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Liquid Crystals

Simulation of real entangled systems based on the model of a pair of entangled solitons

Anastasiya V. Kondakova, T. F. Kamalov

Published Sep 12, 2022• 1 citation
Publisher

Abstract

The features of the propagation of optical solitons in a dielectric are currently actively being applied in the fields of applied use of quantum phenomena. When creating new technologies based on the theory of solitons, the topical issue arises of developing soliton models accessible for practical implementation, suitable for subsequent modelling of real entangled systems. We chose a nematic liquid crystal as a dielectric medium for considering optical 1D envelopes of solitons. On the basis of a mathematical model of the behaviour of a pair of entangled solitons in a medium, a special stochastic representation of the wave function is constructed for subsequent modelling of entangled states of photons. Based on a qualitative analysis, a constructive addition to the entangled photon detector is proposed. The complete replacement of classical elements is discussed with a view to the possible use of the idea in the creation of quantum computers.

DOI
10.1080/02678292.2022.2113833

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The features of the propagation of optical solitons in a dielectric are currently actively being applied in the fields of applied use of quantum phenomena. When creating new technologies based on the theory of solitons, the topical issue arises of developing soliton models accessible for practical implementation, suitable for subsequent modelling of real entangled systems. We chose a nematic liquid crystal as a dielectric medium for considering optical 1D envelopes of solitons. On the basis of a mathematical model of the behaviour of a pair of entangled solitons in a medium, a special stochastic representation of the wave function is constructed for subsequent modelling of entangled states of photons. Based on a qualitative analysis, a constructive addition to the entangled photon detector is proposed. The complete replacement of classical elements is discussed with a view to the possible use of the idea in the creation of quantum computers.
Starting with the projective interpretation of the Hilbert space special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is considered with the aim to model quantum states via classical computer. Entangled solitons construction having been earlier introduced in the nonlinear spinor field model for the calculation of the Einstein-Podolsky-Rosen (EPR) spin correlation for the spin-1/2 particles in the singlet state, the other example is now studied. The latter concerns the entangled envelope solitons in Kerr dielectric with cubic nonlinearity, where we use two-solitons configurations for modeling the entangled states of photons. Finally, the concept of stochastic qubits is used for quantum computing modeling.
Abstract The conditions of soliton formation in a liquid crystal layer for generation of a pair of photons in an entangled quantum state (biphotons) during quantum calculations are considered. The geometrical dimensions of the soliton generated by a pulse of optical radiation, its dynamics and stability are estimated by using the knowledge of the liquid crystal physical parameters as well as its non-linear optical properties. The possibility of overlapping of optical solitons neighboring in space or time (or regions inside the liquid crystal layer, in which the deformation induced by the light wave field from successive light pulses occurs) is considered. In nematic liquid crystals (LCs), it is possible to obtain single solitons with spatial size of several tens of micrometers and less, the formation time from fractions of a millisecond to tens of milliseconds, and the existence time from fractions of the millisecond to hundreds of milliseconds. On this basis, it is possible to “encode” entangled states with a high level of signal distinction and to carry out quantum calculations.
It is an urgent task to create reliable, cost‐effective, simple in technology elements for performing quantum computing with qubits based on pairs of photons having entangled polarizations. The conditions of soliton formation in a liquid crystal (LC) layer for generation of a pair of photons in an entangled quantum state (biphotons) during quantum calculations are considered. The geometrical dimensions of the soliton generated by a pulse of optical radiation, its dynamics and stability are estimated. Besides, propagation of both extraordinary and ordinary rays in the nematic LC with different boundary conditions is calculated. The paper is a demonstration of using display technologies and science for new generation of optical processing tasks. From another side, quantum computing can be used also in images processing for the tasks of display picture rendering.
Special stochastic representation of the wave function in Quantum Mechanics (QM), based on soliton realization of extended particles, is suggested with the aim to model quantum states via classical computer. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein, Podolsky, Rosen (EPR) spin correlation is calculated and shown to coincide with the quantum mechanical one for the spin-1/2 particles in the singlet state. The concept of stochastic qubits is used for quantum computing modelling.
Stochastic realization of the wave function in quantum mechanics with the inclusion of soliton representation of extended particles is discussed. Two-soliton configurations are used for constructing entangled states in generalized quantum mechanics dealing with extended particles, endowed with nontrivial spin S. Entangled solitons construction being introduced in the nonlinear spinor field model, the Einstein-Podolsky-Rosen (EPR) correlation is calculated and shown to coincide with the quantum mechanical one for the 1/2-spin particles. The concept of stochastic qubits is used for quantum computing modeling.
Abstract Liquid crystals, with their ability to self-assemble, strong response to an electric field and integrability into complex systems, are key materials in light-beam manipulation 1 . The recently discovered ferroelectric nematic liquid crystals 2,3 also have considerable second-order optical nonlinearity, making them a potential material for nonlinear optics 4,5 . Their use as sources of quantum light could considerably extend the boundaries of photonic quantum technologies 6 . However, spontaneous parametric down-conversion, the basic source of entangled photons 7 , heralded single photons 8 and squeezed light 9 , has so far not been observed in liquid crystals—or in any liquids or organic materials. Here we implement spontaneous parametric down-conversion in a ferroelectric nematic liquid crystal and demonstrate electric-field tunable broadband generation of entangled photons, with an efficiency comparable to that of the best nonlinear crystals. The emission rate and polarization state of photon pairs is markedly varied by applying a few volts or twisting the molecular orientation along the sample. A liquid-crystal source enables a special type of quasi-phase matching 10 , which is based on the molecular twist structure and is therefore reconfigurable for the desired spectral and polarization properties of photon pairs. Such sources promise to outperform standard nonlinear optical materials in terms of functionality, brightness and the tunability of the generated quantum state. The concepts developed here can be extended to complex topological structures, macroscopic devices and multi-pixel tunable quantum light sources.