Three-Slit Experiments and Quantum Nonlocality

An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson’s bound for the nonlocal correlations. Considering multiple-slit experiments—not only the traditional configuration with two slits, but also configurations with three and more slits—Sorkin detected that third-order (and higher-order) interference is not possible in quantum mechanics. The EPR experiments show that quantum mechanics involves nonlocal correlations which are demonstrated in a violation of the Bell or CHSH inequality, but are still limited by a bound discovered by Tsirelson. It now turns out that Tsirelson’s bound holds in a broad class of probabilistic theories provided that they rule out third-order interference. A major characteristic of this class is the existence of a reasonable calculus of conditional probability or, phrased more physically, of a reasonable model for the quantum measurement process.     

Three Slit Experiments and the Structure of Quantum Theory

In spite of the interference manifested in the double-slit experiment, quantum theory predicts that a measure of interference defined by Sorkin and involving various outcome probabilities from an experiment with three slits, is identically zero. We adapt Sorkin’s measure into a general operational probabilistic framework for physical theories, and then study its relationship to the structure of quantum theory. In particular, we characterize the class of probabilistic theories for which the interference measure is zero as ones in which it is possible to fully determine the state of a system via specific sets of ‘two-slit’ experiments.     

Review of recent experimental progress in foundations of quantum mechanics and quantum information achieved in parametric downconversion experiments at IENGF

We review some recent experimental progress concerning foundations of quantum mechanics and quantum information obtained in the Carlo Novero Quantum Optics Laboratory at IENGF. After a short presentation of our polarization-entangled photon source (based on precise superposition of two type I PDC emissions) and of the results obtained with it, we describe in more detail an innovative double slit experiment where two degenerate photons produced by PDC are each sent to a specific slit. Beyond representing an interesting example of the relation between the visibility of interference and welcher Weg knowledge, this configuration has been suggested for testing de Broglie-Bohm theory (dBB) against standard quantum mechanics (SQM). Our results perfectly fit SQM results but disagree with dBB predictions. Then, we discuss a recent experiment addressed at clarifying the issue of which wave-particle observables are really to be considered when discussing wave-particle duality. This experiments realizes the theoretical proposal of Agarwal et al., overcoming the limitations of a previous experiment. Finally, we hint at the realization of a high-intensity high-spectral-selectivity PDC source to be used for quantum information studies.     

量子理论新方法研究光的双缝衍射

用量子理论新方法研究光的双缝衍射实验现象,首先用光的量子理论计算光在缝中双缝衍射的波函数,再由基尔霍夫定律计算光的衍射波函数,由衍射强度正比于衍射波函数模方,从而得到光双缝衍射强度的解析式,把量子理论计算结果和经典电磁理论计算结果以及与实验数据三者进行比较,发现量子理论结果与实验数据符合更好,而经典电磁理论计算结果与实验有一定偏差.从而说明量子理论更能精确解释光的衍射现象.该方法还可进一步研究光的单缝、多缝以及光栅衍射的实验现象.     

Enhancement of spatial coherence by surface plasmons

We report on a method to generate a stationary interference pattern from two independent optical sources, each illuminating a single slit in Young's interference experiment. The pattern arises as a result of the action of surface plasmons traveling between subwavelength slits milled in a metal film. The visibility of the interference pattern can be manipulated by tuning the wavelength of one of the optical sources.     

Quantum eraser for three-slit interference

It is well known that in a two-slit interference experiment, if the information, on which of the two paths the particle followed, is stored in a quantum path detector, the interference is destroyed. However, in a set-up where this path information is ‘erased’, the interference can reappear. Such a set-up is known as a quantum eraser. A generalization of quantum eraser to a ‘three-slit’ interference is theoretically analysed. It is shown that three complementary interference patterns can arise out of the quantum erasing process.     

Oracles and Query Lower Bounds in Generalised Probabilistic Theories

We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be well-defined. The four principles are: causality (roughly, no signalling from the future), purification (each mixed state arises as the marginal of a pure state of a larger system), strong symmetry (existence of a rich set of nontrivial reversible transformations), and informationally consistent composition (roughly: the information capacity of a composite system is the sum of the capacities of its constituent subsystems). Sorkin has defined a hierarchy of conceivable interference behaviours, where the order in the hierarchy corresponds to the number of paths that have an irreducible interaction in a multi-slit experiment. Given our oracle model, we show that if a classical computer requires at least n queries to solve a learning problem, because fewer queries provide no information about the solution, then the corresponding “no-information” lower bound in theories lying at the kth level of Sorkin’s hierarchy is \(\lceil {n/k}\rceil \). This lower bound leaves open the possibility that quantum oracles are less powerful than general probabilistic oracles, although it is not known whether the lower bound is achievable in general. Hence searches for higher-order interference are not only foundationally motivated, but constitute a search for a computational resource that might have power beyond that offered by quantum computation.     

An explanation of interference effects in the double slit experiment: Classical trajectories plus ballistic diffusion caused by zero-point fluctuations

A classical explanation of interference effects in the double slit experiment is proposed. We claim that for every single “particle” a thermal context can be defined, which reflects its embedding within boundary conditions as given by the totality of arrangements in an experimental apparatus. To account for this context, we introduce a “path excitation field”, which derives from the thermodynamics of the zero-point vacuum and which represents all possible paths a “particle” can take via thermal path fluctuations. The intensity distribution on a screen behind a double slit is calculated, as well as the corresponding trajectories and the probability density current. The trajectories are shown to obey a “no crossing” rule with respect to the central line, i.e., between the two slits and orthogonal to their connecting line. This agrees with the Bohmian interpretation, but appears here without the necessity of invoking the quantum potential.     

Finite groups and quantum physics

Concepts of quantum theory are considered from the constructive “finite” point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution—only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers—a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories—in particular, within the Standard Model.     

Superluminal propagation of evanescent modes as a quantum effect

Contrary to mechanical waves, the two‐slit interference experiment of single photons shows that the behavior of classical electromagnetic waves corresponds to the quantum mechanical one of single photons, which is also different from the quantum‐field‐theory behavior such as the creations and annihilations of photons, the vacuum fluctuations, etc. Owing to a purely quantum effect, quantum tunneling particles including tunneling photons (evanescent modes) can propagate over a spacelike interval. With this picture we conclude that the superluminality of evanescent modes is a quantum mechanical rather than a classical phenomenon.     

Double-Slit Interference Pattern from Single-Slit Screen and Its Gravitational Analogues

The double slit experiment (DSE) is known as an important cornerstone in the foundations of physical theories such as Quantum Mechanics and Special Relativity. A large number of different variants of it were designed and performed over the years. We perform and discuss here a new version with the somewhat unexpected results of obtaining interference pattern from single-slit screen. We show using either the Brill’s version of the canonical formulation of general relativity or the linearized version of it that one may find corresponding and analogous situations in the framework of general relativity.     

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.     

Quantum theory and the nature of interference

It is shown that many of the difficulties associated with the Copenhagen interpretation of quantum theory are resolved by a new interpretation of interference derived from solutions to Maxwell's equations. An infinite wave model of the photon based on these solutions is described and used to explain the interference of single photons as well as the corpuscular behavior evident in the Compton and photoelectric effects. The wave-particle duality and the uncertainty relations are also discussed. According to the new interpretation of interference in a Young's double-slit experiment, photons which pass through the left-hand slit always arrive in the left-hand part of the screen and no photons pass into this area via the right-hand slit. This conclusion is compared with the viewpoint of the Copenhagen school and an experiment to distinguish between them is suggested.     

Analytical solutions for the subsidiary maxima in multiple slit interference

Optical Review - We present analytical solutions for the subsidiary maxima in multiple slit interference up to eleven slits. For the number of slits N, there exist $$N-2$$ subsidiary maxima between...     

Plasmon-assisted two-slit transmission: Young's experiment revisited

We present an experimental and theoretical study of the optical transmission of a thin metal screen perforated by two subwavelength slits, separated by many optical wavelengths. The total intensity of the far-field double-slit pattern is shown to be reduced or enhanced as a function of the wavelength of the incident light beam. This modulation is attributed to an interference phenomenon at each of the slits, instead of at the detector. The interference arises as a consequence of the excitation of surface plasmons propagating from one slit to the other.     

干涉现象中能量叠加的实验研究

经典的波动理论与量子理论均分别对杨氏双缝干涉实验进行了解释。由于两个解释理论一个简单直观、一个复杂抽象,但两者结果一致,使得学生在学习中容易接受波动理论而排斥量子理论。文中通过实验观测了杨氏双缝干涉光场中能量传递与叠加的实际情况,结果显示实验实际情况与波动理论解释明显不相符合,而与量子理论解释完全相符。通过实验,使学生直观地看到波动理论的局限性,并加深学生对量子力学相关理论的理解。     

Surface plasmons modulate the spatial coherence of light in Young's interference experiment

It is shown how surface plasmons that travel between the slits in Young's interference experiment can change the state of spatial coherence of the field that is radiated by the two apertures. Surprisingly, the coherence can both be increased and decreased, depending on the slit separation distance. This results in a modulation of the visibility of the interference fringes. Since many properties of a light field-such as its spectrum, polarization, and directionality - may change on propagation and are dependent on the spatial coherence of the source, our results suggest that the use of surface plasmons provides a new way to alter or even tailor the statistical properties of a light field.     

First-order photon interference of a single photon from a single quantum dot

Photon interference indicating wave-like nature of a single photon emitted from a single quantum dot is demonstrated. Photon state as a superposition of two orthogonal linear polarization modes is prepared inside a solid-state single photon source, which causes the first-order interference analogous to the Young’s double slit experiment. The lack of which-mode information is essential for observing the single photon interference.     

Note on the two-slit experiment

According to the general philosophy of quantum mechanics, a particle whose passage through one of the slits of a two-slit apparatus has been detected does not produce interference. In a previous article this was demonstrated explicitly by solving the Schrödinger equation for a specific model of the detector, but only the first order in the interaction with the detector was considered. In the present note it is shown for the same model that for stronger interactions the interference disappears altogether. When the detector has reached 100% efficiency those particles that have not been detected do not produce interference either, because they are sure to have passed through the other slit.For Oliver Penrose, as a token of esteem.