Higher-order Transitions Research Articles

Ultrafast optical snapshots of hybrid perovskites reveal the origin of multiband electronic transitions

Hybrid organic-inorganic perovskites are a promising class of materials for low-temperature solution-processed thin-film optoelectronic technologies. Here, the authors assign the visible and near-infrared optical transitions in large-grain thin films, using variable temperature transient absorption measurements that provide a sensitive probe of the electronic energy levels. These studies address an ongoing controversy concerning the nature of higher-order subband transitions. The strong visible absorption band is assigned to nearly degenerate transitions originating from different momentum states within the multivalley electronic band structure using symmetry analysis and the response of the optical resonances during the low-temperature structural phase transition.

Anisotropic nonlinear optics based on quantum interference

Weak coherent radiation interacting with multilevel atomic systems can excite a family of higher-order multiphoton transitions in contravention to conventional perturbative analysis. Monochromatic excitation leads to a strong anisotropic response arising from the interference of numerous underlying multiphoton pathways. The interference can be controlled through the polarization content of the input radiation. This anisotropic response is subnatural, quite unlike the anisotropy arising from spontaneous-emission–assisted optical pumping. Its sensitivity to external influences such as magnetic field suggests its utility in magnetometry. Specifically, we discover the presence of an elemental closed loop involving series of absorption and emission cycles that is central to the total response, and is universal to all atomic configurations. However, as not all atomic configurations support such anisotropy, we present a general classification of atomic transitions that exhibit anisotropic nonlinear response through quantum interference.

Capacitive Detection of Low-Enthalpy, Higher-Order Phase Transitions in Synthetic and Natural Composition Lipid Membranes.

In-plane lipid organization and phase separation in natural membranes play key roles in regulating many cellular processes. Highly cooperative, first-order phase transitions in model membranes consisting of few lipid components are well understood and readily detectable via calorimetry, densitometry, and fluorescence. However, far less is known about natural membranes containing numerous lipid species and high concentrations of cholesterol, for which thermotropic transitions are undetectable by the above-mentioned techniques. We demonstrate that membrane capacitance is highly sensitive to low-enthalpy thermotropic transitions taking place in complex lipid membranes. Specifically, we measured the electrical capacitance as a function of temperature for droplet interface bilayer model membranes of increasing compositional complexity, namely, (a) a single lipid species, (b) domain-forming ternary mixtures, and (c) natural brain total lipid extract (bTLE). We observed that, for single-species lipid bilayers and some ternary compositions, capacitance exhibited an abrupt, temperature-dependent change that coincided with the transition detected by other techniques. In addition, capacitance measurements revealed transitions in mixed-lipid membranes that were not detected by the other techniques. Most notably, capacitance measurements of bTLE bilayers indicated a transition at ∼38 °C not seen with any other method. Likewise, capacitance measurements detected transitions in some well-studied ternary mixtures that, while known to yield coexisting lipid phases, are not detected with calorimetry or densitometry. These results indicate that capacitance is exquisitely sensitive to low-enthalpy membrane transitions because of its sensitivity to changes in bilayer thickness that occur when lipids and excess solvent undergo subtle rearrangements near a phase transition. Our findings also suggest that heterogeneity confers stability to natural membranes that function near transition temperatures by preventing unwanted defects and macroscopic demixing associated with high-enthalpy transitions commonly found in simpler mixtures.

Investigation of fundamental and high order optical transitions in α-Fe2O3 thin films using surface barrier electroreflectance

In this paper, we use surface barrier electroreflectance technique to probe the optical transitions in hematite (α-Fe2O3) thin film. An electric field was induced normal to the surface of α-Fe2O3 thin film in an Ag/α-Fe2O3/Ag based capacitor type structure and the corresponding electroreflectance analysis was performed. Based on the electroreflectance analysis, we observed the fundamental as well as two high order critical points associated with α-Fe2O3. Standard critical point model was used to find the exact energy locations and the broadening parameters associated with these critical points. The existence of the fundamental critical point was further confirmed by the spectrophotometric analysis. The quantitative analysis based on the electro-optic energy confirmed that the obtained electroreflectance spectrum was within the low field regime, and the obtained critical points above the fundamental transition were attributed to the high order transitions of electrons from the valence band to the deep in the conduction band.

High Pressure Spectroscopic Investigation on Proton Transfer in Squaric Acid and 4,4\u2032-Bipyridine Co-crystal

In attempt to the obtain detailed geometric information of proton transfer compound (subsequently denote as SQBP) formed between squaric acid (SQ)and 4,4′-bipyridine(BP), and to investigate the mechanisms of pressure-induced double proton transfer and related structural phase transition, we carried out in-situ high pressure Raman spectroscopy of SQBP up to 20 GPa. A solid-solid phase transition together with double proton transfer phenomenon was confirmed by Raman spectroscopy at about 1.5 GPa, and the activation of C = O stretching mode in Raman spectra indicates a square-ring structure of SQ with four symmetric C = O bond formation. These results are further supported by first-principals calculations and in-situ high pressure infrared absorption spectroscopy. Additionally, Raman intensity analysis suggests that a higher-order phase transition with planar BP molecular structure occurred in the pressure range of 3~6 GPa. As a result, the π electron delocalization effect in BP dominated the intensity enhancement of C = O stretching mode in SQ. To the best of our knowledge, this is the first time observation of the intensity enhancement of proton donor’s normal modes induced by proton acceptor’s π electron delocalization.

New higher-order transition in causal dynamical triangulations

We reinvestigate the recently discovered bifurcation phase transition in Causal Dynamical Triangulations (CDT) and provide further evidence that it is a higher order transition. We also investigate the impact of introducing matter in the form of massless scalar fields to CDT. We discuss the impact of scalar fields on the measured spatial volumes and fluctuation profiles in addition to analysing how the scalar fields influence the position of the bifurcation transition.

Supersymmetrical bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states.

Von Neumann and Wigner theorized the bounding and anti-crossing of eigenstates. Experiments have demonstrated that owing to anti-crossing and similar radiation rates, the graphene-like resonance of inhomogeneously strained photonic eigenstates can generate a pseudomagnetic field, bandgaps and Landau levels, whereas exponential or dissimilar rates induce non-Hermicity. Here, we experimentally demonstrate higher-order supersymmetry and quantum phase transitions by resonance between similar one-dimensional lattices. The lattices consisted of inhomogeneous strain-like phases of triangular solitons. The resonance created two-dimensional, inhomogeneously deformed photonic graphene. All parent eigenstates were annihilated. Eigenstates of mildly strained solitons were annihilated at similar rates through one tail and generated Hermitian bounded eigenstates. The strongly strained solitons with positive phase defects were annihilated at exponential rates through one tail, which bounded eigenstates through non-Hermitianally generated exceptional points. Supersymmetry was evident, with preservation of the shapes and relative phase differences of the parent solitons. Localizations of energies generated from annihilations of mildly and strongly strained soliton eigenstates were responsible for geometrical (Berry) and topological phase transitions, respectively. Both contributed to generating a quantum Zeno phase, whereas only strong twists generated topological (Anderson) localization. Anti-bunching-like condensation was also observed.

Higher-order time-symmetry-breaking phase transition due to meeting of an exceptional point and a Fano resonance

We have theoretically investigated the time-symmetry breaking phase transition process for two discrete states coupled with a one-dimensional continuum by solving the nonlinear eigenvalue prob- lem for the effective Hamiltonian associated with the discrete spectrum. We obtain the effective Hamiltonian with use of the Feshbach-Brillouin-Wigner projection method. Strong energy depen- dence of the self-energy appearing in the effective Hamiltonian plays a key role in the time-symmetry breaking phase transition: as a result of competition in the decay process between the Van Hove singularity and the Fano resonance, the phase transition becomes a higher-order transition when both the two discrete states are located near the continuum threshold.

Exploring the new phase transition of CDT

This work focuses on the newly discovered bifurcation phase transition of CDT quantum gravity. We define various order parameters and investigate which is most suitable to study this transition in numerical simulations. By analyzing the behaviour of the order parameters we present evidence that the transition separating the bifurcation phase and the physical phase of CDT is likely a second or higher-order transition, a result that may have important implications for the continuum limit of CDT.

Multidimensional Analysis of Plates with Irregularities Using Higher-Order Finite Elements Based on Lobatto Shape Functions

Direct modeling and simulation of engineering problems with various irregularities are computationally very inefficient and in some cases impossible, even in these days of massively parallel computational systems. As a result, in recent times, a number of schemes have been put forward to tract such problems in a computationally efficient manner. Needless to say, such schemes are still going through evolutionary stages. This paper addresses direct solution based on the selective use of different dimensional models at different regions of the problem domain. For the multidimensional approach, a higher-order transition element is developed to connect the different element types where two- and three-dimensional laminated elements based on higher-order subparametric concept are considered. Modeling simplicity and calculation efficiency of the multidimensional approach are shown for the analysis of cantilever plates with stepped section and patch-repaired plates.

A quantum dot single-photon source with on-the-fly all-optical polarization control and timed emission.

Sources of single photons are key elements for applications in quantum information science. Among the different sources available, semiconductor quantum dots excel with their integrability in semiconductor on-chip solutions and the potential that photon emission can be triggered on demand. Usually, the photon is emitted from a single-exciton ground state. Polarization of the photon and time of emission are either probabilistic or pre-determined by electronic properties of the system. Here, we study the direct two-photon emission from the biexciton. The two-photon emission is enabled by a laser pulse driving the system into a virtual state inside the band gap. From this intermediate state, the single photon of interest is then spontaneously emitted. We show that emission through this higher-order transition provides a versatile approach to generate a single photon. Through the driving laser pulse, polarization state, frequency and emission time of the photon can be controlled on-the-fly.

Dielectric functions and carrier concentrations of Hg1−xCdxSe films determined by spectroscopic ellipsometry

Spectroscopic ellipsometry, ranging from 35 meV to 6 eV, was used to determine the dielectric functions of a series of molecular beam epitaxy-grown Hg1−xCdxSe thin films deposited on both ZnTe/Si(112) and GaSb(112) substrates. The fundamental band gap as well as two higher-order electronic transitions blue-shift with increasing Cd composition in Hg1−xCdxSe, as expected. Representing the free carrier absorption with a Drude oscillator, we found that the effective masses of Hg1−xCdxSe (grown on ZnTe/Si) vary between 0.028 and 0.050 times the free electron mass, calculated using the values of carrier concentration and the mobility obtained through Hall measurements. Using these effective masses, we determined the carrier concentrations of Hg1−xCdxSe samples grown on GaSb, which is of significance as films grown on such doped-substrates posit ambiguous results when measured by conventional Hall experiments. These models can serve as a basis for monitoring Cd-composition during sample growth through in-situ spectroscopic ellipsometry.

Spectral Clustering with Sparse Graph Construction Based on Markov Random Walk

Spectral clustering has become one of the most popular clustering approaches in recent years. Similarity graph constructed on the data is one of the key factors that influence the performance of spectral clustering. However, the similarity graphs constructed by existing methods usually contain some unreliable edges. To construct reliable similarity graph for spectral clustering, an efficient method based on Markov random walk (MRW) is proposed in this paper. In the proposed method, theMRW model is defined on the raw k-NN graph and the neighbors of each sample are determined by the probability of the MRW. Since the high order transition probabilities carry complex relationships among data, the neighbors in the graph determined by our proposed method are more reliable than those of the existing methods. Experiments are performed on the synthetic and real-world datasets for performance evaluation and comparison. The results show that the graph obtained by our proposed method reflects the structure of the data better than those of the state-of-the-art methods and can effectively improve the performance of spectral clustering.

Phase transition and winding properties of a flexible polymer adsorbed to a rigid perioidic copolymer.

Motivated by the noncovalent binding of polypeptides to DNA, the adsorption of a flexible polymer to a rigid periodic copolymer is studied in two dimensions and three dimensions. The fraction of adsorbed monomers, the specific heat, and the Binder cumulant are analyzed and compared with analytical results for an ideal chain. As the interaction strength ε increases, a second-order phase transition occurs from a nonadsorbed state to an adsorbed state, in two dimensions, and a higher-order transition occurs in three dimensions. The transition point is estimated as ε0∼2.2 for d=2 and ε0∼2.1 for d=3, where ε is given in units of kBT. The dependence of the number of adsorbed monomers Nads on the chain length L of the flexible polymer shows a power law scaling relation Nads∼Lϕ, with ϕ∼0.46,0.42 for d=2,3, respectively. We also find an optimal ε∼2.8 for the winding of the flexible polymer around the rigid one in three dimensions. Compared to the adsorbed monomers, the successive nonadsorbed monomers contribute more to the winding. When the interaction is strong, ε>3.5, the winding value or the number of winding turns of the flexible polymer becomes linearly dependent on the chain length.

Towards the free energy landscape for catalysis in mammalian nitric oxide synthases.

The general requirement for conformational sampling in biological electron transfer reactions catalysed by multi-domain redox systems has been emphasized in recent years. Crucially, we lack insight into the extent of the conformational space explored and the nature of the energy landscapes associated with these reactions. The nitric oxide synthases (NOS) produce the signalling molecule NO through a series of complex electron transfer reactions. There is accumulating evidence that protein domain dynamics and calmodulin binding are implicated in regulating electron flow from NADPH, through the FAD and FMN cofactors, to the haem oxygenase domain, where NO is generated. Simple models based on static crystal structures of the isolated reductase domain have suggested a role for large-scale motions of the FMN-binding domain in shuttling electrons from the reductase domain to the oxygenase domain. However, detailed insight into the higher-order domain architecture and dynamic structural transitions in NOS enzymes during enzyme turnover is lacking. In this review, we discuss the recent advances made towards mapping the catalytic free energy landscapes of NOS enzymes through integration of both structural techniques (e.g. cryo-electron microscopy) and biophysical techniques (e.g. pulsed-electron paramagnetic resonance). The general picture that emerges from these experiments is that NOS enzymes exist in an equilibrium of conformations, comprising a 'rugged' or 'frustrated' energy landscape, with a key regulatory role for calmodulin in driving vectorial electron transfer by altering the conformational equilibrium. A detailed understanding of these landscapes may provide new opportunities for discovery of isoform-specific inhibitors that bind at the dynamic interfaces of these multi-dimensional energy landscapes.

Observation and calculation of higher-order sideband transitions in a flux qubit coupled to a SQUID-based resonator

Qubit-resonator coupled systems have been intensively studied because of their potential usefulness in quantum information processing. We investigated a superconducting flux qubit coupled to a resonator mode (SQUID plasma mode) associated with a dc SQUID used to read out the qubit state. Higher-order red and blue sideband transitions with |M| = 1, 2, and 3, where M represents the change in the quantum number of the resonator state, were clearly observed away from the symmetry point. We calculated the transition matrix elements between the dressed states and examined their dependence on both the coupling strength and the flux bias for the qubit. The observation of the sidebands up to |M| = 3 is consistent with the calculation results.

Calculation of beta spectral shapes

Classical beta spectra calculations are briefly described, highlighting the usual assumptions and limitations. To go beyond these usual assumptions, the numerical resolution of the Dirac equation for the atomic and beta electrons is necessary. This allowed us to determine the parameters λi involved in the theoretical shape factors exactly. A systematic comparison between theoretical and experimental shape factors led us to disqualify the usual λi = 1 assumption for all forbidden transitions. The usual ξ-approximation was proved to be incorrect for numerous first forbidden non-unique transitions, and for all higherorder non-unique transitions. A more accurate screening correction was defined and the atomic exchange effect was taken into account, an effect which is always neglected in usual calculations. The beta spectra of 63Ni and 241Pu, recently measured down to very low energies, are well reproduced in our calculations. The exchange effect was demonstrated to have a great influence on the spectral shape within this energy range.

Nature of chiral phase transition inQED3at zero density

Based on the feature of chiral susceptibility and thermal susceptibility at finite temperature, the nature of chiral phase transition around the critical number of fermion flavors ($N_c$) and the critical temperature ($T_c$) at a fixed fermion flavors number in massless QED$_3$ are investigated. It is showed that, at finite temperature the system exhibits a second-order phase transition at $N_c$ or $T_c$ and each of the estimated critical exponents is less than 1, while it reveals a higher-order continuous phase transition around $N_c$ at zero temperature.

Chirality, birefringence, and polarization effects inα-quartzstudied by resonant elastic x-ray scattering

We show that enantiomers are extremely sensitive to the quality of the light polarization in resonant elastic x-ray scattering experiments. In $\ensuremath{\alpha}\text{-quartz}$, the (001) reflection shows a very strong sensitivity to a small fraction of linear component included in nominally circularly polarized light. This fraction induces an important phase difference between the angular dependence of the recorded intensity from each enantiomer. We are thus able to model all aspects of the resonant scattering and determine the dominant physics, extract the crystal chirality, and obtain very precise values for the Stokes polarization parameters. Effects of birefringence and of higher-order electric transitions are also quantified and it is shown that in comparison they are negligible.

A mixture of transition models for heterogeneous longitudinal ordinal data: with applications to longitudinal bacterial vaginosis data

Markov models used to analyze transition patterns in discrete longitudinal data are based on the limiting assumption that individuals follow the common underlying transition process. However, when one is interested in diseases with different disease or severity subtypes, explicitly modeling subpopulation-specific transition patterns may be appropriate. We propose a model which captures heterogeneity in the transition process through a finite mixture model formulation and provides a framework for identifying subpopulations at different risks. We apply the procedure to longitudinal bacterial vaginosis study data and demonstrate that the model fits the data well. Further, we show that under the mixture model formulation, we can make the important distinction between how covariates affect transition patterns unique to each of the subpopulations and how they affect which subgroup a participant will belong to. Practically, covariate effects on subpopulation-specific transition behavior and those on subpopulation membership can be interpreted as effects on short-term and long-term transition behavior. We further investigate models with higher-order subpopulation-specific transition dependence.