# Optics and Spectroscopy (v.112, #3)

Quantum entanglement in a two-electron quantum dot in magnetic field by R. G. Nazmitdinov; A. V. Chizhov

*(319-322)*. The properties of quantum entanglement of the ground state in an exactly solvable model of a two-electron QD have been investigated. It is shown that the degree of entanglement increases with enhancement of interaction between electrons, irrespective of the shape of electron confining potential in a QD. A magnetic field destroys electron entanglement. However, the entanglement in deformed QDs is more stable against magnetic field.

A quantum steganography protocol based on

*W*class entangled states by A. M. Basharov; V. N. Gorbachev; A. I. Trubilko*(323-326)*. The condition of ɛ-security based on the quantum relative entropy is presented and a protocol that uses decoherence-free states is considered for the quantum steganography system.

Optimization of optical fiber parameters to reduce errors of quantum key distribution using entangled polarization states of biphotons by G. P. Miroshnichenko; A. A. Sotnikova

*(327-334)*. A phenomenological Hamiltonian of photons in single-mode stochastic fiber depending on the vector of random parameters is proposed. The time dynamics of single-photon density matrix in the basis of states with orthogonal polarizations is considered. The fiber-parameter-averaged quantum bit error rate (QBER) in a sifted quantum key distributed over the BB84 protocol using entangled polarization states of biphotons is found. It is shown that QBER can be significantly reduced even at large dispersions of random fiber parameters. To this end, identically fabricated fibers must be used for quantum channels A and B. The choice of pairs of fiber segments must be correlated, with a correlation coefficient close to unity. This approach is based on a remarkable property of the singlet biphoton state, which is “free of collective decoherence.” A correlated choice of fiber segments for channels A and B reduces significantly QBER, making its value below critical (i.e., equal to 0.11, a level below which a distributed key is accepted for cryptographic purposes).

Quantum key distribution with time coding on linearly dependent states by D. B. Horoshko; D. I. Pustakhod; S. Ya. Kilin

*(335-341)*. A quantum key distribution protocol with information coding by the time of photon arrival based on four linearly dependent single-photon states is proposed and the resistance of the protocol to a realistic intercept-resend attack is analyzed. The protocol on four linearly independent states is shown to be sensitive to an attack with unambiguous discrimination of all states when the level of losses in the quantum channel is higher than 7.2 dB.

Langevin and generalized Langevin types of spontaneous emission of quantum particles by A. M. Basharov

*(342-351)*. In the effective Hamiltonian representation, we have obtained a quantum stochastic differential equation of a generalized Langevin type for the evolution operator of an atomic ensemble in a microcavity in an external broadband quantized field and in a nonresonant field of the microcavity. We show that, depending on the number of particles in the atomic ensemble, its dynamics demonstrates both the Langevin and the generalized Langevin types of the two-photon spontaneous decay. In this case, one photon is emitted into the cavity mode, whereas the other photon is emitted into the external broadband electromagnetic field. The Langevin type is determined by a considerable Stark interaction of the atomic ensemble with the broadband photon-free quantized field. We show that, here, the Stark interaction is represented by a quantized Poisson process and, depending on its magnitude (at certain numbers of atoms in the ensemble), the two-photon collective spontaneous emission of microcavity atoms can be completely suppressed. In this case, the two-photon spontaneous emission of the singly excited atomic ensemble is described by the two-level model, while the atom-photon cluster of the microcavity under the described conditions is an artificial two-level quantum particle with a strong Stark interaction.

Transformation of quantum correlations between systems of different physical nature by V. N. Gorbachev; A. I. Trubilko

*(352-358)*. Using the general equation for two independent two-level atoms in a broadband two-component entangled bath, the problem of transforming quantum correlations from light to atoms is considered. To identify the transfer of inseparability, it is proposed to choose an adequate observable. Finally, we consider the average fidelity, which is a characteristic of the channel in the teleportation process.

Relaxation equation for muon spin tomogram in probability representation by Yu. M. Belousov; S. N. Filippov; V. I. Man’ko; I. V. Traskunov

*(359-364)*. The relaxation equations for spin density matrix has been widely used for the description of MuSR, NMR and in other areas. In this article the equation for spin tomogram of muon with taking into account relaxation phenomenon is written. The properties of tomographic probability distribution for the evolution tomogram are discussed.

Evolution of microwave quantum states in terms of measurable ordered moments of creation and annihilation operators by S. N. Filippov; V. I. Man’ko

*(365-372)*. The detection of microwave states is complicated by strong thermal noise, which is inevitably introduced by linear amplifiers. We show how to extract from measured data normally or anti-normally ordered moments of photon creation and annihilation operators, the set of which contains complete information on the quantum state of an electromagnetic field. Equations for the evolution of the quantum state are derived in terms of moments. Using this approach, we consider in detail issues of decoherence and thermalization of microwave quantum states. Results are illustrated using the examples of Fock, coherent, squeezed, thermal, and even and odd coherent states (Schrödinger cat states).

The effect of parametric oscillatory instability in a Fabry-Perot cavity of the Einstein telescope by S. E. Strigin

*(373-376)*. The nonlinear effect of a parametric oscillatory instability in a Fabry-Perot cavity of the Einstein Telescope is investigated. Unstable combinations of elastic and optical modes are calculated for two possible configurations of the third-generation gravitational-wave detector. The results are compared with those for the LIGO gravitational-wave interferometer.

Negative optical inertia in optomechanical systems by N. V. Voronchev; S. L. Danilishin; F. Ya. Khalili

*(377-385)*. A method of improving the sensitivity of laser-interferometer-based gravitational-wave detectors by using double (two-frequency) optical pumping is proposed. Proper selection of the optical parameters of each pump wave allows implementation of the so-called “negative inertia,” that is, an increase in the detector’s mechanical response to an external force in a wide frequency range, which is equivalent to the reduction of the inertial masses of the test bodies of the detector, while their gravitational masses remain the same. This effect allows overcoming the standard quantum limit of sensitivity for a free mass in a wide frequency range due to an enhanced signal response, rather than due to the mutual compensation of quantum noises, as in other methods. The advantage of the proposed method is its much higher immunity to the noise caused by optical losses as compared to schemes based on mutual compensation of quantum noises. A practical scheme of the gravitational-wave detector based on the “negative-inertia” effect is explored, and a set of optimal optical parameters facilitating achieving a maximum signal-to-noise ratio for the main types of astrophysical gravitational-wave sources is obtained.

Optical rigidity in a stable double-resonance regime by A. A. Rakhubovskii

*(386-393)*. The properties of the optical rigidity created by double pumping in an interferometric gravitational-wave antenna are investigated. The double-resonance regime takes place when two eigenfrequencies of the system coincide with each other. A simple criterion of the stability of the optical rigidity is proposed and is applied to calculations of the double-resonance regime. The schemes of gravitational-wave antennas using such a regime are very promising because they allow overcoming the Standard Quantum Limit. We show that a stable double-resonance regime can be realized in laboratory prototypes before its implementation in full-scale gravitational-wave detectors.

Quantum computers on multiatomic ensembles in quantum electrodynamic cavity by S. N. Andrianov; S. A. Moiseev

*(394-400)*. Schemes for the construction of quantum computers on multiatomic ensembles in quantum electrodynamic cavity are considered. With that, both encoding of physical qubits on each separate multiatomic ensemble and logical encoding of qubits on the pairs of ensembles are introduced. Possible constructions of swapping (

*SWAP*, $sqrt {SWAP} $ ) and controlled swapping gates (*CSWAP*) are analyzed. Mechanism of collective blockade and dynamical elimination procedure are proposed for realization of these gates. The comparison of the scheme solutions is carried out for the construction of quantum computer at using of physical and logical qubits. The influence of collective effects on the propagation of electromagnetic radiation in dense ultracold atomic ensembles by A. S. Kuraptsev; I. M. Sokolov; Ya. A. Fofanov

*(401-409)*. Based on the already-developed general theory (I.M. Sokolov, D.V. Kupriyanov, and M.D. Havey, JETP

*112*(2), 246 (2011)), we have studied the spatial distribution of excited atoms and of the atomic polarization that a weak monochromatic field creates in a dense ultracold atomic medium. We show that, in the case of a homogeneous random spatial distribution of atoms, the amplitude of atomic polarization averaged over spatial configurations decreases outside boundary regions according to an exponential law, while its phase linearly increases. Based on this, we have numerically determined the extinction coefficient and the light wavelength in the medium, as well as its dielectric permittivity. The dispersion of the permittivity at different concentrations has been studied. We show that, for dense clouds, the real part of the dielectric permittivity acquires negative values in a certain frequency range. Based on the calculation of the spatial distribution of excited atoms, we have analyzed the character of the transfer and trapping of quasi-resonant radiation in atomic clouds of differing density. Control for atom response in multicomponent laser fields by A. V. Andreev; S. Yu. Stremoukhov; O. A. Shutova

*(410-419)*. A theory of the nonlinear optical response of an atom interacting with a superposition of arbitrarily polarized fields is developed. The theory is based on the analytical solution of the boundary-value problem for an electron moving in a spherically symmetric intraatomic field and in the field of an external electromagnetic field. By means of the example of an argon atom interacting with a bichromatic field formed by the first and second harmonics of a Ti:sapphire laser, it is shown that, when an atom interacts with the field of two polarized pulses the polarization directions of which are not collinear, the response spectrum significantly depends on the laser radiation parameters—the duration and intensity of pulses, the time of delay between them, and the angle between the directions of polarization vectors. Generation of THz radiation is shown to be possible in the ionization-free regime due to intraatomic nonlinearity.

Calculation of vibrational energy levels of triatomic molecules with the

*C*_{2v}and*C**s*_{ }symmetries by summing divergent series of the Rayleigh-Schrödinger perturbation theory by A. D. Bykov; K. V. Kalinin*(420-430)*. The Rayleigh-Schrödinger perturbation theory is applied to calculation of vibrational energy levels of triatomic molecules with the

*C*_{2v}and*C**s*_{ }symmetries: SO_{2}, H_{2}S, F_{2}O, HOF, HOCl, and DOCl. Particular attention is given to the states coupled by anharmonic resonances; for such states, the perturbation theory series diverge. To sum these series, the known methods of Padé, Padé-Borel, and Padé-Hermite and the method of power moments are used. For low-lying levels, all the summation methods give satisfactory results, while the method of quadratic Padé-Hermite approximants appears to be more efficient for high-excited states. Using these approximants, the structure of singularities of the vibrational energy, as a function in the complex plane, is studied. Validated spectrophotometric method for the determination, spectroscopic characterization and thermal structural analysis of duloxetine with 1,2-naphthoquinone-4-sulphonate by Sevgi Tatar Ulu; Fikriye Tuncel Elmali

*(431-437)*. A novel, selective, sensitive and simple spectrophotometric method was developed and validated for the determination of the antidepressant duloxetine hydrochloride in pharmaceutical preparation. The method was based on the reaction of duloxetine hydrochloride with 1,2-naphthoquinone-4-sulphonate (NQS) in alkaline media to yield orange colored product. The formation of this complex was also confirmed by UV-visible, FTIR,

^{1}H NMR, Mass spectra techniques and thermal analysis. This method was validated for various parameters according to ICH guidelines. Beer’s law is obeyed in a range of 5.0–60 μg/mL at the maximum absorption wavelength of 480 nm. The detection limit is 0.99 μg/mL and the recovery rate is in a range of 98.10–99.57%. The proposed methods was validated and applied to the determination of duloxetine hydrochloride in pharmaceutical preparation. The results were statistically analyzed and compared to those of a reference UV spectrophotometric method. Determination of the effective nuclear charge from EPR data using a modified crystal-field theory by R. Yu. Babkin; K. V. Lamonova; S. M. Orel; Yu. G. Pashkevich; V. F. Meshcheryakov

*(438-442)*. We propose a scheme for determining the effective nuclear charge

*Z*_{ef}^{CF}of a 3*d*ion placed in a crystal field of arbitrary symmetry. As an example, we consider the Co^{2+}ion in a matrix MCO_{3}(M = Ca, Cd). We show that the effective nuclear charge*Z*_{ef}^{CF}correlates with a change in the degree of the bond covalence. Effect of the fluorine substitution in ethyl groups of 1,4-distyrylbenzene on the fine structure fluorescence and fluorescence excitation spectra by I. A. Vasil’eva; N. A. Voitova; R. N. Nurmukhametov

*(443-452)*. The fine-structure fluorescence and fluorescence excitation spectra of conjugated chain compounds, 1,4-distyrylbenzene (DSB) and its fluorine-substituted derivative α,ω-1,4-distyrylbenzene, have been obtained by the Shpolskii method in an

*n*-octane matrix at a temperature of 4.2 K. These spectra have been simulated by representing the band of each of the vibronic transitions as the sum of a zero-phonon line and a phonon wing with the corresponding parameters, such as the half-widths of the spectral lines and the Debye-Waller factors. Based on this simulation, the relative intensities of vibronic transitions have been determined and the frequencies of normal vibrations in the*S*_{0}and*S*_{1}^{*}states have been refined. It has been found that the energy of the purely electronic transition in the molecule of the fluorine-substituted derivative is higher by 950 cm^{−1}compared to the unsubstituted DSB. The parameters of the Franck-Condon and Herzberg-Teller interactions have been determined. The observed violation of the mirror symmetry between the conjugated spectra is explained by the interference of intramolecular interactions. The effect of spin-orbit interaction on the dynamics of ultimately short pulses in graphene systems by N. N. Yanyushkina; M. B. Belonenko; N. G. Lebedev

*(453-456)*. The effect of the spin-orbit interaction of graphene electrons placed on a Ni (111) surface on the dynamics ultimately short pulses is considered. The dispersion law of electrons in graphene is calculated on the basis of the Rashba Hamiltonian. The dynamics of an ultimately short electromagnetic pulse considering the Rashba interaction and without it is under investigation.

Quantum dynamics of formation of an unstable field state in the process of intracavity third-harmonic generation by S. T. Gevorkian; M. S. Gevorkian

*(457-464)*. The dynamics of the Wigner functions and quantum entropy of the fundamental and third-harmonic modes is studied for the process of intracavity third-harmonic generation. It is shown that quantum dynamics of the system strongly depends on the coupling coefficient of the interacting modes. The dynamics of the transition of the system from a stable to an unstable state is investigated.

Kinetics of the refractive index change in the core of active fibers, doped with Yb

^{3+}and Er^{3+}ions, under pulsed optical pumping by V. V. Gainov; O. A. Ryabushkin*(465-473)*. The kinetics of refractive index change (RIC) in the core of Yb

^{3+}/Er^{3+}fibers at a radiation wave-length lying beyond the range of resonant absorption of active ions under pulsed pumping of fiber laser has been analyzed. The measurement of RIC kinetics with a Mach-Zehnder interferometer makes it possible to separate the contributions of the electronic and thermal RIC mechanisms and determine quantitatively the temperature profile inhomogeneity in the fiber. The measured values are compared with the numerical estimates derived from the spectral properties of the active medium in order to check the modern models of RIC in active fibers. The phenomenon of conical refraction in a thin-layer periodic semiconductor-dielectric structure in a magnetic field by A. A. Bulgakov; I. V. Fedorin

*(474-481)*. The propagation of electromagnetic waves along the optical axes of a thin-layer periodic semiconductor-dielectric structure in an external magnetic field (i.e., under conditions of external and internal conical refraction) has been investigated. It is shown that the conditions for conical refraction can be implemented in certain regions by changing the external magnetic field, wave frequency, and thickness of the layers forming the structure. By varying the above-mentioned characteristics, one can efficiently control the conical refraction parameters; in particular, the opening angles of the cone of internal and external conical refraction and the inclination of the optical axes with respect to the periodicity axis can be varied in a wide range. The results of this study may be useful for designing millimeter-wave, submillimeter-wave, and IR devices.