Duality In Quantum Mechanics Research Articles

Quantum Interference and Coherent Population Trapping in a Double Quantum Dot.

Quantum interference is a natural consequence of wave-particle duality in quantum mechanics, and is widely observed at the atomic scale. One interesting manifestation of quantum interference is coherent population trapping (CPT), first proposed in three-level driven atomic systems and observed in quantum optical experiments. Here, we demonstrate CPT in a gate-defined semiconductor double quantum dot (DQD), with some unique twists as compared to the atomic systems. Specifically, we observe CPT in both driven and nondriven situations. We further show that CPT in a driven DQD could be used to generate adiabatic state transfer. Moreover, our experiment reveals a nontrivial modulation to the CPT caused by the longitudinal driving field, yielding an odd-even effect and a tunable CPT. Our results broaden the field of CPT, and open up the possibility of quantum simulation and quantum computation based on adiabatic passage in quantum dot systems.

Particle-continuum duality of skyrmions

Topological solitons are crucial to many branches of physics, such as models of fundamental particles in quantum field theory, information carriers in nonlinear optics, and elementary entities in quantum and classical computations. Chiral magnetic materials are a fertile ground for studying solitons. In the past a few years, a huge number of all kinds of topologically protected localized magnetic solitons have been found. The number is so large, and a proper organization and classification is necessary for their future developments. Here we show that many topological magnetic solitons can be understood from the duality of particle and elastic continuum-medium nature of skyrmions. In contrast to the common belief that a skyrmion is an elementary particle that is indivisible, skyrmions behave like both particle and continuum media that can be tore apart to bury other objects, reminiscing particle-wave duality in quantum mechanics. Skyrmions, like indivisible particles, can be building blocks for cascade skyrmion bags and target skyrmions. They can also act as bags and glues to hold one or more skyrmions together. The principles and rules for stable composite skyrmions are explained and presented, revealing their rich and interesting physics.

Wave-particle duality and the zitterbewegung

In previous work, the Hamilton-Jacobi equation has been associated with the metrics of general relativity and shown to be a generalized Dirac equation for quantum mechanics. This lends itself to a natural definition of wave-particle duality in quantum mechanics. This theory is now further developed to show that a free spinless quantum particle moving with velocity v obeys the standard wave equation of electro-magnetism. We also discuss the implications for the zitterbewegung problem and its relationship to isotropy. Moreover, it is also shown that for the theory to be consistent, the momentum defined by the Hamilton-.!acobi function presupposes the existence of a universal parameter internal to the system. In the case of particles with mass this invariant can be defined by dX = dt/m(t) where t has the units of time and m = m(t) has the units of mass.

Classical model of a delayed-choice quantum eraser

Wheeler's delayed-choice experiment was conceived to illustrate the paradoxical nature of wave-particle duality in quantum mechanics. In the experiment, quantum light can exhibit either wave-like interference patterns or particle-like anti-correlations, depending upon the (possibly delayed) choice of the experimenter. A variant known as the quantum eraser uses entangled light to recover the lost interference in a seemingly nonlocal and retrocausal manner. Although it is believed that this behavior is incompatible with classical physics, here we show that the observed quantum phenomena can be reproduced by adopting a simple deterministic detector model and supposing the existence of a random zero-point electromagnetic field.

A New Understanding of the Origin of Wave-Particle Duality in Quantum Mechanics

The wave-particle duality of quantum mechanics has always been an unsolved problem in physics. This article attempts to use one of the properties to explain the other, so as to eliminate the confusion of quantum mechanics probability waves. Specifically, this article finds that the discreteness of energy is the inherent property of all waves, so this article explains the particle nature of light from the perspective of light wave, thereby eliminating the confusion of light’s wave-particle duality; in addition, this article found that microscopic matter particles are only suitable for discussing the number of scattered particles or energy flow density, not their position and momentum, when they are forced to discuss their position and momentum, it will inevitably lead to confusion about probability waves, when only discussing the number of scattered particles or energy flow density, its volatility can be explained from the perspective of particle nature, thereby eliminating the confusion of microscopic matter particle probability waves. When the attribute of light as a wave is established, the light needs to overcome the Hamiltonian of the medium in different constraint systems (gravitational fields) during the propagation process, which will produce a universal redshift phenomenon, this can provide a new understanding of cosmic redshift; when the property of light as a wave is established, it means that the speed of light is a constant speed relative to the medium, which can provide a new understanding of the principle of constant speed of light.

The reflection phenomenon and complexity engine as statistical physics tools for the advanced evolution phenomenon

We intend to uncover generative principles for complex, biological systems, looking the reflections as well as the analogs of decision making property in quantum physics: measurement, self-interaction of the electron, Berry phase and quantum anomalies. We assume that classical analogs of the mentioned phenomena could be related to the evolvability, growing of complexity and decision making in biological systems. The reflection is a map (coarse graining) from microscopic motions to a macroscopic scale that relates with a free-energy cost and is often accompanied by the emergence of order-parameters. In this context we identify the self-reflection phenomenon, which is exemplified by cognition, information transfer near the error threshold, and tightly related evolution-ecology phenomena. We propose that complex systems that have similar reflection structure are to be described by similar mathematical tools including stochastic (information) thermodynamics and the large deviation theory. We introduce the concept of complexity engine: the group of two (or more) autonomous features of complex systems that are in a partial conflict with each other. Analogues of this are wave-particle duality in quantum mechanics and data-program duality in digital life. We formulate a fundamental problem: does the three-dimensional space provide a complexity engine for the emergence of life?

Wave-particle duality: tribute to the memory of Yves Couder

The story of wave-particle duality in quantum mechanics has been told a thousand times. This modest contribution is to get back to a few points, including memories of a discussion we had on a possible experimental evidence of quantum effects at macroscopic scale, but in a way totally unrelated to the experiments he and his group made quite later to exhibit a model of wave-particle duality. The more general question of interpreting/understanding quantum mechanics will be also scrutinized once more.

Quantum Particles as 3D Differentiable Manifolds

As shown in our work on spacetime structures of quantum particles, Schrödinger wavefunctions in quantum mechanics can be utilised to construct the geometric structures of quantum particles which are considered to be three-dimensional differentiable manifolds. In this work we will extend this kind of geometric formulation of quantum particles by showing that wavefunctions that are normally used to describe wave phenomena in classical physics can in fact also be utilised to represent three-dimensional differentiable manifolds which in turns are identified with quantum particles. We show that such identification can be achieved by using a three-dimensional wave equation to construct three-dimensional differentiable manifolds that are embedded in a four-dimensional Euclidean space. In particular, the dual character that is resulted from the identification of a wavefunction with a three-dimensional differentiable manifold may provide a classical basis to interpret the wave-particle duality in quantum mechanics.

Semisuper Efimov Effect of Two-Dimensional Bosons at a Three-Body Resonance.

Wave-particle duality in quantum mechanics allows for a halo bound state whose spatial extension far exceeds a range of the interaction potential. What is even more striking is that such quantum halos can be arbitrarily large on special occasions. The two examples known so far are the Efimov effect and the super Efimov effect, which predict that spatial extensions of higher excited states grow exponentially and double exponentially, respectively. Here, we establish yet another new class of arbitrarily large quantum halos formed by spinless bosons with short-range interactions in two dimensions. When the two-body interaction is absent but the three-body interaction is resonant, four bosons exhibit an infinite tower of bound states whose spatial extensions scale as R_{n}∼e^{(πn)^{2}/27} for a large n. The emergent scaling law is universal and is termed a semisuper Efimov effect, which together with the Efimov and super Efimov effects constitutes a trio of few-body universality classes allowing for arbitrarily large quantum halos.

Erasing the orbital angular momentum information of a photon

Quantum erasers with paths in the form of physical slits have been studied extensively and proven instrumental in probing wave-particle duality in quantum mechanics. Here we replace physical paths (slits) with abstract paths of orbital angular momentum (OAM). Using spin-orbit hybrid entanglement of photons we show that the OAM content of a photon can be erased with a complimentary polarization projection of one of the entangled pair. The result is the (dis)appearance of azimuthal fringes based on whether the \which-OAM" information was erased. We extend this concept to a delayed measurement scheme and show that the OAM information and fringe visibility are complimentary.

Weak measurement combined with quantum delayed-choice experiment and implementation in optomechanical system

Weak measurement [1,19] combined with quantum delayed-choice experiment that use quantum beam splitter instead of the beam splitter give rise to a surprising amplification effect, i.e., counterintuitive negative amplification effect. We show that this effect is caused by the wave and particle behaviours of the system to be and can't be explained by a semiclassical wave theory, due to the entanglement of the system and the ancilla in quantum beam splitter. The amplification mechanism about wave-particle duality in quantum mechanics lead us to a scheme for implementation of weak measurement in optomechanical system.

Weak coupling chambers in [formula omitted] BPS quiver theory

Using recent results on BPS quiver theory, we develop a group theoretical method to describe the quiver mutations encoding the quantum mechanical duality relating the spectra of distinct quivers. We illustrate the method by computing the BPS spectrum of the infinite weak chamber of some examples of N=2 supersymmetric gauge models without and with quark hypermultiplets.

Does an atom interferometer test the gravitational redshift at the Compton frequency?

Atom interferometers allow the measurement of the acceleration of freely falling atoms with respect to an experimental platform at rest on Earth's surface. Such experiments have been used to test the universality of free fall by comparing the acceleration of the atoms to that of a classical freely falling object. In a recent paper, Müller et al (2010 Nature 463 926–9) argued that atom interferometers also provide a very accurate test of the gravitational redshift (or universality of clock rates). Considering the atom as a clock operating at the Compton frequency associated with the rest mass, they claimed that the interferometer measures the gravitational redshift between the atom-clocks in the two paths of the interferometer at different values of gravitational potentials. In this paper, we analyze this claim in the frame of general relativity and of different alternative theories. We show that the difference of ‘Compton phases’ between the two paths of the interferometer is actually zero in a large class of theories, including general relativity, all metric theories of gravity, most non-metric theories and most theoretical frameworks used to interpret the violations of the equivalence principle. Therefore, in most plausible theoretical frameworks, there is no redshift effect and atom interferometers only test the universality of free fall. We also show that frameworks in which atom interferometers would test the redshift pose serious problems, such as (i) violation of the Schiff conjecture, (ii) violation of the Feynman path integral formulation of quantum mechanics and of the principle of least action for matter waves, (iii) violation of energy conservation, and more generally (iv) violation of the particle-wave duality in quantum mechanics. Standard quantum mechanics is no longer valid in such frameworks, so that a consistent interpretation of the experiment would require an alternative formulation of quantum mechanics. As such an alternative has not been proposed to date, we conclude that the interpretation of atom interferometers as testing the gravitational redshift at the Compton frequency is unsound.

Behavior of Electronic Interferometers in the Nonlinear Regime

We investigate theoretically the behavior of the current oscillations in an electronic Mach-Zehnder interferometer (MZI) as a function of its source bias. Recently, the MZI visibility data showed an unexplained lobe pattern with a peculiar phase rigidity. Moreover, the effect did not depend on the MZI path length difference. We argue that these effects may be a new many-body manifestation of particle-wave duality in quantum mechanics. When biasing the interferometer sources so much that multiple electrons are on each arm at any instant in time, quantum shot noise (a particle phenomena) must affect the interference pattern of the electrons that create it. A solution to the interaction Hamiltonian presented here shows that the interference visibility has a lobe pattern with applied bias that has a period proportional to the average path length and independent of the path length difference, together with a phase rigidity.

Duality, Quantum Mechanics and (Almost) Complex Manifolds

The classical mechanics of a finite number of degrees of freedom requires a symplectic structure on phase space [Formula: see text], but it is independent of any complex structure. On the contrary, the quantum theory is intimately linked with the choice of a complex structure on [Formula: see text]. When the latter is a complex-analytic manifold admitting just one complex structure, there is a unique quantization whose classical limit is [Formula: see text]. Then the notion of coherence is the same for all observers. However, when [Formula: see text] admits two or more nonbiholomorphic complex structures, there is one different quantization per different complex structure on [Formula: see text]. The lack of analyticity in transforming between nonbiholomorphic complex structures can be interpreted as the loss of quantum-mechanical coherence under the corresponding transformation. Observers using one complex structure perceive as coherent the states that other observers, using a different complex structure, do not perceive as such. This is the notion of a quantum-mechanical duality transformation: the relativity of the notion of a quantum.

Use of the track structure approach in TEM

Track structures can be usefully used to understand concepts and measurements not adequately treated by conventional scattering theory using the Born approximation. An example is the impact parameter used experimentally in energy-loss and energy-dispersive spectroscopies in the transmission electron microscope. An anomaly is discussed which derives from the wave–particle duality in quantum mechanics in the context of near relativistic speeds encountered in the electron microscope.

On complementarity?a rebuttal

A refutation is offered of the need for a quantum mechanical duality in developing a model for the dynamics of the living organism or the social organism. Its model is derived from a more classical physics of homeokinetic irreversible thermodynamics. On the other hand, the process duality of thought and action, as a complementarity, does furnish the gradient basis for language.