Quantum Electronics

Modelling the mechanisms of quantum logic using the method of superimposed Fourier holograms based on the nonlinearity of the exposure characteristics of holographic recording media

Alexander V. Pavlov, Vyatcheslav V. Orlov

Published Mar 1, 2019• 6 citations

Abstract

A Fourier-holography scheme with superimposed holograms and phase conjugation is considered. It is shown that the sub-holograms, arising from the recording of superimposed holograms due to quadratic nonlinearity of the exposure characteristics of holographic recording media, form the connections necessary for the realisation of the quantum-logic mechanism of sequential projection of the input vector onto the subspaces of the recorded images. A classical mechanism of the 'Linda' cognitive phenomenon belonging to the category of quantum-like ones is described. An experimental illustration of the self-sustained formation of sub-holograms due to the nonlinearity of the exposure characteristics of holographic recording media is given.

DOI: 10.1070/qel16748

Related papers

Simulation of quantum logic by linear recording of superimposed Fourier holograms: Linda phenomenon

Alexander V. Pavlov

Abstract The classical mechanism of the quantum-like cognitive phenomenon of ‘Linda’ is demonstrated, which operates by linear recording of Fourier superimposed holograms in a phase-conjugate 4f-scheme. The results of numerical experiments are presented.

Quantum ElectronicsJul 31, 20192 citations

Holographic implementation of quantum-like cognitive models

Alexander V. Pavlov

Subject of study. A 4 f Fourier-holography scheme with phase conjugation in the correlation plane and the corresponding Grossberg “Instar” neural-network model were examined to assess the feasibility of implementing quantum-like models of information processing. Aim of study. The aim was to develop a Fourier-holography scheme model consistent with the mathematical formalism of quantum mechanics used in quantum-like cognitive models. Method. Analytical modeling and numerical simulations were performed by representing the processed information with a homogeneous isotropic random field model. Main results. The results showed that the Fourier-holography setup incorporating nonlinear phase conjugation in the correlation plane could serve as a limited analog of a quantum system in terms of parallel processing and choice from a superposition. In this case, the choice was not random; rather, it was determined by the nonlinear transfer function of the phase-conjugating mirror. The shift-invariance, ensured by a thin Fourier hologram, imparted an additional capability—making decisions in the form of a superposition described by a linear prediction model; some researchers consider this approach as a possible mechanism underlying the phenomenon of intuition. Practical significance. An analytical description, consistent with the information-processing model, is required for developing holographic simulators of quantum information-processing systems and computing devices.

Journal of Optical TechnologyJun 1, 20250 citations

Modeling of quantum-like cognitive phenomena by the Fourier-holography technique under the choice of alternatives

Alexander V. Pavlov

The article is dedicated to the search for a biologically motivated mechanism of the cognitive phenomenon of violation of the classical formula of total probability for the disjunction of incompatible events, which is considered by a number of researchers as a quantum-like phenomenon. A classical mechanism implemented by the 6f Fourier holography scheme of the resonant architecture that does not require reference to quantum mechanics either in its physical nature or at the level of formalism is demonstrated. In the analysis, the decision-making is interpreted as a choice of alternatives by using the non-cooperative game "Prisoner's Dilemma". The approach to the task is based on the search for a mechanism for forming a conditional estimate under a condition that contradicts the rule of monotonous decision logic. It is demonstrated that this estimate, in contrast to the unconditional and conditional one with a non-contradictory condition, is formed by logic with exception. The ring architecture of the holographic setup corresponds to the biologically inspired neural network concept of the excitation ring and implements cognitive dissonance on logic with exception. Conditions and ranges of violation of the classical formula of total probability in relation to the correlation radius of the reference image recorded in a hologram storing the monotone logic inference rule are analytically determined. The analytical model is confirmed by a quantitative coincidence of the results of numerical modeling with the published results of natural experiments.

Computer OpticsAug 1, 20212 citations

Quantum holography

Sergey N. Andrianov, А. С. Алимбекова

The possibility of quantum holography in the medium of in homogeneously broadened two-level atoms for two-photon regime of operation proposed by A. Rebane is discussed and peculiarities of such holographic process are considered. The experimental scheme for recording of such holograms is suggested. The conditions for realization of quantum holographic process with this scheme are considered. Also, the original approach for quantum holography in homogeneously broadened three-level atomic system using “stopping of light” procedure is proposed and the theory of such process is constructed

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEApr 20, 20040 citations

Nonlinear hologram recording in resonant media and optical control of diffraction efficiency

Alexei L. Tolstik, Omar A. Ormachea

The schemes for nonlinear recording of dynamic holograms in multilevel resonant media, in conditions when the fifth- and higher-order nonlinearities are exhibited, have been studied both theoretically and experimentally. The optical methods to control the diffraction efficiency of nonlinear dynamic holograms with the use of an additional light beam tuned out into the absorption band from the ground or excited state of the molecules have been considered.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEMay 20, 20060 citations

Interference-holographic processes of light field transformation by multiwave mixing in resonant media

Alexei L. Tolstik

This paper presents the results of theoretical and experimental studies into the processes of light field transformations upon multiwave mixing. The principal aim is to develop a theory of multiwave mixing in complex molecular media in conditions of exhibited internal (scattering from dynamic gratings) and external (resonator) feedback, to determine a mechanism of light field transformations at the dynamic holograms and by nonlinear interferometers, to work out and introduce into practice novel nonlinear-optical methods for the control over the energy and spatial-temporal characteristics of light beams. The possibilities for phase conjugation with simultaneous frequency conversion of a signal wave are analyzed. The methods aimed at the realization of various types of optical bistability, spatial hysteresis, regular and chaotic intensity oscillations are proposed and investigated

International Conference on Laser and Fiber-Optical Networks ModelingDec 22, 20050 citations