Rabi Waves and Peculiarities of Raman Scattering in Carbon Nanotubes, Produced by High Energy Ion Beam Modification of Diamond Single Crystals

QED-model for multichain coupled qubit system, proposed in \cite{Part1}, was confirmed by Raman scattering studies of carbon zigzag-shaped nanotubes, produced by high energy ion beam modification of natural diamond single crystals. New quantum optics phenomenon - Rabi waves - has been experimentally identified for the first time. Raman spectra in perfect quasi-1D carbon nanotubes are quite different in comparison with well known Raman spectra in 2D carbon nanotubes of larger diameter. They characterized by vibronic mode of Su-Schriffer-Heeger $\sigma$-polaron lattice and its revival part in frequency representation, which is the consequence of Rabi wave packet formation.Comment: 10 pages, 3 figure

Rabi Waves in Carbon Nanotubes

QED-model for the multichain qubit system with interactions of qubits and chains between themselves on the example of the system of $\sigma$-polarons in carbon zigzag nanotubes, interacting with quantized EM-field, is considered analytically. The possibility of experimental detection of Rabi waves in conventional stationary optical experiments for any quasi-1D system with strong electron-photon interaction is predicted.Comment: 4 pages, 2 figure

Rabi Waves in Carbon Nanotubes - Experiment

Rabi waves have been experimentally registered for the first time by Raman scattering studies of zigzag nanotubes, produced by high energy ion beam modification of natural diamond single crystals. Antiferroelectric spin wave resonance has been detected for the first time in Raman spectroscopy practice in given samples. Substantial qualitative and quantitative changes in Raman spectra in dependence on propagation direction of laser excitation wave have been found.Comment: 5 pages, 3 figures. Author list is correcte

Symmetry of Differential Equations and Quantum Theory

The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered within the frames of the number theory) determine the mathematical nature of the quantities, incoming in given equations. It allowed to proof the main postulate of quantum mechanics, consisting in that, that to any mechanical quantity can be set up into the correspondence the Hermitian matrix by quantization. High symmetry of Maxwell equations allows to show, that to quantities, incoming in given equations can be set up into the correspondence the Quaternion (twice-Hermitian) matrix by their quantization. It is concluded, that the equations of the dynamics of mechanical systems are not invariant under transformations of quaternion multiplicative group and, consecuently, direct application of quaternions with usually used basis \{e, i, j, k \} to build the new version of quantum mechanics, which was undertaken in the number of modern publications, is incorrect. It is the consequence of non-abelian character of given group. At the same time we have found the correct ways for the creation of the new versions of quantum mechanics on the quaternion base by means of choice of new bases in quaternion ring, from which can be formed the bases for complex numbers under multiplicative groups of which the equations of the dynamics of mechanical systems are invariant.Comment: arXiv admin note: substantial text overlap with arXiv:1102.2619, arXiv:1101.188

Quantum-mechanical equation for spectroscopic transitions in ordered ferroelectric and ferromagnetic chains

Transition operator method is proposed for description of the dynamics of spectroscopic transitions. Quantum-mechanical analogue of Landau-Lifshitz equation has been derived for the system representing itself the periodical ferroelectrically (ferromagnetically) ordered chain of $N$ equivalent elements, interacting with external oscillating electromagnetic field. Landau-Lifshitz equation was represented in Lorentz invariant form by using Hilbert space over the ring of quaternions. It has been shown, that spin vector can be considered to be quaternion vector of the state of the system studied. From comparison with experiment for the first time from pure optical measurements the value of spin $S = 1/2$ for optically active centers - spin-Peierls solitons in carbon chains - has been obtained. The ratio of imagine to real components of complex charge is evaluated for given centers to be $\frac{g}{e} \approx (1.1 - 1.3)10^{2}$.Comment: 9 pages, revtex

Classical and Quantum Electrodynamics Concept Based on Maxwell Equations' Symmetry

The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. It has in general case quaternion single structure, consisting of four independent field constituents, which differ with each other by the parities under space inversion and time reversal. Generalized Maxwell equations for quaternion four-component EM-field are obtained. Invariants for EM-field, consisting of dually symmetric parts are found. It is shown, that there exists physical conserving quantity, which is simultaneously invariant under both Rainich dual and additional hyperbolic dual symmetry transformation of Maxwell equations. It is spin in general case and spirality in the geometry, when electrical and magnetic vectors $\vec{E}$, $\vec{H}$ are directed along coordinate axes in ($\vec{E}$, $\vec{H}$) functional space. It is additional proof for quaternion four component structure of EM-field to be a single whole. Canonical Dirac quantization method is developed in two aspects. The first aspect is its application the only to observable quantities. The second aspect is the realization along with well known time-local quantization of space-local quantization and space-time-local quantization. It is also shown, that Coulomb field can be quantized in 1D and 2D systems. New model of photons is proposed. The photons in quantized EM-field are main excitations in oscillator structure of EM-field, which is equivalent to spin S = 1 "boson-atomic" structure, like matematically to well known spin S = 1 boson matter structure - carbon atomic backbone chain structure in many conjugated polymers. They have two kind nature. The photons of the first kind and the second kind represent themselves respectively neutral chargeless EM-solitons and charged spinless EM-solitons of Su-Schrieffer-Heeger family.Comment: 44 pages. arXiv admin note: substantial text overlap with arXiv:1102.2619, arXiv:cond-mat/0106126, arXiv:0902.0173, arXiv:cond-mat/991114

Analytical Solution of Mathieu Equation

The general solution of the homogeneous damped Mathieu equation in the analytical form, allowing its practical using in many applications, including superconductivity studies, without numerical calculations has been found.Comment: 5 page

Coherent Quantum Optics Phenomena in Carbon Low-Dimensional Systems

Brief review of the theoretical and experimental results, based mainly on the works of authors, in the application of quantum field theory to the study of carbon low-dimensional systems - quasi-1D carbon nanotubes, carbynes and graphene with emphasis on formation of longlived coherent states of joint photon-electron and joint resonance phonon-electron systems of given materials is presented

Quantum Field Effects in Stationary Electron Spin Resonance Spectroscopy

It is proved on the example of electron spin resonance (ESR) studies of anthracites, that by strong electron-photon and electron-phonon interactions the formation of the coherent system of the resonance phonons takes place. The acoustic quantum Rabi oscillations were observed for the first time in ESR-spectroscopy. Its Rabi frequency value on the first damping stage was found to be equal 920.6 kHz, being to be independent on the microwave power level in the range 20 - 6 dB [0 dB corresponds to 100 mW]. By the subsequent increase of the microwave power the stepwise transition to the phenomenon of nonlinear quantum Rabi oscillations, characterised by splitting of the oscillation group of lines into two subgroups with doubling of the total lines' number takes place. Linewidth of an individual oscillation line becomes approximately the twofold narrower, being to be equal the only to $0.004 \pm 0.001$ G. Along with the absorption process of EM-field energy the emission process was observed. It was found, that the emission process is the realization of the acoustic spin resonance, the source of acoustic wave power in which is the system of resonance phonons, accumulated in the samples by the registration with AFC. It has been found, that the lifetime of coherent state of a collective subsystem of resonance phonons in anthracites is very long and even by room temperature it is evaluated by the value exceeding 4.6 minutes. The model of new kinds of instantons was proposed. They are considered to be similar in the mathematical structure to Su-Schrieffer-Heeger solitons with "propagation" direction along time $t$-axis instead of space $z$-axis. The proof, that the superconductivity state in the anthracite samples studied is produced at the room temperature in ESR conditions in the accordance with the theory of the quantised acoustic field, has experimentally been obtained.Comment: arXiv admin note: text overlap with arXiv:0907.5484, arXiv:1407.1950 by other author

Ferrimagnetic Spin Wave Resonance and Superconductivity in Carbon Nanotubes

The phenomenon of ferrimagnetic spin wave resonance [uncompensated antiferromagnetic spin wave resonance] has been detected for the first time. It has been observed in carbon nanotubes, produced by high energy ion beam modification of diamond single crystals in $\$ direction. Peculiarities of spin wave resonance observed allow to insist on the formation in given nanotubes of $s^+$ superconductivity at room temperature, coexisting with uncompensated antiferromagnetic ordering.Comment: arXiv admin note: substantial text overlap with arXiv:1201.028