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22 pages, 454 KiB

Open AccessArticle

From Stochastic Optics to the Wigner Formalism: The Role of the Vacuum Field in Optical Quantum Communication Experiments

by Alberto Casado, Santiago Guerra and José Plácido

Atoms 2019, 7(3), 76; https://doi.org/10.3390/atoms7030076 - 07 Aug 2019

Cited by 6 | Viewed by 2703

Abstract

The Wigner formalism in the Heisenberg picture constitutes a bridge that connects Quantum Optics to Stochastic Optics. The vacuum field appears explicitly in the formalism, and the wavelike aspects of light are emphasised. In addition, the zeropoint intensity as a threshold for detection [...] Read more.

The Wigner formalism in the Heisenberg picture constitutes a bridge that connects Quantum Optics to Stochastic Optics. The vacuum field appears explicitly in the formalism, and the wavelike aspects of light are emphasised. In addition, the zeropoint intensity as a threshold for detection is a common denominator in both theories. In this paper, after summarising the basic rules of the Wigner approach and its application to parametric down-conversion, some new results are presented that delve into the physical meaning of the zeropoint field in optical quantum communication. Specifically, the relationship between Bell-state distinguishability and the number of sets of zeropoint modes that take part in the experiment is analysed in terms of the coupling between the phases of the different fields involved and the subtraction of the zeropoint intensity at the detectors. Additionally, the connection between the compatibility theorem in quantum cryptography and zeropoint field is stressed. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

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10 pages, 276 KiB

Open AccessArticle

Stochastic Electrodynamics: Lessons from Regularizing the Harmonic Oscillator

by Theodorus Maria Nieuwenhuizen

Atoms 2019, 7(2), 59; https://doi.org/10.3390/atoms7020059 - 10 Jun 2019

Cited by 5 | Viewed by 2515

Abstract

In this paper, the harmonic oscillator problem in Stochastic Electrodynamics is revisited. Using the exact shape of the Lorentz damping term prevents run-away effects. After introducing a cut-off in the stochastic power spectrum and regularizing the stochastic force, all relevant integrals are dominated [...] Read more.

In this paper, the harmonic oscillator problem in Stochastic Electrodynamics is revisited. Using the exact shape of the Lorentz damping term prevents run-away effects. After introducing a cut-off in the stochastic power spectrum and regularizing the stochastic force, all relevant integrals are dominated by resonance effects only and results are derived that stem from those in the quantum ground state. For an orbit with specific position and momentum at an initial time, the average energy and the average rate of energy change are evaluated, which stem with each other. Resonance effects are highlighted along the way. An outlook on the hydrogen ground state problem is provided. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

18 pages, 3680 KiB

Open AccessArticle

Extraction of Zero-Point Energy from the Vacuum: Assessment of Stochastic Electrodynamics-Based Approach as Compared to Other Methods

by Garret Moddel and Olga Dmitriyeva

Atoms 2019, 7(2), 51; https://doi.org/10.3390/atoms7020051 - 23 May 2019

Cited by 1 | Viewed by 8711

Abstract

In research articles and patents several methods have been proposed for the extraction of zero-point energy from the vacuum. None of the proposals have been reliably demonstrated, yet they remain largely unchallenged. In this paper the underlying thermodynamics principles of equilibrium, detailed balance, [...] Read more.

In research articles and patents several methods have been proposed for the extraction of zero-point energy from the vacuum. None of the proposals have been reliably demonstrated, yet they remain largely unchallenged. In this paper the underlying thermodynamics principles of equilibrium, detailed balance, and conservation laws are presented for zero-point energy extraction. The proposed methods are separated into three classes: nonlinear processing of the zero-point field, mechanical extraction using Casimir cavities, and the pumping of atoms through Casimir cavities. The first two approaches are shown to violate thermodynamics principles, and therefore appear not to be feasible, no matter how innovative their execution. The third approach, based upon stochastic electrodynamics, does not appear to violate these principles, but may face other obstacles. Initial experimental results are tantalizing but, given the lower than expected power output, inconclusive. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

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14 pages, 274 KiB

Open AccessArticle

Energy Considerations of Classical Electromagnetic Zero-Point Radiation and a Specific Probability Calculation in Stochastic Electrodynamics

by Daniel C. Cole

Atoms 2019, 7(2), 50; https://doi.org/10.3390/atoms7020050 - 21 May 2019

Cited by 3 | Viewed by 2660

Abstract

The zero-point (ZP) radiation field in stochastic electrodynamics (SED) is considered to be formally infinite, or perhaps bounded by mechanisms yet to be revealed someday. A similar situation holds in quantum electrodynamics (QED), although there the ZP field is considered to be “virtual”. [...] Read more.

The zero-point (ZP) radiation field in stochastic electrodynamics (SED) is considered to be formally infinite, or perhaps bounded by mechanisms yet to be revealed someday. A similar situation holds in quantum electrodynamics (QED), although there the ZP field is considered to be “virtual”. The first part of this article addresses the concern by some about the related disturbing concept of “extracting energy” from this formally, enormous source of energy. The second part of this article introduces a new method for calculating probabilities of fields in SED, which can be extended to linear oscillators in SED. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

8 pages, 298 KiB

Open AccessArticle

CHSH-Type Inequality Involving Commuting Continuous Variables

by Andrea Valdés-Hernández, Ana María Cetto and Luis de la Peña

Atoms 2019, 7(2), 46; https://doi.org/10.3390/atoms7020046 - 25 Apr 2019

Viewed by 2244

Abstract

The correlation of projections of the momentum operators of two particles is used to derive a quantum inequality for continuous variables, which must be satisfied by any bipartite system in a pure state. This inequality resembles a Clauser–Horne–Shimony–Holt (CHSH)-type inequality except for additional [...] Read more.

The correlation of projections of the momentum operators of two particles is used to derive a quantum inequality for continuous variables, which must be satisfied by any bipartite system in a pure state. This inequality resembles a Clauser–Horne–Shimony–Holt (CHSH)-type inequality except for additional terms related to the imaginary component of the weak value of the momentum, which normally remains concealed in the usual quantum description but turns out to be of relevance for entangled states. Our results shed new light on the link between noncommutativity, entanglement and nonlocality of the quantum description. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

12 pages, 696 KiB

Open AccessArticle

The Role of Vacuum Fluctuations and Symmetry in the Hydrogen Atom in Quantum Mechanics and Stochastic Electrodynamics

by G. Jordan Maclay

Atoms 2019, 7(2), 39; https://doi.org/10.3390/atoms7020039 - 31 Mar 2019

Cited by 1 | Viewed by 3377

Abstract

Stochastic Electrodynamics (SED) has had success modeling black body radiation, the harmonic oscillator, the Casimir effect, van der Waals forces, diamagnetism, and uniform acceleration of electrodynamic systems using the stochastic zero-point fluctuations of the electromagnetic field with classical mechanics. However the hydrogen atom, [...] Read more.

Stochastic Electrodynamics (SED) has had success modeling black body radiation, the harmonic oscillator, the Casimir effect, van der Waals forces, diamagnetism, and uniform acceleration of electrodynamic systems using the stochastic zero-point fluctuations of the electromagnetic field with classical mechanics. However the hydrogen atom, with its 1/r potential remains a critical challenge. Numerical calculations have shown that the SED field prevents the electron orbit from collapsing into the proton, but, eventually the atom becames ionized. We look at the issues of the H atom and SED from the perspective of symmetry of the quantum mechanical Hamiltonian, used to obtain the quantum mechanical results, and the Abraham-Lorentz equation, which is a force equation that includes the effects of radiation reaction, and is used to obtain the SED simulations. We contrast the physical computed effects of the quantized electromagnetic vacuum fluctuations with the role of the real stochastic electromagnetic field. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

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14 pages, 801 KiB

Open AccessArticle

Entanglement, Complementarity, and Vacuum Fields in Spontaneous Parametric Down-Conversion

by Ralf Menzel, Axel Heuer and Peter W. Milonni

Atoms 2019, 7(1), 27; https://doi.org/10.3390/atoms7010027 - 19 Feb 2019

Cited by 5 | Viewed by 3868

Abstract

Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in [...] Read more.

Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong–Ou–Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

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Review

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10 pages, 218 KiB

Open AccessReview

Stochastic Electrodynamics: The Closest Classical Approximation to Quantum Theory

by Timothy H. Boyer

Atoms 2019, 7(1), 29; https://doi.org/10.3390/atoms7010029 - 01 Mar 2019

Cited by 21 | Viewed by 3925

Abstract

Stochastic electrodynamics is the classical electrodynamic theory of interacting point charges which includes random classical radiation with a Lorentz-invariant spectrum whose scale is set by Planck’s constant. Here, we give a cursory overview of the basic ideas of stochastic electrodynamics, of the successes [...] Read more.

Stochastic electrodynamics is the classical electrodynamic theory of interacting point charges which includes random classical radiation with a Lorentz-invariant spectrum whose scale is set by Planck’s constant. Here, we give a cursory overview of the basic ideas of stochastic electrodynamics, of the successes of the theory, and of its connections to quantum theory. Full article

(This article belongs to the Special Issue Stochastic Electrodynamics)

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