Pair interaction of localized topological structures in confined chiral media.

We study pairwise interactions between localized topological structures in chiral magnetic and cholesteric liquid crystal (CLC) systems confined in the planar geometry. Our calculations for magnetics are based on the lattice model that takes into account the bulk and surface anisotropies along with the exchange and the Dzyaloshinskii-Moriya interactions. In CLC cells, these anisotropies describe the energy of interaction with an external magnetic or electric field and the anchoring energy assuming that the magnetic or electric anisotropy is negative and the boundary conditions are homeotropic. We have selected the region of the phase diagram, where various localized solitonlike structures, including skyrmion tubes, torons, and leeches, embedded in the ground state of the z-cone (conical phase) coexist, and carried out numerical analysis of the distance dependencies of the effective intersoliton interaction potentials. For skyrmions and torons, the potentials are found to be attractive in the large separation region. It turned out that for these potentials, the effects of axial asymmetry are negligible. By contrast, it turned out that for the intermediate structures between the skyrmions and torons known as the leeches, the leech-leech potentials generally depend on the orientation of the intersoliton separation vector and their large distance parts may become repulsive at certain directions of the vector. All the potentials have the short distance repulsive parts and the local minima located at the equilibrium separations. It is found that the skyrmion-skyrmion potential has an additional metastable configuration shifted towards the short-distance region.

Speed of Evolution and Correlations in Multi-Mode Bosonic Systems.

We employ an exact solution of the thermal bath Lindblad master equation with the Liouvillian superoperator that takes into account both dynamic and environment-induced intermode couplings to study the speed of evolution and quantum speed limit (QSL) times of a open multi-mode bosonic system. The time-dependent QSL times are defined from quantum speed limits, giving upper bounds on the rate of change of two different measures of distinguishability: the fidelity of evolution and the Hilbert-Schmidt distance. For Gaussian states, we derive explicit expressions for the evolution speed and the QSL times. General analytical results are applied to the special case of a two-mode system where the intermode couplings can be characterized by two intermode coupling vectors: the frequency vector and the relaxation rate vector. For the system initially prepared in a two-mode squeezed state, dynamical regimes are generally determined by the intermode coupling vectors, the squeezing parameter and temperature. When the vectors are parallel, different regimes may be associated with the disentanglement time, which is found to be an increasing (a decreasing) function of the length of the relaxation vector when the squeezing parameter is below (above) its temperature-dependent critical value. Alternatively, we study dynamical regimes related to the long-time asymptotic behavior of the QSL times, which is characterized by linear time dependence with the proportionality coefficients defined as the long-time asymptotic ratios. These coefficients are evaluated as a function of the squeezing parameter at varying temperatures and relaxation vector lengths. We also discuss how the magnitude and orientation of the intermode coupling vectors influence the maximum speed of evolution and dynamics of the entropy and the mutual information.

Topological structures in chiral media: Effects of confined geometry.

We theoretically study orientational structures in chiral magnetics and cholesteric liquid crystal (CLC) nanosystems confined in the slab geometry. Our analysis is based on the model that, in addition to the exchange and the Dzyaloshinskii-Moriya interactions, takes into account the bulk and surface anisotropies. In CLC films, these anisotropies describe the energy of interaction with external magnetic/electric field and the anchoring energy assuming that magnetic/electric anisotropy is negative and the boundary conditions are homeotropic. We have computed the phase diagram and found that the ground state of the film is represented by various delocalized structures depending on the bulk and surface anisotropy parameters, κ^{b} and κ^{s}. These include the z helix and the z cone states, the oblique, and the x helicoids. The minimum energy paths connecting the ground state and metastable helicoids and the energy barriers separating these states are evaluated. We have shown that there is a variety of localized topological structures such as the skyrmion tube, the toron, and the bobber that can be embedded in different ground states including the z cone (conical phase) and tilted fingerprint states. We have also found the structure called the leech that can be viewed as an intermediate state between the toron and the skyrmion tube.

Lindblad Dynamics and Disentanglement in Multi-Mode Bosonic Systems.

In this paper, we consider the thermal bath Lindblad master equation to describe the quantum nonunitary dynamics of quantum states in a multi-mode bosonic system. For the two-mode bosonic system interacting with an environment, we analyse how both the coupling between the modes and the coupling with the environment characterised by the frequency and the relaxation rate vectors affect dynamics of the entanglement. We discuss how the revivals of entanglement can be induced by the dynamic coupling between the different modes. For the system, initially prepared in a two-mode squeezed state, we find the logarithmic negativity as defined by the magnitude and orientation of the frequency and the relaxation rate vectors. We show that, in the regime of finite-time disentanglement, reorientation of the relaxation rate vector may significantly increase the time of disentanglement.

Phase-only modulation of light.

We disclose the method to obtain polarization insensitive phase-only modulation that preserves both the state and the degree of polarization of light modulated using a medium with controlled birefringence. We find that, in the double-pass configuration involving reflection from the Faraday rotator mirror, such a medium acts as the phase-only modulator. The experimental data measured in the Michelson-interferometer-based setup for deformed-helix ferroelectric liquid crystal cells are found to be in good agreement with the theoretical results. For such cells, we experimentally demonstrate high-frequency (4 kHz modulation rate) 2π phase-only light modulation governed by the average phase shift and solve the problem of optical axes switching.

Multiple minimum-energy paths and scenarios of unwinding transitions in chiral nematic liquid crystals.

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 Fréedericksz 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.

Modulation of unpolarized light in planar-aligned subwavelength-pitch deformed-helix ferroelectric liquid crystals.

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.

Light modulation in planar aligned short-pitch deformed-helix ferroelectric liquid crystals.

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, the azimuthal angle of the in-plane optical axis and electrically controlled parts of the principal in-plane refractive indices are 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 the ferroelectric liquid crystal (FLC) are used to fit the experimental data. The 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 the phase and amplitude modulation of light in the DHFLC cell. We demonstrate that if the thickness of the DHFLC layer is about 50µm, 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.

Optics of short-pitch deformed-helix ferroelectric liquid crystals: symmetries, exceptional points, and polarization-resolved angular patterns.

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.

Enhanced orientational Kerr effect in vertically aligned deformed helix ferroelectric liquid crystals.

We disclose the vertically aligned deformed helix ferroelectric liquid crystal whose Kerr constant (Kkerr≈130 nm/V2 at λ=543 nm) is around 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 2π has been obtained at subkilohertz frequency.

Light-induced pitch transitions in photosensitive cholesteric liquid crystals: effects of anchoring energy.

We experimentally study how the cholesteric pitch P depends on the equilibrium pitch P0 in planar liquid crystal (LC) cells with both strong and semistrong anchoring conditions. The cholesteric phase was induced by dissolution in the nematic LC of the right-handed chiral dopant 7-dehydrocholesterol (7-DHC, provitamin D3) 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 the dependencies of isomer concentrations and, therefore, of the equilibrium pitch on the 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 2D/P (D is the cell thickness) on the free twisting number parameter 2D/P0 shows jumplike behavior and agrees well with the known theoretical results for the anchoring potential of Rapini-Papoular form.

Orientational Kerr effect and phase modulation of light in deformed-helix ferroelectric liquid crystals with subwavelength pitch.

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 an 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 2π phase modulation of light, which is caused by one of the induced refractive indices, is observed without changes in ellipticity of incident light.

Photoinduced reordering in thin azo-dye films and light-induced reorientation dynamics of the nematic liquid-crystal easy axis.

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 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 the liquid-crystal easy axis on photoaligned azo-dye substrates.

Polarization-gratings approach to deformed-helix ferroelectric liquid crystals with subwavelength pitch.

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 bounding surfaces. 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 electric field and compare the computed curves with the experimental data. The theoretical and experimental results are found to be in good agreement.

Electrically assisted light-induced azimuthal gliding of the nematic liquid-crystal easy axis on photoaligned substrates.

We study azimuthal gliding of the easy axis that occurs in nematic liquid crystals brought in contact with the photoaligned substrate (initially irradiated azo-dye film) under the action of reorienting UV light combined with 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 nonpolarized light. Another effect is that 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.

Energy representation for nonequilibrium brownian-like systems: steady states and fluctuation relations.

Stochastic dynamics in the energy representation is used as a method to represent nonequilibrium 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. From this theorem, a number of entropy and fluctuation relations such as the Evans-Searles fluctuation theorem, the Hatano-Sasa identity, and the Jarzynski's equality are derived.

Kinetics of photoinduced ordering in azo-dye films: two-state and diffusion models.

We theoretically study the kinetics of photoinduced ordering in azo-dye 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 the one-particle distribution functions of an ensemble of two-level molecular systems by specifying the angular redistribution probabilities and by expressing the order parameter correlation functions in terms of the order parameter tensor. Using an alternative approach that describes light-induced reorientation of azo-dye molecules in terms of a rotational Brownian motion, we formulate the two-dimensional 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 defined in terms of the principal extinction (absorption) coefficients. Using the exact solution to the light transmission problem for a biaxially anisotropic absorbing layer, these coefficients are extracted from the absorbance-vs-incidence angle curves measured at different irradiation doses for the probe light linearly polarized parallel and perpendicular to the plane of incidence. It is found that, in the azo-dye films, the transient photoinduced structures are biaxially anisotropic whereas the photosteady and the initial states are uniaxial.

Liquid-crystal anchoring transitions on aligning substrates processed by a plasma beam.

We have studied a sequence of anchoring transitions observed in nematic liquid crystals (NLCs) sandwiched between hydrophobic polyimide substrates treated with a plasma beam. There is a pronounced continuous transition from a homeotropic to a slightly tilted (nearly planar) alignment with the easy axis parallel to the incidence plane of the plasma beam (the zenithal transition) which takes place as the exposure dose increases. In NLCs 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 twofold degenerate alignment characteristic of second-order anchoring transitions. In contrast to the critical behavior of anchoring, the contact angle of the NLC and water on the treated substrates declines monotonically with increasing 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 generalized polar and nonpolar anchoring models.

Switching dynamics of surface stabilized ferroelectric liquid crystal cells: effects of anchoring energy asymmetry.

We study both theoretically and experimentally switching dynamics in asymmetric surface stabilized ferroelectric liquid crystal cells where the bounding surfaces are treated differently to produce asymmetry in their anchoring properties. Our electro-optic measurements of the switching voltage thresholds, V+ and -V{-}, that are determined by the peaks of the reversal polarization current reveal the frequency dependent shift of the hysteresis loop, V{+}-V{-}. We examine the predictions of the uniform dynamic 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 dynamic equation (cycles). For this purpose, we apply the method linking the cycles and the fixed points of the composition of two parametrized half-period mappings for the approximate model. It is found that the cycles are unstable and can only be formed if the driving frequency is lower than its critical value. The polar anchoring parameter is estimated by making a comparison between the results of modeling and the experimental data for the shift vs frequency curve.

Singularities in polarization resolved angular patterns: transmittance of nematic liquid crystal cells.

We study the angular structure of polarization of light transmitted through a nematic liquid crystal (NLC) cell by theoretically analysing the polarization state as a function of the incidence angles. For a uniformly aligned NLC cell, the 4 × 4 matrix formalism and the orthogonality relations are used to derive the exact 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 such as C-points (points of circular polarization) and L-lines (lines of linear polarization). For 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 director orientation and biaxiality.