Double-slit Research Articles

A high order efficient numerical method for 4-D Wigner equation of quantum double-slit interferences

We propose a high order numerical method for computing time dependent 4-D Wigner equation with unbounded potentials and study a canonical quantum double-slit interference problem. To address the difficulties of 4-D phase space computations and higher derivatives from the Moyal expansion of the nonlocal pseudo-differential operator for unbounded potentials, an operator splitting technique is adopted to decompose the 4-D Wigner equation into two sub-equations, which can be computed either analytically or numerically with high efficiency. The first sub-equation contains only a linear convection term in (x,t)-space and can be solved with an upwinding characteristic method, while the second involves the pseudo-differential term and can be approximated by a plane wave expansion in k-space. By exploiting properties of Fourier transformations, the expansion coefficients for the second sub-equation have explicit forms and the resulting scheme is shown to be unconditionally stable for any high order derivatives in the Moyal expansion, ensuring the feasibility of 4-D Wigner numerical simulations for quantum double-slit interferences. Numerical experiments demonstrate the spectral convergence in (x,k)-space and provide highly accurate information on the number, position, and intensity of the interference fringes for different types of slits, quantum particle masses, and initial states (pure and mixed).

Resolving Phonon Fock States in a Multimode Cavity with a Double-Slit Qubit

We resolve phonon number states in the spectrum of a superconducting qubit coupled to a multimode acoustic cavity. Crucial to this resolution is the sharp frequency dependence in the qubit-phonon interaction engineered by coupling the qubit to surface acoustic waves in two locations separated by $\sim40$ acoustic wavelengths. In analogy to double-slit diffraction, the resulting self-interference generates high-contrast frequency structure in the qubit-phonon interaction. We observe this frequency structure both in the coupling rate to multiple cavity modes and in the qubit spontaneous emission rate into unconfined modes. We use this sharp frequency structure to resolve single phonons by tuning the qubit to a frequency of destructive interference where all acoustic interactions are dispersive. By exciting several detuned yet strongly-coupled phononic modes and measuring the resulting qubit spectrum, we observe that, for two modes, the device enters the strong dispersive regime where single phonons are spectrally resolved.

Double-slit experiment at Fermi scale: Coherent photoproduction in heavy-ion collisions

The double-slit experiment has become a classic thought experiment, for its clarity in expressing the central puzzle of quantum mechanics -- wave-particle complementarity. Such wave-particle duality continues to be challenged and investigated in a broad range of entities with electrons, neutrons, helium atoms, C$_{60}$ fullerenes, Bose-Einstein condensates and biological molecules. All existing experiments are performed with the scale larger than angstrom. In this article, we present a double-slit scenario at fermi scale with new entities -- coherent photon products in heavy-ion collisions. Virtual photons from the electromagnetic fields of relativistic heavy ions can fluctuate to quark-antiquark pairs, scatter off a target nucleus and emerge as vector mesons. The two colliding nuclei can take turns to act as targets, forming a double-slit interference pattern. Furthermore, the `which-way' information can be partially solved by the violent strong interactions in the proposed scenario, which demonstrates a key concept of quantum mechanics -- complementary principle.

Quantum fluctuations and the double-slit experiment

The double-slit experiment is a demonstration of wave-particle duality and one of the most fundamental experiments that help us understand the nature of quantum mechanics. In this work, we give a new explanation of this experiment in terms of the uncertainty principle and vacuum fluctuations. This explanation allows one to understand why the electron interferes with itself when being shot through the double-slit.

The ontological basis of quantum theory, nonlocality and local realism

In considering models of reality we must consider the fundamental nature of quantum mechanics, which has had great success in describing the spectrum of light from distant stars and galaxies, formulating the properties of the strong, electro-weak or electromagnetic and weak decay forces, and explaining atomic order formulated as the atomic periodic table and atomic spectra. A vast array of technologies has resulted from quantum theory, from semiconductors to NMR machines, nuclear reactors and possibly encryption secured, fast quantum computers. Quantum theory, however, has yet to fully engage with the gravitational force. With the advent of quantum theory, several major issues stand out, leaving us with major philosophical questions on the nature of physics and reality, and our ability to comprehend them. The issues involve the interpretation of quantum measurement, the Heisenberg uncertainty principle on the completeness of quantum theory and nonlocality. The frontiers of science continue to open new concepts based on a multidimensional reality which we use to address these issues, including solving the Schrödinger and Dirac equations in complex Minkowski eight space. We also formulate Bell’s theorem and the Young’s double slit experiment in Rauscher’s complex eight-space. We formulate an interpretation of the quantum that yields locality in a hyper-dimensional complex space and that maintains the completeness of quantum theory and nonlocality in usual four space, with local connectivity and the Lorentz invariant conditions, where subluminal and luminal signaling are maintained. Are we really forced to choose between two alternate views of reality? One view that external reality exists independent of the observer, and the other that the observer somehow is a participator or an integral part of all of nature. Must we choose between these or is there another way out? We find our way out and we satisfy both Bohr (Copenhagen) and Einstein (determinism) in bringing about a practical outcome of the debate. By developing and applying complex eight space, we can accommodate locality or local realism in terms of contiguous event connections in complex eight space. In four space, nonlocality dominates and also can be considered locality in eight space. The determination of the state of a system naturally collapses to its final state where quantum mechanics is functioning completely in four and in eight dimensional spaces.

Quantum interference of three dimensional plasmon excitations

In this paper, the quantum interference of plasmon excitations in the presence of charges or multipolar sources/sinks is investigated. The effective Schrödinger-Poisson system for dynamical description of the arbitrary degenerate fermi gas is reduced to a set of coupled linear pseudoforce system, and it is shown that this system admits a general multipolar solution in the 3D Cartesian coordinate. The obtained solution is then used to study well-known problems such as the double and quadruple charge interference effects. The double source interference produces patterns quite reminiscent of that of the double slit interference with the corresponding matter-wavelength matching that of the de Broglie wavelength of the electrons. It is found that the collective electrostatic interactions of quantum electron gas leads to the electrostatic energy depletion around the pole which causes electrostatic polar binding in the electron fluid. The later effect which has also been previously reported in some research seems to be an appropriate description of attractive metallic bindings. The current model is then extended to electronic interference effects in a crystal lattice with the quasiperiodic electronic states. The periodic arrangement of ionic cores in a crystal is shown to produce different density and electrostatic potential patterns for given energy eigenvalues of the fermi gas. Moreover, a generalized expression is obtained for electron probability current in the Schrödinger-Poisson model. The current model may provide a better platform for studying the quantum interference phenomenon in complex environments such as nanocompounds and plasmonic crystals.

A double-slit proposal for quantum annealing

We formulate and analyze a double-slit proposal for quantum annealing, which involves observing the probability of finding a two-level system (TLS) undergoing evolution from a transverse to a longitudinal field in the ground state at the final time tf. We demonstrate that for annealing schedules involving two consecutive diabatic transitions, an interference effect is generated akin to a double-slit experiment. The observation of oscillations in the ground state probability as a function of tf (before the adiabatic limit sets in) then constitutes a sensitive test of coherence between energy eigenstates. This is further illustrated by analyzing the effect of coupling the TLS to a thermal bath: increasing either the bath temperature or the coupling strength results in a damping of these oscillations. The theoretical tools we introduce significantly simplify the analysis of the generalized Landau-Zener problem. Furthermore, our analysis connects quantum annealing algorithms exhibiting speedups via the mechanism of coherent diabatic transitions to near-term experiments with quantum annealing hardware.

Swapping Space for Time: An Alternative to Time-Domain Interferometry

Young's double-slit experiment requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present as long as one cannot tell for sure which slit is chosen by the object. The more we know about the path, the worse the interference. In the paper we show that quantum mechanics allows for a dual version of the phenomenon: self-interference of waves propagating through a single slit but at different moments of time. The effect occurs for time-independent Hamiltonians and thus should not be confused with Moshinsky-type time-domain interference, a consequence of active modulation of parameters of the system (oscillating mirrors, chopped beams, time-dependent apertures, moving gratings, etc.). The discussed phenomenon is counterintuitive even for those who are trained in quantum interferometry. For example, the more we know about the trajectory in space, the better the interference. Exactly solvable models lead to formulas deceptively similar to those from a Youngian analysis. There are reasons to believe that this new type of quantum interference was already observed in atomic interferometry almost three decades ago, but was misinterpreted and thus rejected as an artifact of unknown origin.

An alternative derivation of orbital-free density functional theory.

Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is constructed directly from a Hamiltonian so that the results are, in principle, valid at finite temperatures. The main governing equations are found to be a set of modified diffusion equations, and the set of self-consistent equations are essentially identical to those of a ring polymer system. The equations are shown to be equivalent to Kohn-Sham density functional theory and to reduce to classical density functional theory, each under appropriate conditions. The obtained noninteracting kinetic energy functional is, in principle, exact but suffers from the usual orbital-free approximation of the Pauli exclusion principle in addition to the exchange-correlation approximation. The equations are solved using the spectral method of polymer self-consistent field theory, which allows the set of modified diffusion equations to be evaluated for the same computational cost as solving a single diffusion equation. A simple exchange-correlation functional is chosen, together with a shell-structure-based Pauli potential, in order to compare the ensemble average electron densities of several isolated atom systems to known literature results. The agreement is excellent, justifying the alternative formalism and numerical method. Some speculation is provided on considering the timelike parameter in the diffusion equations, which is related to temperature, as having dimensional significance, and thus picturing pointlike quantum particles instead as nonlocal, polymerlike, threads in a higher dimensional thermal-space. A consideration of the double-slit experiment from this point of view is speculated to provide results equivalent to the Copenhagen interpretation. Thus, the present formalism may be considered as a type of "pilot-wave," realist, perspective on density functional theory.

Fringe visibility, which-way information and weak value

We show how to obtain both complete which-way information and a perfect interference pattern simultaneously in a double-slit experiment using a quantum weak value scheme. It does not violate the wave-particle duality since we select only part of the interference data based on the post-selection of the final state following the idea of a weak value. We also show that our scheme is robust in consideration of generalized set-ups using spin models.

Analysis of double-slit interference experiment at the atomic level

I argue that the marquis characteristics of the quantum-mechanical double-slit experiment (point detection, random distribution, Born rule) can be explained using Schroedinger's equation alone, if one takes into account that, for any atom in a detector, there is a small but nonzero gap between its excitation energy and the excitation energies of all other relevant atoms in the detector (isolated-levels assumption). To illustrate the point I introduce a toy model of a detector. The form of the model follows common practice in quantum optics and cavity QED. Each detector atom can be resonantly excited by the incoming particle, and then emit a detection signature (e.g., bright flash of light) or dissipate its energy thermally. Different atoms have slightly different resonant energies per the isolated-levels assumption, and the projectile preferentially excites the atom with the closest energy match. The toy model permits one easily to estimate the probability that any atom is resonantly excited, and also that a detection signature is produced before being overtaken by thermal dissipation. The end-to-end detection probability is the product of these two probabilities, and is proportional to the absolute-square of the incoming wavefunction at the atom in question, i.e. the Born rule. I consider how closely a published neutron interference experiment conforms to the picture developed here; I show how this paper's analysis steers clear of creating a scenario with local hidden variables; I show how the analysis steers clear of the irreversibility implicit in the projection postulate; and I discuss possible experimental tests of this paper's ideas. Hopefully, this is a significant step toward realizing the program of solving the measurement problem within unitary quantum mechanics envisioned by Landsman, among others.

O experimento virtual da dupla fenda ao nível do ensino médio (Parte II): uma análise quântica do comportamento corpuscular e ondulatório da luz

Nosso trabalho analisa o experimento virtual da dupla fenda e está dividido em duas partes: a Parte I (publicada) que tratou da análise clássica do comportamento (corpuscular e ondulatório) e a Parte II (o presente artigo) que aborda o comportamento quântico da luz (fótons). Nosso processo metodológico se dividiu em 3 (três) etapas: (i) analisamos, primeiramente, com o auxílio de experimentos virtuais, o comportamento de um feixe de luz que atravessou uma parede com duas fendas. Neste caso, percebe-se que a luz sofre interferência. (ii) Em seguida, utilizamos o mesmo experimento, mas agora com fótons individuais. Os fótons se comportam como ondas e sofrem interferência, como antes. (iii) Finalmente, para descobrir o que estava acontecendo, colocamos um detector próximo às fendas. Nesta situação, estranhamente, os fótons se comportaram como partículas (corpúsculos). Com o objetivo de explicar estes resultados, utilizamos a notação de brackets proposta por Paul Dirac (1902-1984) que nos permite representar os vetores de estado, os quais nos propiciam mostrar, matematicamente, o que ocorre no experimento da dupla fenda com objetos quânticos. Devido à complexidade matemática (para o ensino médio) intrínseca à notação de Dirac fizemos uma espécie de “tradução” deste recurso matemático para este nível de ensino. Acreditamos que este artifício poderá ser útil para a compreensão de outros conceitos da mecânica quântica, tais como spin 1/2 e sistemas de dois níveis.

Atom interferometers with weak-measurement path detectors and their quantum mechanical analysis**Project supported by the National Key Research and Development Program of China (Grant No. 2018YFA 0306200), the National Natural Science Foundation of China (Grant No. 11434017), and the Guangdong Innovative and Entrepreneurial Research Team Program, China (Grant No. 2016ZT06C594).

According to the orthodox interpretation of quantum physics, wave-particle duality (WPD) is the intrinsic property of all massive microscopic particles. All gedanken or realistic experiments based on atom interferometers (AI) have so far upheld the principle of WPD, either by the mechanism of the Heisenberg’s position-momentum uncertainty relation or by quantum entanglement. In this paper, we propose and make a systematic quantum mechanical analysis of several schemes of weak-measurement atom interferometer (WM-AI) and compare them with the historical schemes of strong-measurement atom interferometer (SM-AI), such as Einstein’s recoiling slit and Feynman’s light microscope. As the critical part of these WM-AI setups, a weak-measurement path detector (WM-PD) deliberately interacting with the atomic internal electronic quantum states is designed and used to probe the which-path information of the atom, while only inducing negligible perturbation of the atomic center-of-mass motion. Another instrument that is used to directly interact with the atomic center-of-mass while being insensitive to the internal electronic quantum states is used to monitor the atomic center-of-mass interference pattern. Two typical schemes of WM-PD are considered. The first is the micromaser-cavity path detector, which allows us to probe the spontaneously emitted microwave photon from the incoming Rydberg atom in its excited electronic state and record unanimously the which-path information of the atom. The second is the optical-lattice Bragg-grating path detector, which can split the incoming atom beam into two different directions as determined by the internal electronic state and thus encode the which-path information of the atom into the internal states of the atom. We have used standard quantum mechanics to analyze the evolution of the atomic center-of-mass and internal electronic state wave function by directly solving Schrödinger’s equation for the composite atom-electron-photon system in these WM-AIs . We have also compared our analysis with the theoretical and experimental studies that have been presented in the previous literature. The results show that the two sets of instruments can work separately, collectively, and without mutual exclusion to enable simultaneous observation of both wave and particle nature of the atoms to a much higher level than the historical SM-AIs, while avoiding degradation from Heisenberg’s uncertainty relation and quantum entanglement. We have further investigated the space–time evolution of the internal electronic quantum state, as well as the combined atom–detector system and identified the microscopic origin and role of quantum entanglement, as emphasized in numerous previous studies. Based on these physics insights and theoretical analyses, we have proposed several new WM-AI schemes that can help to elucidate the puzzling physics of the WPD of the atoms. The principle of WM-AI scheme and quantum mechanical analyses made in this work can be directly extended to examine the principle of WPD for other massive particles.

Complementarity via Minimum Error Measurement in a Two-Path Interferometer**Supported by the National Natural Science Foundation of China under Grant Nos 11434011 and 11575058.

We study the fringe visibility and the which-path information (WPI) of a general Mach–Zehnder interferometer with an asymmetric beam splitter (BS). A minimum error measurement in the detector is used to extract the WPI. Both the fringe visibility V and the WPI Ipath are affected by the initial state of the photon and the second asymmetric BS. The condition in which the WPI takes the maximum is obtained. The complementarity relationship is found, and the conditions for equality are also presented.

Local realism quantum mechanics can be established: a review of the book of quantum mechanics’ return to local realism

All the experiments that prove that Einstein is wrong and Bohr won have a serious flaw or loophole that is difficult to overcome — Have to subjectively judge the state of the system before the measurement. Undoubtedly, the establishment of quantum mechanics of local realism is a strong support for Einstein.<strong> </strong>Many people are dissatisfied with the quantum mechanics of non-local realism and want to establish the quantum mechanics of local realism. But they did not break through the bottleneck. The concept of wave function is widely used in existing quantum mechanics. However, the nature of the wave function is unanswerable. The model of "real wave curling inside the particle" determines that the wave function is the motion equation of localized real wave. The wave mechanics based on such wave functions is quantum mechanics of localized realism. The mathematical formal system of local realism quantum mechanics is the same as the existing one. Explanation of double slit diffraction can be experiment by directional quantization. The explanation system of local realism quantum mechanics is established, and it is guaranteed that this system can also be organically combined with the existing mathematical formal systems of quantum mechanics. Local realism quantum mechanics has all the elements of a valuable new theory, and its birth conforms to the law of theoretical development.

The Nature of the Heisenberg-von Neumann Cut: Enhanced Orthodox Interpretation of Quantum Mechanics

We examine the issue of the Heisenberg-von Neumann cut in light of recent interpretations of quantum eraser experiments which indicate the possibility of a universal Observer outside space-time at an information level of existence. The delayed-choice aspects of observation, measurement, the role of the observer, and information in the quantum framework of the universe are discussed. While traditional double-slit experiments are usually interpreted as indicating that the collapse of the wave function involves choices by an individual observer in space-time, the extension to quantum eraser experiments brings in some additional subtle aspects relating to the role of observation and what constitutes an observer. Access to, and the interpretation of, information outside space and time may be involved. This directly ties to the question of where the Heisenberg-von Neumann cut is located and what its nature is. Our model is an interpretation which we term the Enhanced Orthodox Interpretation of Quantum Mechanics. It does not contradict the standard orthodox interpretation, but we believe it extends it by approaching von Neumann’s work in a new way. The Enhanced Orthodox Interpretation accepts the presence of a universal Observer, retaining the importance of observation augmented by the role of information. There is a possibility that individual observers making choices in space and time are actually aspects of the universal Observer, a state masked by assumptions about individual human minds that may need further development and re-examination.

Arbitrarily distorted 2-dimensional pulse-front measurement and reliability analysis.

A method of 2-dimensional (2-D) space-scanned (in the x-y plane) spatiotemporal double-slit interference is used to reconstruct the 2-D pulse-front (in the x-y-t domain) of a femtosecond pulsed beam. While comparing with recent other methods, the method possesses two advantages: no reference pulse/beam is required anymore, and an arbitrarily distorted pulse-front, not just pulse-front tilt and pulse-front curvature, could be detected. Meanwhile, the influence of different factors of unknown pulsed beams and optical elements on the measurement reliability is also analyzed for engineering applications.

Probing the spatial coherence of wide X-ray beams with Fresnel mirrors at BL25SU of SPring-8.

Probing the spatial coherence of X-rays has become increasingly important when designing advanced optical systems for beamlines at synchrotron radiation sources and free-electron lasers. Double-slit experiments at various slit widths are a typical method of quantitatively measuring the spatial coherence over a wide wavelength range including the X-ray region. However, this method cannot be used for the analysis of spatial coherence when the two evaluation points are separated by a large distance of the order of millimetres owing to the extremely narrow spacing between the interference fringes. A Fresnel-mirror-based optical system can produce interference patterns by crossing two beams from two small mirrors separated in the transverse direction to the X-ray beam. The fringe spacing can be controlled via the incidence angles on the mirrors. In this study, a Fresnel-mirror-based optical system was constructed at the soft X-ray beamline (BL25SU) of SPring-8. The relationship between the coherence and size of the virtual source was quantitatively measured at 300 eV in both the vertical and horizontal directions using the beam. The results obtained indicate that this is a valuable method for the optimization of optical systems along beamlines.

Propagation of a polariton condensate in a one-dimensional microwire at room temperature

We study the propagation of a polariton condensate in a one-dimensional ZnO microwire at room temperature. We demonstrate that the energy and profile of the polariton condensate fluid in momentum space are well preserved for tens of micrometers during the propagation, without obvious dispersion phenomena over the experimental range. We demonstrate the spatial coherence of the extended condensate by carrying out a Young’s double-slit experiment. Our system practically leads to high-fidelity information carried by a polariton propagating in a waveguide device.

Testing Quantum Coherence in Stochastic Electrodynamics with Squeezed Schrödinger Cat States

The interference pattern in electron double-slit diffraction is a hallmark of quantum mechanics. A long-standing question for stochastic electrodynamics (SED) is whether or not it is capable of reproducing such effects, as interference is a manifestation of quantum coherence. In this study, we used excited harmonic oscillators to directly test this quantum feature in SED. We used two counter-propagating dichromatic laser pulses to promote a ground-state harmonic oscillator to a squeezed Schrödinger cat state. Upon recombination of the two well-separated wavepackets, an interference pattern emerges in the quantum probability distribution but is absent in the SED probability distribution. We thus give a counterexample that rejects SED as a valid alternative to quantum mechanics.