dressing effect. It not only increases the nonlinear susceptibility, but also produces 15 or 16 resonance positions in the dressing state picture. In addition, with the energy conservation of these positions, 12 coherent channels can be generated in this system. According to the interference between multichannels of the quadphoton, the quadphoton coincidence count appears as a damped Rabi oscillation, which has eight or ten oscillation periods. If only the nonlinear optical response is considered, the coincidence counts of the quadphoton behave as a damped Rabi oscillation with periods that can be controlled by the dressing field. These outcomes may contribute to a new promising method for quantum communication.     

Nonlocally correlated trajectories in two-particle quantum mechanics

In this paper we present a series of computer calculations carried out in order to demonstrate exactly how the de Broglie-Bohm interpretation works for two-particle quantum mechanics. In particular, we show how the de Broglie-Bohm interpretation can account for the essential features of nonrelativistic, two-particle quantum mechanics in terms of well-defined, correlated, individual particle trajectories and spin vectors. We demonstrate exactly how both quantum statistics and the correlations observed in Einstein-Podolsky-Rosen experiments can be explained in terms of nonlocal quantum potentials and nonlocal quantum torques which act on the well-defined individual particle coordinates and spin vectors.     

Entanglement in the Schrödinger experiment

The mixed and entanglement states have been analyzed in the Schrödinger experiment. It is known that, in an open system, the “Schrödinger cat” paradox is explained by the decoherence phenomenon, but, in a closed system, it is explained by the Everett-Wheeler many-world interpretation of quantum mechanics. The quantum real world can be presented as a complex multispatial geometric figure and the classical world is one of the faces of this figure. In this paper it is shown that this figure is the simplex that is well known in the functional analysis. Such an interpretation of quantum mechanics enables one to obtain the nonuniform wave equation, and the Schrödinger equation is the uniform equation of this one. Perhaps this equation is the equation of the subquantum world about which Einstein has written.     

Proposed experimental test of wave packet reduction and the uncertainty principle

A practical experiment using coincidence techniques is suggested to test the validity of the following concepts:(1) wave packet reduction and(2) the measurement-uncertainty principle for position and momentum. The suggested experiment uses the time-of-flight method to determine an electron's momentum and a coincident photon, emitted from a system excited by the electron, to determine its initial position. It is shown that this method does constitute a simultaneous measurement of position and momentum for a single system. Also, it is pointed out that the traditional statement of the measurementuncertainty principle must be slightly modified even within the Copenhagen interpretation of quantum mechanics.Work supported by the Leverhulme Trust Foundation and the National Aeronautics and Space Administration under Grant No. NSG-1378.