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We consider the generation of Schr\"odinger cat states using a quantum measurement-induced logical gate where entanglement between the input state of the target oscillator and the Fock state of the ancillary system produced by the quantum non-demolition entangling $C_Z$ operation is combined with the homodyne measurement. We utilize the semiclassical approach to construct both the input-output mapping of the field variables in the phase space and the wave function of the output state. This approach is found to predict that the state at the gate output is represented by a minimum disturbed cat-like state which is a superposition of two initial state copies symmetrically displaced by momentum variable. For the target oscillator prepared in the coherent state, we show that the fidelity between the exact solution for the gate output state and the "perfect" Schr\"odinger cat reconstructed from the semiclassical theory can reach high values exceeding 0.99., Comment: 14 pages, 12 figures

We develop the algebraic method based on the Lie algebra of quadratic combinations of left and right superoperators associated with matrices to study the Lindblad dynamics of multimode bosonic systems coupled a thermal bath and described by the Liouvillian superoperator that takes into account both dynamical (coherent) and environment mediated (incoherent) interactions between the modes. Our algebraic technique is applied to transform the Liouvillian into the diagonalized form by eliminating jump superoperators and solve the spectral problem. The temperature independent effective non-Hermitian Hamiltonian, $\hat{H}_{eff}$, is found to govern both the diagonalized Liouvillian and the spectral properties. It is shown that the Liouvillian exceptional points are represented by the points in the parameter space where the matrix, $H$, associated with $\hat{H}_{eff}$ is non-diagonalizable. We use our method to derive the low-temperature approximation for the superpropagator and to study the special case of a two mode system representing the photonic polarization modes. For this system, we describe the geometry of exceptional points in the space of frequency and relaxation vectors parameterizing the intermode couplings and, for a single-photon state, evaluate the time dependence of the speed of evolution as a function of the angles characterizing the couplings and the initial state., Comment: 19 pages, 3 figures, a continuation of arxiv:2207.01383

Spectral loopholes in the 1000-2100 nm range have been the focus of attention of quantum hacking research aimed at searching and elimination of vulnerabilities in quantum key distribution systems. In this work, we concentrate on shorter wavelengths ranged from 400 nm up to 800 nm and experimentally study spectra of insertion losses for a number of fiber optical components to assess potentials for their implementation as countermeasures. We show that efficiency of the elements commonly used as countermeasures against hacking attacks in the telecom range can be significantly impaired in the visible range. It is found that the vulnerabilities detected in this range play an increasingly important role for hacking strategies such as the induced-photorefraction attack whose efficiency improves when the wavelength decreases., Comment: 11 pages, 7 figures

The open water surface is known to be charged. Yet, the magnitude of the charge and the physical mechanism of the charging remain unclear, causing heated debates across the scientific community. Here we directly measure the charge Q of microdrops ejected from hydrophilic and hydrophobic capillaries and show that the water surface can take both positive or negative charge values depending on pH and the capillary type. Our experiments, theory, and simulations provide evidence that a junction of two aqueous interfaces with a different ion adsorption energy (e.g., liquid-solid and liquid-air interfaces) develops a pH-dependent contact potential difference {\Delta}{\phi} up to 52 mV. The longitudinal charge transfer between the interfaces stimulated by {\Delta}{\phi} determines the charge of the open water surface. The suggested static electrification mechanism provides far-reaching insights into the origin of electrical potentials in biological and electrochemical energy systems., Comment: 21 pages main text, 4 figures, supporting information, including the theory of the charge transfer between two dissimilar aqueous interfaces induced by the contact potential difference, details of molecular dynamics simulations, and additional graphs, photos, and diagrams, including Figures S1 to S18 and Table S1

We present a scheme of quantum repeater that uses entangled multimode coherent states which are obtained by electro-optic modulation of symmetric and antisymmetric Schr\"odinger cat states. In this method subcarrier modes of the phase modulated states generated by the remote parties are sent to a symmetric beam splitter at the central node. The entangled coherent states are heraldedly prepared by photon counting measurements at the output channels of the beam splitter. We study how the effects of decoherence in the quantum channel affect statistics of photocounts and corresponding fidelity. We show how the proposed scheme can be useful for extending range of quantum key distribution with sub carrier wave encoding by exploiting quantum teleportation with the generated entanglement., Comment: 18 pages, 10 figures

We introduce algebraic approach for superoperators that might be useful tool for investigation of quantum (bosonic) multi-mode systems and its dynamics. In order to demonstrate potential of proposed method we consider multi-mode Liouvillian superoperator that describes relaxation dynamics of a quantum system (including thermalization and intermode coupling). Considered algebraic structure of superoperators that form Liouvillian and their algebraic properties allows us to diagonilize multi-mode Liouvillian to find its spectrum. Also it allows to derive linear by mean number of thermal (environmental) photons approximation for time-evolution superoperator that keeps amount of considered dimensions in Fock space finite (assuming initial amount of dimensions finite) that might be helpful regarding entanglement dynamics problems. Conjugate Liouvillian is considered as well in order to perform analysis in Heisenberg picture, it can be implemented for multi-time correlation functions derivation.

In this paper, using the full security framework for continuous variable quantum key distribution (CV-QKD), we provide a composable security proof for the CV-QKD system in a realistic implementation. We take into account equipment losses and contributions from various components of excess noise and evaluate performance against collective and coherent attacks assuming trusted hardware noise. The calculation showed that the system remains operable at channel losses up to 10.2 dB in the presence of collective attacks and up to 7.5 dB in the presence of coherent ones., Comment: 28 pages, 5 figures

The renewable energy sector critically needs low-cost and environmentally neutral energy storage solutions throughout the entire device life cycle. However, the limited performance of standard water-based electrochemical systems prevents their use in specific applications. Meanwhile, recent fundamental studies revealed dielectric anomalies of water near solid-liquid interfaces of carbon-based nanomaterials. In contrast to the bulk water properties, these anomalies of water under nano-confinement and in the presence of electric fields have not yet been understood and used. Here, we experimentally study the ability of the interfacial water layer to engender and store charge in electrochemical double-layer capacitance. We demonstrate the prototype of a 'water only' membrane-electrode assembly. The prototype exhibits characteristics with a perspective of competing with existing batteries and supercapacitors without using electrolytes as ionic carriers. The results provide the impetus for developing high-energy-density electrochemical double-layer capacitors and open up other avenues for ecologically-neutral batteries, fuel cells, and nanofluidic devices., Comment: 21 pages, 3 figures. The supplementary information includes Samples preparation and treatment, Measurement methods, Figures S1 to S10, and Table S1

We study minimum-energy pathways (MEPs) between the branches of metastable helical structures in chiral nematic liquid crystals (CNLCs)subjected to the electric field applied across the cell. By performing stability analysis we have found that, for the branches with non-vanishing half-turn number, the threshold (critical) voltage of the Freedericksz transition is an increasing function of the free twisting wave number. The curves for the threshold voltage depend on the elastic anisotropy and determine the zero-field critical free twisting number where the director out-of-plane fluctuations destabilize the CNLC helix. For each MEP passing through a first order saddle point we have computed the energy barrier as the energy difference between the saddle-point and the initial structures at different values of the applied field. In our calculations, where the initial approximation for a MEP at the next step was determined by the MEP obtained at the previous step, the electric field dependence of the energy barrier is found to exhibit the hysteresis. This is the hysteresis of electrically driven transition of the saddle-point configuration between the planar and the tilted structures involving out-of-plane director deformations. It turned out that, by contrast to the second-order Freedericksz transition, this transition is first order and we have studied how it depends on the zenithal anchoring energy strength., Comment: revtex 4-2, 10 pages, 7 figures, a continuation of arXiv:1911.03987 [cond-mat.soft]

We examine different methods to implement coherent detection in the subcarrier wave quantum key distribution (SCW QKD) systems. For classical wavefields, we present the models describing homodyne-type and heterodyne-type coherent detection schemes needed to extract information from the quadrature phase-coded multimode signals used in SCW QKD. Practical feasibility of the proposed schemes is corroborated by the experiments., Comment: 14 pages, 10 figures

We apply the minimum energy paths (MEPs) approach to study the helix unwinding transition in chiral nematic liquid crystals. A mechanism of the transition is determined by a MEP passing through a first order saddle point on the free energy surface. The energy difference between the saddle point and the initial state gives the energy barrier of the transition. Two starting approximations for the paths are used to find the MEPs representing different transition scenarios: (a) the director slippage approximation with in-plane helical structures; and (b) the anchoring breaking approximation that involves the structures with profound out-of-plane director deviations. It is shown that, at sufficiently low voltages, the unwinding transition is solely governed by the director slippage mechanism with the planar saddle point structures. When the applied voltage exceeds its critical value below the threshold of the Freedericksz transition, the additional scenario through the anchoring breaking transitions is found to come into play. For these transitions, the saddle point structure is characterized by out-of-plane deformations localized near the bounding surface. The energy barriers for different paths of transitions are computed as a function of the voltage and the anchoring energy strengths., Comment: revtex4-1, 13 pages, 12 figures

We employ the transfer matrix approach combined with the Green's function method to theoretically study polarization resolved far-field angular distributions of photoluminescence from quantum nanorods (NRs) embedded in an anisotropic polymer film. The emission and excitation properties of NRs are described by the emission and excitation anisotropy tensors. These tensors and the solution of the emission problem expressed in terms of the evolution operators are used to derive the orientationally averaged coherency matrix of the emitted wavefield. For the case of in-plane alignment and unpolarized excitation, we estimate the emission anisotropy parameter and compute the angular profiles for the photoluminescence polarization parameter such as the degree of linear polarization, the Stokes parameter $s_1$, the ellipticity and the polarization azimuth. We show that the alignment order parameter has a profound effect on the angular profiles., Comment: revtex4-1, 25 pages, 13 figures, corrected version

We perform direct numerical simulations of the settling of an ice sphere in an ambient fluid accounting for heat and mass transfer with the aim of studying in a meteorological context the case of falling graupel in humid air. The study is motivated by the fact that falling graupels in clouds are heated by the latent heat released during the accretion of liquid water droplets. They may therefore be considerably warmer than their surrounding and evaporate water vapor, which mixes with the surrounding air in the wake of the graupel, thereby creating transient zones of supersaturation there. The problem of a falling graupel is modeled as that of a heated sphere falling in a quiescent ambient fluid under the action of gravity. The coupling between the temperature and velocity fields is accounted for by the Boussinesq approximation. This problem can be parameterized by four parameters: the particle/fluid density ratio, the Galileo number, the Prandtl number, and the Richardson number. A separate scalar transport equation accounts for the vapor transport. Typical cloud conditions involve small temperature differences between the sphere and the surrounding, yielding relatively small Richardson numbers for both heat and mass transport. We give a special emphasis to the Galileo numbers 150, 170, 200 and 300 in order to analyze the specificities of each settling regime. The questions addressed in this study are mainly methodological and concern the influence of the settling regime and the mobility of the sphere on the structure of the scalar fields, the possible influence of modest Richardson numbers on the structure of the wake, and the possible application of this simulation framework to the investigation of the saturation in the wake of a falling graupel.

We theoretically analyze the waveguide regime of light propagation in a cylindrical pore of a polymer matrix filled with liquid crystals assuming that the effective radial optical anisotropy is biaxial. From numerical analysis of the dispersion relations, the waveguide modes are found to be sensitive to the field-induced changes of the anisotropy. The electro-optic properties of the polymer porous polyethylene terephthalate (PET) films filled with the nematic liquid crystal 5CB are studied experimentally and the experimental results are compared with the results of the theoretical investigation., Comment: 15 pages, 10 figures, revtex4-1

In our investigation into the effects of the degree of polarization in modulation of partially polarized light we assume general settings of the interferometry of partially polarized lightwaves and perform theoretical analysis of the Uhlmann and the interferometric phases. We introduce the relative Uhlmann phase determined by the Uhlmann holonomies of interfering beams and show that the interferometric phase generalized to the case of nonunitary evolution can, similar to the Uhlmann phase, be cast into the holonomy defined form. By using the technique based on a two-arm Mach-Zehnder interferometer, two different dynamical regimes of light modulation are experimentally studied: (a) modulation of the input light by the rotating quarter-wave plate (QWP); and (b) modulation of the testing beam by a birefringent plate with electrically controlled anisotropy represented by the deformed-helix ferroelectric liquid crystal (DHFLC) cell. In the setup with the rotating QWP, the interferometric phase is found to be equal to the relative Uhlmann phase. Experimental and theoretical results being in excellent agreement both show that this phase is an oscillating function of the QWP angle and increases with the degree of polarization. For modulation by the DHFLC cell, the data derived from our electro-optic measurements are fitted using the theory of the orientational Kerr effect in FLCs. This theory in combination with the results of fitting is used to evaluate electric field dependencies of the interferometric and the Uhlmann phases., Comment: revtex 4.1, 19 pages, 12 figures (published version)

We study the electro-optic properties of subwavelength-pitch deformed-helix ferroelectric liquid crystals (DHFLC) illuminated with unpolarized light. In the experimental setup based on the Mach-Zehnder interferometer, it was observed that the reference and the sample beams being both unpolarized produce the interference pattern which is insensitive to rotation of in-plane optical axes of the DHFLC cell. We find that the field-induced shift of the interference fringes can be described in terms of the electrically dependent Pancharatnam relative phase determined by the averaged phase shift, whereas the visibility of the fringes is solely dictated by the phase retardation., Comment: 8 pages, 7 figures, revised version. arXiv admin note: text overlap with arXiv:1508.04964

We theoretically study electro-optic light modulation based on the quantum model where the linear electro-optic effect and the externally applied microwave field result in the interaction between optical cavity modes. The model assumes that the number of interacting modes is finite and effects of the mode overlapping coefficient on the strength of the intermode interaction can be taken into account through dependence of the coupling coefficient on the mode characteristics. We show that, under certain conditions, the model is exactly solvable and, in the semiclassical approximation where the microwave field is treated as a classical mode, can be analyzed using the technique of the Jordan mappings for the su(2) Lie algebra. Analytical results are applied to study effects of light modulation on the frequency dependence of the photon counting rate. We also establish the conditions of validity of the semiclassical approximation by applying the methods of polynomially deformed Lie algebras for analysis of the model with quantized microwave field., Comment: 13 pages; 7 figures, revised version

We use the T-matrix formalism in combination with the method of far-field matching to evaluate the optical force exerted by Laguerre-Gaussian (LG) light beams on a spherical (Mie) particle. For both non-vortex and optical vortex LG beams, the theoretical results are used to analyze the optical-force-induced dynamics of the scatterer near the trapping points represented by the equilibrium (zero-force) positions. The regimes of linearized dynamics are described in terms of the stiffness matrix spectrum and the damping constant of the ambient medium. For the purely azimuthal LG beams, the dynamics is found to be locally non-conservative and is characterized by the presence of conditionally stable equilibria (unstable zero-force points that can be stabilized by the ambient damping). The effects related to the Mie resonances that under certain conditions manifest themselves as the points changing the trapping properties of the particles are discussed., Comment: 29 pages, 17 figures. corrected and expanded version; a continuation of our study arXiv:1401.7585

We study both experimentally and theoretically modulation of light in a planar aligned deformed-helix ferroelectric liquid crystal (DHFLC) cell with subwavelength helix pitch, which is also known as a short-pitch DHFLC. In our experiments, azimuthal angle of the in-plane optical axis and electrically controlled parts of the principal in-plane refractive indices were measured as a function of voltage applied across the cell. Theoretical results giving the effective optical tensor of a short-pitch DHFLC expressed in terms of the smectic tilt angle and the refractive indices of FLC are used to fit the experimental data. Optical anisotropy of the FLC material is found to be weakly biaxial. For both the transmissive and reflective modes, the results of fitting are applied to model phase and amplitude modulation of light in the DHFLC cell. We demonstrate that, if the thickness of the DHFLC layer is about 50 $\mu$m, the detrimental effect of field-induced rotation of the in-plane optical axes on the characteristics of an axicon designed using the DHFLC spatial light modulator in the reflective mode is negligible., Comment: 14 pages, 11 figures

In order to explore electric-field-induced transformations of polarization singularities in the polarization-resolved angular (conoscopic) patterns emerging after deformed helix ferroelectric liquid crystal (DHFLC) cells with subwavelength helix pitch, we combine the transfer matrix formalism with the results for the effective dielectric tensor of biaxial FLCs evaluated using an improved technique of averaging over distorted helical structures. Within the framework of the transfer matrix method, we deduce a number of symmetry relations and show that the symmetry axis of L lines (curves of linear polarization) is directed along the major in-plane optical axis which rotates under the action of the electric field. When the angle between this axis and the polarization plane of incident linearly polarized light is above its critical value, the C points (points of circular polarization) appear in the form of symmetrically arranged chains of densely packed star-monstar pairs. We also emphasize the role of phase singularities of a different kind and discuss the enhanced electro-optic response of DHFLCs near the exceptional point where the condition of zero-field isotropy is fulfilled., Comment: 36 pages, 14 figures

We study Mie scattering of Laguerre-Gaussian (LG) light beams remodelled using the method of far-field matching. The theoretical results are used to analyze the optical field in the near-field region for purely azimuthal LG beams characterized by a nonzero azimuthal mode number $m_{LG}$. The mode number $m_{LG}$ is found to have a profound effect on the morphology of photonic nanojets and the near-field structure of optical vortices associated with the components of the electric field., Comment: 22 pages, 7 figures

We disclose the vertically aligned deformed helix ferroelectric liquid crystal (VADHFLC) whose Kerr constant ($K_{\mathrm{kerr}}\approx 130$~nm/V$^2$ at $\lambda=543$~nm) is one order of magnitude higher than any other value previously reported for liquid crystalline structures. Under certain conditions, the phase modulation with ellipticity less than 0.05 over the range of continuous and hysteresis free electric adjustment of the phase shift from zero to 2$\pi$ have been obtained at sub-kilohertz frequency., Comment: revtex4-1, 4 pages, 5 figures

We experimentally study how the cholesteric pitch, $P$, depends on the equilibrium one, $P_0$, in planar liquid crystal (LC) cells with both strong and semistrong anchoring conditions. The cholesteric phase was induced by dissolution in the nematic LC the right-handed chiral dopant 7-DHC (7-dehydrocholesterol, provitamin $D_3$) which transforms to left-handed tachysterol under the action of UV irradiation at the wavelength of 254 nm. By using the model of photoreaction kinetics we obtain dependencies of isomers concentrations and thus the equilibrium pitch on UV irradiation dose. The cholesteric pitch was measured as a function of irradiation time using the polarimetry method. In this method, the pitch is estimated from the experimental data on the irradiation time dependence of the ellipticity of light transmitted through the LC cells. It is found that the resulting dependence of the twist parameter, $2 D/P$ ($D$ is the cell thickness), on the free twisting number parameter, $2 D/P_0$, shows the jump-like behaviour and agrees well with the known theoretical results for the anchoring potential of the Rapini-Papoular form., Comment: 21 pages, 9 figures, published paper with extended Appendix

We study both theoretically and experimentally the electro-optical properties of vertically aligned deformed helix ferroelectric liquid crystals (VADHFLC) with subwavelength pitch that are governed by the electrically induced optical biaxiality of the smectic helical structure. The key theoretical result is that the principal refractive indices of homogenized VADHFLC cells exhibit the quadratic nonlinearity and such behavior might be interpreted as the orientational "Kerr effect" caused by the electric-field-induced orientational distortions of the FLC helix. In our experiments, it has been observed that, for sufficiently weak electric fields, the magnitude of biaxiality is proportional to the square of electric field in good agreement with our theoretical results for the effective dielectric tensor of VADHFLCs. Under certain conditions, the 2$\pi$ phase modulation of light, which is caused by one of the induced refractive indices, is observed without changes in ellipticity of incident light., Comment: revtex4-1, 8 pages, 6 figures

The phenomenological torque balance model previously introduced to describe the electrically assisted light-induced gliding is generalized to study the reorientation dynamics of the nematic liquid crystal easy axis at photoaligned azo-dye films under the combined action of in-plane electric field and reorienting UV light linearly polarized at varying polarization azimuth, $\varphi_p$. We systematically examine the general properties of the torque balance model by performing analysis of the bifurcations of equilibria at different values of the polarization azimuth and apply the model to interpret the experimental results. In our experiments, it is found that, in contrast to the case where $\varphi_p=0$ and the light polarization vector is parallel to the initial easy axis, at $\varphi_p\ne 0$, the pronounced purely photoinduced reorientation occurs outside the interelectrode gaps. It is also observed that, in the regions between electrodes with non-zero electric field, the dynamics of reorientation slows down with $\varphi_p$ and the sense of easy axis rotation is independent of the sign of $\varphi_p$., Comment: revtex4, 15 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1109.2170, arXiv:1004.3863

We theoretically study the kinetics of photoinduced reordering triggered by linearly polarized (LP) reorienting light in thin azo-dye films that were initially illuminated with LP ultraviolet (UV) pumping beam. The process of reordering is treated as a rotational diffusion of molecules in the light intensity-dependent mean-field potential. The two dimensional diffusion model which is based on the free energy rotational Fokker-Planck equation and describes the regime of in-plane reorientation is generalized to analyze the dynamics of the azo-dye order parameter tensor at varying polarization azimuth of the reorienting light. It is found that, in the photosteady state, the intensity of LP reorienting light determines the scalar order parameter (the largest eigenvalue of the order parameter tensor), whereas the steady state orientation of the corresponding eigenvector (the in-plane principal axis) depends solely on the polarization azimuth. We show that, under certain conditions, reorientation takes place only if the reorienting light intensity exceeds its critical value. Such threshold behavior is predicted to occur in the bistability region provided that the initial principal axis lies in the polarization plane of reorienting light. The model is used to interpret the experimental data on the light-induced azimuthal gliding of liquid-crystal easy axis on photoaligned azo-dye substrates., Comment: 27 pages, 11 fugures

We experimentally study the reorientation dynamics of the nematic liquid crystal easy axis at photoaligned azo-dye films under the combined action of in-plane electric field and reorienting UV light linearly polarized at varying polarization azimuth, $\phi_p$. In contrast to the case where the light polarization vector is parallel to the initial easy axis and $\phi_p=0$, at $\phi_p\ne 0$, the pronounced purely photoinduced reorientation is observed outside the interelectrode gaps. In the regions between electrodes with non-zero electric field, it is found that the dynamics of reorientation slows down with $\phi_p$ and the sense of easy axis rotation is independent of the sign of $\phi_p$., Comment: revtex-4.1, 4 pages, 3 figures

Electro-optical properties of deformed helix ferroelectric liquid crystal (DHFLC) cells are studied by using a general theoretical approach to polarization gratings in which the transmission and reflection matrices of diffraction orders are explicitly related to the evolution operator of equations for the Floquet harmonics. In the short-pitch approximation, a DHFLC cell is shown to be optically equivalent to a uniformly anisotropic biaxial layer where one of the optical axes is normal to the substrates. For in-plane anisotropy, orientation of the optical axes and birefringence are both determined by the voltage applied across the cell and represent the parameters that govern the transmittance of normally incident light passing through crossed polarizers. We calculate the transmittance as a function of the applied voltage and compare the computed curves with the experimental data. The theoretical and experimental results are found to be in good agreement., Comment: 26 pages, 8 figures, revtex 4.1

We study azimuthal gliding of the easy axis that occurs in nematic liquid crystals brought in contact with the photoaligned azo-dye film under the action of reorienting UV light combined with an in-plane electric field. For irradiation with the linearly polarized light, dynamics of easy axis reorientation is found to be faster as compared to the case of non-polarized light. In addition, it slows down with the initial irradiation dose used to prepare the azo-dye film. This effect is interpreted by using the previously suggested phenomenological model. We present the theoretical results computed by solving the torque balance equations of the model that agree very well with the experimental data., Comment: revtex4-1, 7 pages, 5 figure

Stochastic dynamics in the energy representation is employed as a method to study non-equilibrium Brownian-like systems. It is shown that the equation of motion for the energy of such systems can be taken in the form of the Langevin equation with multiplicative noise. Properties of the steady states are examined by solving the Fokker-Planck equation for the energy distribution functions. The generalized integral fluctuation theorem is deduced for the systems characterized by the shifted probability flux operator. There are a number of entropy and fluctuation relations such as the Hatano-Sasa identity and the Jarzynski's equality that follow from this theorem., Comment: revtex4-1, 18 pages, extended discussion, references added

We theoretically investigate into the effects of the incidence angles in light transmission of cholesteric liquid crystal two-layer sandwich structures with twist defects created by rotation of the one layer about the helical axis.The conoscopic images and polarization resolved patterns are obtained for thick layers by computing the intensity and the polarization parameters as a function of the incidence angles.In addition to the defect angle induced rotation of the pictures as a whole, the rings of defect mode resonances are found to shrink to the origin and disappear as the defect twist angle varies from zero to its limiting value and beyond., Comment: revtex4, 7 pages, 4 figures

We study the kinetics of photoinduced ordering in the azo-dye SD1 photoaligning layers and present the results of modeling performed using two different phenomenological approaches. A phenomenological two state model is deduced from the master equation for an ensemble of two-level molecular systems. Using an alternative approach, we formulate the two-dimensional (2D) diffusion model as the free energy Fokker-Planck equation simplified for the limiting regime of purely in-plane reorientation. The models are employed to interpret the irradiation time dependence of the absorption order parameters extracted from the available experimental data by using the exact solution to the light transmission problem for a biaxially anisotropic absorbing layer. The transient photoinduced structures are found to be biaxially anisotropic whereas the photosteady and the initial states are uniaxial., Comment: revtex4, 34 pages, 9 figures

We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by analyzing the polarization state as a function of the incidence angles and the polarization of the incident wave. The polarization resolved angular patterns emerging after the NLC cell illuminated by the convergent light beam are described in terms of the polarization singularities such as C-points (points of circular polarization) and L-lines (lines of linear polarization). For the homeotropically aligned cell, the Stokes polarimetry technique is used to measure the polarization resolved conoscopic patterns at different values of the ellipticity of the incident light impinging onto the cell. Using the exact analytical expressions for the transfer matrix we show that variations of the ellipticity induce transformations of the angular pattern exhibiting the effect of avoided L-line crossings and characterized by topological events such as creation and annihilation of the C-points. The predictions of the theory are found to be in good agreement with the experimental results., Comment: revtex4, 29 pages, 10 figures

We observe a sequence of the anchoring transitions in nematic liquid crystals (NLC) sandwiched between the hydrophobic polyimide substrates treated with the plasma beam. There is a pronounced continuous transition from homeotropic to low tilted (nearly planar) alignment with the easy axis parallel to the incidence plane of the plasma beam (the zenithal transition) that takes place as the exposure dose increases. In NLC with positive dielectric anisotropy, a further increase in the exposure dose results in in-plane reorientation of the easy axis by 90 degrees (the azimuthal transition). This transition occurs through the two-fold degenerated alignment characteristic for the second order anchoring transitions. In contrast to critical behavior of anchoring, the contact angle of NLC and water on the treated substrates monotonically declines with the exposure dose. It follows that the surface concentration of hydrophobic chains decreases continuously. The anchoring transitions under consideration are qualitatively interpreted by using a simple phenomenological model of competing easy axes which is studied by analyzing anchoring diagrams of the generalized polar and non-polar anchoring models., Comment: revtex4, 18 pages, 10 figures

We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by theoretically analyzing the polarization state as a function of the incidence angles. For a uniformly aligned NLC cell, the $4\times 4$ matrix formalism and the orthogonality relations are used to derive the analytical expressions for the transmission and reflection matrices. The polarization resolved angular patterns in the two-dimensional projection plane are characterized in terms of the polarization singularities: C points (points of circular polarization) and L lines (lines of linear polarization). In the case of linearly polarized plane waves incident on the homeotropically aligned cell, we present the results of detailed theoretical analysis describing the structure of the polarization singularities. We apply the theory to compute the polarization patterns for various orientational structures in the NLC cell and discuss the effects induced by the director orientation and biaxiality., Comment: pdflatex, rextex4, 22 pages, 7 figures (jpeg)

We study both theoretically and experimentally switching dynamics in surface stabilized ferroelectric liquid crystal cells with asymmetric boundary conditions. In these cells the bounding surfaces are treated differently to produce asymmetry in their anchoring properties. Our electro-optic measurements of the switching voltage thresholds that are determined by the peaks of the reversal polarization current reveal the frequency dependent shift of the hysteresis loop. We examine the predictions of the uniform dynamical model with the anchoring energy taken into account. It is found that the asymmetry effects are dominated by the polar contribution to the anchoring energy. Frequency dependence of the voltage thresholds is studied by analyzing the properties of time-periodic solutions to the dynamical equation (cycles). For this purpose, we apply the method that uses the parameterized half-period mappings for the approximate model and relate the cycles to the fixed points of the composition of two half-period mappings. The cycles are found to be unstable and can only be formed when the driving frequency is lower than its critical value. The polar anchoring parameter is estimated by making a comparison between the results of modelling and the experimental data for the shift vs frequency curve. For a double-well potential considered as a deformation of the Rapini-Papoular potential, the branch of stable cycles emerges in the low frequency region separated by the gap from the high frequency interval for unstable cycles., Comment: 35 pages, 15 figures

We study both theoretically and experimentally anchoring properties of photoaligning azo-dye films in contact with a nematic liquid crystal depending on photoinduced ordering of azo-dye molecules. In the mean field approximation, we found that the bare surface anchoring energy linearly depends on the azo-dye order parameter and the azimuthal anchoring strength decays to zero in the limit of vanishing photoinduced ordering. From the absorption dichroism spectra measured in the azo-dye films that are prepared from the azo-dye derivative with polymerizable terminal groups (SDA-2) we obtain dependence of the dichroic ratio on the irradiation dose. We also measure the polar and azimuthal anchoring strengths in nematic liquid crystal (NLC) cells aligned by the azo-dye films and derive the anchoring strengths as functions of the dichroic ratio. Though linear fitting of the experimental data for both anchoring strengths gives reasonably well results, it, in contradiction with the theory, predicts vanishing of the azimuthal anchoring strength at certain nonzero value of the azo-dye order parameter. By using a simple phenomenological model we show that this discrepancy can be attributed to the difference between the surface and bulk order parameters in the films., Comment: revtex4, 25 pages, 9 figures

We study dynamical optical response of a nematic liquid crystal cell that undergoes the splay-bend transition after applying the voltage across the cell. We formulate a simplified model that takes into account both the flexoelectric coupling and the surface rotational viscosity. The dynamic equations of the model were solved numerically to calculate temporal evolution of the director profile and the transmittance. We evaluate the response time as a function of a number of parameters characterising dielectric and elastic anisotropies, asymmetry of the surface pretilt angles, anchoring energy, surface rotational viscosity and flexoelectricity., Comment: uses revtex4, 14 pages, 10 figures

The supersymmetry self-consistent approximation for the model of non-equilibrium thermodynamic system with quenched disorder is derived from the dynamical action calculated by means of generalized second Legendre transformation. The equations for adiabatic and isothermal susceptibilities, memory and field induced parameters are obtained on the basis of asymptotic analysis of dynamical Dyson equations. It is shown that the marginal stability condition that defines the critical point is governed by fluctuations violating FDT. The temperature of ergodicity breaking transition is calculated as a function of quenched disorder intensities. Transformation of superfields related to the mapping between an instanton process and the corresponding causal solution is discussed., Comment: 20 pages, 3 figures, LaTeX2e, uses feynmf.sty

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The concept of broken symmetry is used to study bifurcations of equilibria and dynamical instabilities in dynamic model of one-mode laser (nonresonant complex Lorenz model) on the basis of modified Hopf theory. It is shown that an invariant set of stationary points bifurcates into an invariant torus (doubly-periodic branching solution). Influence of the symmetry breaking on stability of branching solutions is investigated as a function of detuning. The invariant torus is found to be stable under the detuning exceeds its critical value, so that dynamically broken symmetry results in the apprearance of low-frequency Goldstone-type mode. If the detuning then goes downward and pumping is kept above the threshold, numerical analysis reveals that after a cascade of period-doublings the strange Lorenz attractor is formed at small values of detuning. It is found that there are three types of the system behavior as pumping increases depending on the detuning. Quantum counterpart of the complex Lorenz model is discussed., Comment: 23 pages (LaTeX), 8 figures, uses epsf.sty (submitted to J. of Phys. A)