We discuss a procedure of measurement of an arbitrary quantum state of an optical system in Hilbert space with the dimension d=4. Such states can be realized using a collinear frequency-nondegenerate regime of spontaneous parametric down-conversion. The method has been tested for a number of polarization states of a biphoton field. A high accuracy of the reconstruction of the states (above 99%) indicates that the procedures proposed for reconstructing the quantum state of the system are adequate.

The Jaynes-Cummings model (JCM) of two-level atom interacting with the photon mode in ideal cavity plays an essential role in modern quantum optics. In previous papers ^1,2 an exact form of density matrix of the JCM with fixed atom position and photons dissipation was found. Here, taking into account the classical motion of the atom through the cavity, it is considered a case of nonideal cavity with zero temperature. We have obtained an exact expression for density matrix and calculated photon spectra and spectra of the mean number of photons in a cavity and and time dependencies of some values relevant for the one-atom maser theory.

Basing on approach developed in work¹ geometric phase for one atom maser model is calculated. Dynamics of coherent state vector on SU(2) group of "effective" Hamiltonian is investigated.

The entanglement between two identical two-level atoms interacting with two mode thermal field through a nondegenerate two-photon process has been suggested. The role of detuning has been illustrated by the example of simple one-mode two-atom model.

Rydberg matter is a condensed excited state made of highly excited atoms. State of art of research in the field of Rydberg matter is briefly reviewed. Special attention is focused on the contribution of Russian and Swedish scientists' groups to the analysis of this problem. Most attention is concentrated on physical principles of pseudopotential method and density functional theory used to describe the Rydberg matter. The description of Rydberg matter as an excited state becomes viable after the formal replacement of excited atoms by ground state pseudoatoms. This procedure has been used to find parameters of Rydberg matter made of highly excited cesium atoms. Theoretical estimations conform to experimental data available.

We treat semiclassical nonlinear dynamics of a two-level atom in the strong standing-wave field created in a high-quality cavity and in a free space with the help of two counterpropagating laser beams. First of all, we consider the dynamics of the strongly coupled atom-field system in an ideal cavity without any losses and discuss briefly nonlinear dynamical effects of random walking of an atom in a fully deterministic standing wave and Hamiltonian dynamical fractals. Then we study how these effects change in a free space when we take into account relaxation and external pumping of the standing wave. We discuss briefly new dissipative effects of synchronization between electronic and mechanical degrees of freedom of atoms, limit cycles of different periods and their bifurcations, and strange atomic attractors. Finally, we treat spontaneous relaxation as a random events in the equations of motion and study what happens with atomic fractality and limit cycles. It is shown that a self-similar structure of the scattering function (at least, on a few first levels) is conserved in the presence of spontaneous jumps. As to limit cycles, we could not resolve limit cycles of different period, but the fact of synchronization of internal and external atomic degrees of freedom is strictly established in the system with spontaneous jumps.

Notion of distance between quantum states is reviewed using Hellinger distance between probability distributions and classical formulations of quantum mechanics based on tomography scheme. The Hellinger distances between the states of damped oscillator (considered in the frame of Caldirola-Kanai model) with delta-kicked frequencies in the regime of weak and strong damping, between the photon number distribution functions in SRS process, and between spin tomograms are considered.

The notion and main conceptual and operational characteristics of the polarization state of quantum radiation are defined within the framework of the P - quasispin formalism developed earlier by the author. This state is shown to be described fully by the polarization density matrix obtained via reducing the field density operator. Basic operational quantities (quantum polarization degree, polarization "noises" , etc.), measured in quantum experiments and displaying peculiarities of polarization states, are defined with the help of P - quasispin components. The idea and features of polarization nonclassical states of quantum light are discussed. In this approach a series of nonclassical states of the biphoton radiation, manifesting unusual (for classical optics) polarization features, are analyzed. Some of applied possibilities of such states are briefly discussed.

The possibilities of spectroscopic investigations by means of correlated photon pairs (biphotons) generated in spontaneous parametric down-conversion are analyzed. It is shown that modulation of the single-photon wave packets allows one to determine the form of absorption line even if spectral width of that is much less than spectral resolution of monochromator.

This work describes some schemes using entangled photons for quantum key distribution which is fundamental of the new field called quantum communication. Depending on the circumstances, various protocols are used for the exchange of information.

Coherent responses of resonance atom layer to short optical pulse excitation are numerically considered. The inhomogeneous broadening of one-photon transition, the near dipole-dipole interaction, and the substrate dispersion are involved in analysis. Under certain intensity of incident pulses, a strong coherent interaction in the form of sharp spikes of superradiation is observed in transmitted radiation. The Lorentz field correction and the substrate dispersion weaken the effect, providing additional spectral shifts. Specific features of photon echo in the form of multiple echoes to a double or triple pulse excitation in the presence ofnear dipole-dipole interaction is discussed.

The near dipole-dipole interatomic interaction effect on transients in dense Yb vapors is considered. The influence of excitation-induced-dephasing as well as the frequency shift on signals of nonstationary nutation, free polarization decay and photon echo are taken into account. The conditions of intrinsic optical bistability occurrence in dense resonant media are discussed. The local field is shown to result in multiple single-pulse echo signals. Besides, in such media one can observe a lot of primary photon echo responses under various phase-matching conditions.

Analytical expression for a single-pulse nuclear echo signal in magnetically ordered materials has been obtained taking into account inhomogeneous broadening of spectroscopic transition and inhomogeneous distribution of enhancement factor with average value of 1. The summation of oscillations of nuclear magnetic moments with equal amplitudes and phases has been shown to take place every time in this signal. The cause for the effective suppression of oscillation of nuclear magnetic moments at the beginning of the free precession of the signal has been determined by analytical methods. The character of the dependence of a single-pulse echo signal amplitude on the tension of the external variable magnetic field, pulse duration and the width of the enhancement factor distribution has been revealed. The obtained results have been compared with experimental data observed in ferromagnetic polycrystalline sample Co₂MnSi.

Principle possibility of construction of optical echo-processors with hypercomplex architecture on the basis of physics of photon echo for computational process is shown. Mathematical basis of presentation of quaternion type in optical echo processor is developed. Coding and decoding protocols of information processing with quaternion type are offered. Example of calculating quaternion Fourier transform is demonstrated.

Given work is devoted to investigation of effect of non-Faraday rotation of polarization vector of a photon echo at influence of a constant magnetic field on the resonant environment (molecular iodine vapors) in a longitudinal direction^1-4. Magnetic field was created by the solenoid. The time interval between excite pulses accepts one of the fixed values. Experimental devices for detection of non-Faraday rotation of polarization vector of photon echo are developed and experimental dependences of an angle of this rotation from the value of magnetic field intensity and electric current are received. The method on the basis of a photon echo of intensity registration of magnetic field and electric current is developed. Accuracy of magnetic field parameters registration on the basis of the offered method of measurement is determined. Recommendations to use this method for the control of current of electro transmission line are produced.

The theory of multi-channel optical memory based on photon echo is developed. It is shown that under long-lived photon echo regime the writing and reading of information with code division is possible using phase modulation of reference and reading pulses. A simple method for construction of a system of noise-like signals, which is based on the segmentation of Frank sequence is proposed. It is shown that in comparison to the system of random biphase signals this system leads to the efficient decreasing of mutual influence of channels and increasing of random/noise ratio under reading of information.

The problem of coherent acousto-to-optic image transformation in solid-state three-level systems is theoretically studied. The graphical method of calculation of coherent responses of such systems is used. Developing method of acousto-to-optic wave-fronts transformation is of interest for processing and visualization of acoustic images of the objects which are being in sea water.

The method of registration of weak light pulses in a mode of the photon counting is discussed. The principle of photon counting, its key points and operating circuit configuration, as well as characteristics of photomultiplier tubes and basic characteristics of the photon counting is explained. The appendix of techniques of the photon counting for experiments in the field of a photon echo is considered.

The nonstationary nutation in the two-level spin-system (E'₁ -centers in crystalline quartz) dressed by microwave field is analyzed at the time of action of pulsed linearly polarized radio-frequency field applied along the static magnetic field.

We derive nonlinear evolution equations describing parametric up- and down-conversion under the conditions when either of the two interacting waves is in resonance with a material transition, e.g., with plasmonic oscillations. Using perturbation theory in the limit of the large wave-number mismatch we drive analytical expressions for two families of quasi-solitonic solutions. If material transition is in resonance with the second-harmonic then the quasi-solitons are of the Nonlinear-Schrodinger type. If the fundamental frequency is in resonance then the reduced system is the paraxial wave equation coupled to the nonlinear classical oscillator. The latter system is integrated analytically and localized solutions are presented.

The effect of continuous transformation down of laser pulse frequency due to the mechanism of quadratic nonlinearity in the uni-axial crystal is investigated. Under condition of Zakharov-Benney resonance this red frequency shift is proportional to the input intensity of a pulse, which is polarized in the plane of ordinary wave.

Transverse-longitudinal dynamics of few-cycle pulses, propagation under any angle to axis of the optical anisotropy of uniaxial crystal is researched. In such media pulses are divided on ordinary and extraordinary components, interacting between itself in nonlinear mode. It is shown that spectrum of ordinary wave depends on sign of birefringence and angle of propagation. Condition on the wave length of transverse perturbations under which diffraction able to suppress self-focusing is received.

The transverse structure of extremely short pulses propagating in two-level off-resonance medium in more than one space dimension is examined. The consideration based on the averaged Lagrangian method. The approximate solution of nonlinear wave equation in form of multidimensional stationary localized soliton-like pulse is found.

The results of the influence of the transversal perturbations on the self-similar ultra short pulse, propagating in the inversed (gain) media are studied. The two possible modes are found: self-focusing and blowup defocusing with the forming the one-dimension pulse. The mode is determined by the value of the parameter μ, that defines the attitude of characteristic lengths of diffraction and dispersion.

The solutions of the reduced Maxwell-Bloch equations for an anisotropic two-level medium, which describe the propagation of electromagnetic pulses having a duration from a few field oscillations, are studied. An influence of the permanent dipole moment of the quantum transition on dynamics of the pulses and their spectrum is considered.

The distinctive features of passing of the two-component extremely short pulses through the nonlinear media are discussed. The equations considered describe the propagation in the two-level anisotropic medium of the electromagnetic pulses consisting of ordinary and extraordinary components and an evolution of the transverse-longitudinal acoustic pulses in a crystal that contains the paramagnetic impurities with effective spin S = 1/2. The solutions decreasing exponentially and algebraically are studied.

The specific feature of propagation of extremely short pulse passing through a multilevel medium in a direction orthogonal to a magnetic induction field is discussed. The equations of the pulse propagation in such medium are obtained. It is supposed, that the pulse spectrum overlaps all allowed quantum transitions.

New effect of mismatched parametric reflection due to noncollinear three-wave interaction in quadratic and cubic medium is studied. Original theory of this phenomenon is developed. Simple expression for the parametric reflection critical angle is found. Theoretical results are confirmed by numerical simulation.

In the article a solitonic mechanism for state transfer between qubits at low temperatures is suggested, which is based on the Tanamoto quantum computer model (represented in the form of a qubit chain). The basic properties of solitons alongside with their disturbance resistance are determined. The core difficulties of the given approach are discussed.

We searched spreading of an ultra-short laser impulse in the substance considering effects concerned with dipole-dipole interaction and photo-refraction. Special photo-refracting model was chosen using experiments on ferroelectric crystals. We derived an effective equation and performed solutions of soliton type. We also elaborated these solutions for transverse stability and stability with respect to higher non-linearities. We searched dependencies ofderived solutions on the problem parameters.

In the present paper, an effective equation that looks like the nonequilibrium equation of Kadomtsev-Petviashvili and describes dynamics of an ultra-short laser impulse in two-level media with a Stark effect was got. The reduction that transforms this equation to cylindrical Korteweg-de Vries was performed and analyzed. It was got and elaborated an asymptotic equation of discrete spectra state corresponding to scattering in Laks problem for cylindrical Korteweg-de Vries.

In the present paper we found out two-dimensional long-living state of soliton type in order-disorder type ferroelectrics at spreading of an ultra-short laser impulse. We showed evolution in time of initial fuse polarization states to such formations depending on different parameters. We also searched influence of ferroelectric parameters on long-living state parameters.

Holograms recorded in planar optical waveguides by 30 fs pulses from the second harmonic of a Ti:Sapphire laser (λ is about 400 nm) are investigated. The 20 μm thick films of dichromated gelatin (n₂ = 1 .54) deposited on a polished quartz substrate (n₁ = 1 .456) is used as a planar waveguide model. The recording pulses enter the planar waveguide through its upper surface. Reconstruction in the waveguide regime is investigated for the cases when λ ≅633 nm and λ lies between 1150 and 1250 nm.

Investigation of photo-induced processes in Sn nanocrystals covered by a submonolayer of C₆₀ anions was performed with femtosecond pump-probe method. Samples in thin films were excited by 150 fs laser pulse at 400 nm (10⁹ W/cm²). Dynamics of difference transmission and reflection has been measured in the spectral range of 1 100-1700 nm. The dynamics of relaxation are quite different for various nanostructures depending on the deposition mode and the ratio of tin and fullerene content. Relaxation, observed in the samples, is explained by electron transfer from excited anions to metal followed by energy transfer from excited C₆₀ molecules to anions in the ground state.

In the framework of nonequilibrium statistical operator, the equations are derived for number of phonons, photons and collective population difference, describing the process of laser cooling for solids. With the use of these equations, the expressions are obtained for the coefficient of performance of optical thermal machine in reverse thermodynamic cycle and for limiting temperature of cooling. The criteria are formulated for the determination of type of samples, of temperature diapasons and spectral ranges that are the most perspective for the experiments on laser cooling. Numerical calculations substituting these conclusions are carried out.

Theoretical model is constructed for radiation balanced solid state lasers with up-conversion cooling effect. Kinetic equations are derived for such lasers in the framework of nonequilibrium statistical operator method and estimations are made for limiting temperatures of generation. Calculations are performed also for radiation balanced pulsed lasers where excess heat is removed by induced radiation.

Brane model of universe is considered for mass-less particle. Conservation laws inside the brane are obtained using the symmetry properties ofthe brane. Equation of Wheeler - de Wilt type is derived for mass-less particle using variation principle from these conservation laws. This equation includes term accounting the variation of brane topology. Solutions are obtained analytically at some simplifications and the dispersion relations are derived for frequency of wave associated with the particle.

The peculiarities of superfluorescence in systems consisting of a few neighbor particles (clusters), when exchange or/and electrostatic multipole interactions between particles become significant, are investigated theoretically. It is shown that interaction between particles in the cluster leads to superpuassonian statistics of emitted photons and the intensity I of quadrupole superfluorescence on the double frequency depends on the number N of active centers as I~N^α, where α> 2. In particular, α = 3 , when N >> 1. Possible schemes of cluster construction in nuclei systems are considered and prospects of observation of multipole gamma superfluorescence are discussed.

The vacuum polarization effects in the muonic atoms are investigated within the framework of the generalized quantum dynamics. We show that the effect of nonlocality in time of the interaction of a muon with a nuclei caused by the polarization on the properties of the muonic atoms can be very significant. New possibilities that the generalized quantum dynamics opens in the theory of the muonic atoms are discussed.

We investigate the effects of the nonlocality in time of the effective interaction of atoms with quantum fields, arising after integrating out certain degrees of freedom. We show that these effects can be described, in a natural way, within the formalism of the generalized quantum dynamics developed in [J. Phys. A 32, 5657 (1999)]. The new possibilities that the generalized quantum dynamics opens for solving the problem are demonstrated by using the example of a muonic atom interacting with the electronic vacuum.

Last time theoretical research on non-linear processes in ferroelectrics with hydrogen bonds have been done without consideration of the fact that an admixture subsystem can play an important role in dynamics and kinetics of perturbations. In the present paper we have searched polarization dynamics in the one-dimensional system of admixture atoms. We have also discussed effects concerned with existing of non-linear waves of Cn-Jacobi type in such structures.

Lasing (dipole nanolaser) and photo-effect in a nanostructure consisted of metallic nanoparticles and two-level systems (as quantum dots) are predicted. Experimental results on various methods of manufacturing and studying of optical properties of heterogeneous thin layers with nanoparticles of noble metals for future applications in nanolasers and photo voltaic cells are presented.

A quantum-mechanical description of a radiation-balanced solid-state laser is presented. The impurity ion levels are coupled both by the phonons of the host lattice and by the radiation field. The set of dynamic Heisenberg-Langevine equations for the material system and the phonon operators has been derived. These equations include radiative and nonradiative damping terms and quantum-stochastic forces. This description could be used for investigation of the influence of phonon dynamics on laser stability.

A lot of methods that allow analyzing of complex contours are known. In the case of the analytical type of the peak is known the least squares method is usually used. Nevertheless, if the noise level is high enough, LSM method can't be used because of the large distortions of the results. In this paper alternative way based on a wavelet-derivative spectroscopy to analyze complex contours is suggested. The efficiency of the method is demonstrated using the model data and experimental JR spectrum of polyetherimide.

In the paper we deal with the removal of a noise from a high-resolution stellar spectra. For this purpose we use the wavelet denoising along with a minimal energy criteria that allows one to effectively divide into a "useful" and a parasite components. We test this approach on an example of reconstruction of a model signal blurred by a random fractal noise.

Infrared absorption spectra and internal rotation of 1,2-di-(3,4-dinitrophenyl)ethane in crystalline phase, solutions in various temperatures have been investigated. The thermodynamic parameters of the conformational equilibrium have been determined. Quantum chemical ab initio energy calculations are carried out. The obtained data on the free energy, enthalpy and entropy differences of the conformations are discussed in terms of the reaction field model and compared with responsible results for 1 ,2-di(paranitrophenyl)ethane and 1,2-di(phenyl)ethane. The presence of the compensation effect (enthalpy-entropy compensation) in thermodynamics of conformational equilibria is confirmed.

The advantages of the probe with the optimal form are illustrated using numerical calculations for TM_1m modes. The conducted calculations show 10 times greater light throughput and the reception possibility of the more compactly localized light at the output probe aperture which could indicate better spatial resolution of the optical images in near-field optical technique using optimal probe.

Spectroscopic study of fluoride crystals with various concentrations of terbium and cerium is performed. Analysis of these spectra shows that change of nature of rare-earth centers takes place under the variation of concentration of rare-earth ions. It leads to modification of energy transfer at various concentrations of rare-earth ions and, as consequence, to modification of observed spectra.

Last time modulated structures forming in solid matter are intensively searched. They are explained as soliton lattices. In the present paper we searched domain structure dynamics in ferroelectrics with relax type absorption at interaction with laser impulses that leads to forming of regular two-dimensional soliton lattices. We also pointed out parameters at which such soliton lattices can exist.

In the present paper we discussed possibility of localized states existence in the system of admixture atoms considering dipole-dipole interactions. At viewing admixture atoms we searched a two-level system model assuming that higher levels are not disturbed in the definite temperature interval. For calculating of localized states energies in the system of admixture atoms we used the direct variational method.