Two-mode Model Research Articles

Exploring global symmetry-breaking superradiant phase via phase competition.

Superradiant phase transitions play a fundamental role in understanding the mechanism of collective light-matter interaction at the quantum level. Here we investigate multiple superradiant phases and phase transitions with different symmetry-breaking patterns in a two-mode V-type Dicke model. Interestingly, we show that there exists a quadruple point where one normal phase, one global symmetry-breaking superradiant phase, and two local symmetry-breaking superradiant phases meet. Such a global phase results from the phase competition between two local superradiant phases and cannot occur in the standard Λ- and Ξ-type three-level configurations in quantum optics. Moreover, we exhibit a sequential first-order quantum phase transition from one local to the global again to the other local superradiant phase. Our study opens up a perspective of exploring multilevel quantum critical phenomena with global symmetry breaking.

Analysis of Optical Bi-wave Solutions in a Two-mode Model Arising from the Unstable Schrödinger Equation

Analysis of Optical Bi-wave Solutions in a Two-mode Model Arising from the Unstable Schrödinger Equation

Analysis of resonant/nonresonant vibrations of simply-supported Kirchhoff nanoplates under in–plane magnetic field based on a strongly coupled two-mode model

The paper aims to study the nonlinear vibrations of simply supported square and rectangular nanoplates in the 2D magnetic field. The investigated model is developed in the framework of the von Kármán nonlinear theory, whereas nonlocal effects are taken into consideration due to the Eringen nonlocal theory of elasticity. PDEs governing system dynamics include the stress function. Both an in-plane magnetic field caused by the Lorentz force yielded by Maxwell's equations, as well as a transverse harmonical excitation are taken into account. The obtained results are based on the Bubnov–Galerkin approach and the two-mode deflection approximation. The latter reduces the problem of infinite dimensions to the system of coupled nonlinear ODEs, which is investigated by the multiple scale method (MSM). The employed MSM in the framework of Mathematica symbolic computations yielded the analytical approximate solutions, which were validated via the numerical Adams method. Both nonresonant and external/internal resonances exhibited by the studied nanoplates are thoroughly analysed. Numerous novel nonlinear phenomena are detected and analysed, with emphasis put on their physical interpretation.

Degeneracy and Photon Trapping in a Dissipationless Two-Mode Optomechanical Model.

In this work, we theoretically study a finite and undamped two-mode optomechanical model consisting of a high quality optical cavity containing a thin, elastic, and dielectric membrane. The main objective is to investigate the precursors of quantum phase transition in such a model by studying the behavior of some observables in the ground state. By controlling the coupling between membrane and modes, we find that the two lowest energy eigenstates become degenerate, as is indicated by the behavior of the mean value of some operators and by other quantifiers as a function of the coupling. Such degenerate states are characterized by a coherent superposition of eigenstates describing one of the two modes preferentially populated and the membrane dislocated from its equilibrium position due the radiation pressure (Schrödinger's cat states). The delocalization of the compound system photons+membrane results in an increase in fluctuations as measured by Robertson-Schrödinger uncertainty relations.

Noise-Induced Defects in Honeycomb Lattice Structure: A Phase-Field Crystal Study

One of the classes of the kinetic phase-field model in the form of the two-mode hyperbolic phase-field crystal model (modified PFC model) is used for the study of the noise effect of the crystalline structure. Special attention is paid to the origin of the defect’s microstructure in the crystalline honeycomb lattice due to induced colored noise. It shows that the noise–time correlation coefficient τζ, comparable to the diffusion time, enhances the grain boundary mobilities. Instead, a small spatial correlation coefficient, λζ, close to the first lattice parameter of the honeycomb crystal, stabilizes the structure. The finite non-zero value of the relaxation time τ for the atomic flux significantly slows the local relaxation of the fluctuated field and leads to the grains’ fragmentation and formation of the disordered phases. The obtained results are applicable to the hexagonal atomic structures and, in particular, to honeycomb crystals, such as boron nitride, in which the lattice defects might be simulated through the induced colored noise.

Interacting two-mode model for ultracold quantum interferometers

Ultracold gases provide an excellent platform for the realization of quantum interferometers. In the case of implementations based on Bose-Einstein condensates in double well potentials, an effective two-mode model allows to study how the interactions among particles affect the sensitivity of the interferometer. In this work we review the properties of such a model and its application to interferometric protocols, focusing on the achievable sensitivity in the presence of interactions turned on. In particular we study the full interferometric sequence when the initial state is a Twin Fock state, which is perfectly number squeezed. We found that in the presence of interactions and for certain values of the holding time in which a phase difference between the two modes is accumulated, the same sensitivity as in the non interacting case is recovered when using the population imbalance between the two wells as observable. Finally, we characterize the behaviour of the sensitivity by looking at the δ-derivative and the variance of the operator used for the measurement and studying the squeezing parameters.

Short-term damping estimation for time-varying vibrating structures in nonstationary operating conditions

Various structures exhibit time-varying modal properties driven by short-term variability of environmental and operational conditions, which can cause considerable short-term variations in the modal characteristics, and modal damping, in particular. This study focuses on short-term damping estimation based on operational response measurements, for which a Gaussian process time-dependent auto-regressive moving average time series model is proposed. The model coefficients are represented by basis functions which express dependence on influencing environmental and operational variables, to account for various phenomena driving the time-varying nature of the modal characteristics. The method is verified by estimating short-term damping from the response of a simulated two-mode model. The applicability of the method for more complex cases is demonstrated by estimating the short-term damping of a multi-megawatt wind turbine in operation (and during an extreme wind gust) by means of its simulated edgewise blade response. The results demonstrate that the proposed method offers an enabling approach towards short-term damping and natural frequency estimation based on response measurements.

A Discrete-Variable Local Diabatic Representation of Conical Intersection Dynamics.

Conical intersections (CIs) are ubiquitous in polyatomic molecules and are responsible for a wide range of phenomena in photochemistry and photophysics. Modeling the conical intersection dynamics with adiabatic electronic states is hindered by the divergence of the first- and second-order derivative couplings at CIs due to electronic degeneracy. We introduce and implement a novel diabatic representation for exact correlated electron-nuclear wave packet dynamics through conical intersections. It directly employs the adiabatic electronic states but avoids the singular first- and second-order derivative couplings and is robust to different gauge choices of the electronic wave function phases. The reference nuclear geometries defining the adiabatic electronic states are determined by a discrete-variable representation of the nuclear coordinates. The nonadiabatic effects are accounted for by the electronic overlap matrix instead of derivative couplings as in the adiabatic representation. Illustrated by a two-mode conical intersection model, this representation captures all nonadiabatic effects, including electronic transitions, electronic coherence, and geometric phases. Thus, this representation provides a singularity-free framework for modeling ab initio conical intersection wave packet dynamics.

Bekenstein-Smarr formula and quantization of Kerr black holes

By solving the zero surface equation and studying the black holes law, we derive the equivalent Bekenstein-Smarr formula for Kerr black holes. With the reduced phase space method and canonical transformation, we establish the quantum mechanical model for Kerr black hole which is a standard two-mode simple harmonic oscillator model. With the help of this model, we further derive the spectra of the event horizon area and corresponding eigen wave functions for the Kerr black holes, which are proved that the area of a black hole event horizon is quantized.

Chaotic vibrations of double-layer graphene sheet system

Nonlinear vibrations of double-layer nanoplate system are studied by numerical simulation. The governing equations are derived on a base of the nonlocal elasticity theory, von Kármán nonlinear theory, and Kirchhoff’s hypotheses. Both layers are assumed to be with the same material properties, while interaction between them is taken by the Winkler model. Discretization of the system of governing differential equations is performed by the Bubnov-Galerkin method with the two-mode approximation model, and the obtained system of ordinary differential equations is analysed by the Runge–Kutta method. The study of a linearized system allows the construction of regions of instability. The application of nonlinear dynamics methods made it possible to determine the nature of oscillations when stability is lost, and when small-scale effects are manifested.

Improved two-mode dynamic model for external-cavity quantum cascade lasers under strong optical feedback

In this paper, we propose an improved model for describing the dynamical behavior and mode selection mechanism of an external-cavity quantum-cascade laser (EC-QCL) when subject to strong optical feedback. Theoretical analysis including the dynamical effective reflectivity model, two-mode rate-equation model and Lang-Kobayashi equations are employed to carry out the laser output characteristics under the multiple feedback effects. A main aspect of the model is that the excess mirror loss caused by the EC effective reflectivity is incorporated into the laser dynamical equations as a nonlinear dynamical variable. Because of accounting the multiple round-trip feedback terms in the EC effective reflectivity, the analysis is valid for the arbitrary feedback regimes from weak to strong levels. Besides the stationary characteristics, the model accurately predicts the dynamical competition between the fundamental laser-cavity mode and the desired EC mode that reflected strongly by external diffraction grating. The results are in well agreement with theoretical and experimental data reported earlier for the EC-QCLs.

Ground-state phase diagram, symmetries, excitation spectra and finite-frequency scaling of the two-mode quantum Rabi model

We investigate the two-mode quantum Rabi model (QRM) describing the interaction between a two-level atom and a two-mode cavity field. The quantum phase transitions are found when the ratio η of transition frequency of atom to frequency of cavity field approaches infinity. We apply the Schrieffer–Wolff (SW) transformation to derive the low-energy effective Hamiltonian of the two-mode QRM, thus yielding the critical point and rich phase diagram of quantum phase transitions. The phase diagram consists of four regions: a normal phase, an electric superradiant phase, a magnetic superradiant phase and an electromagnetic superradiant phase. The quantum phase transition between the normal phase and the electric (magnetic) superradiant phase is of second order and associates with the breaking of the discrete Z 2 symmetry. On the other hand, the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1) symmetry. Several important physical quantities, for example the excitation energy and average photon number in the four phases, are derived. We find that the excitation spectra exhibit the Nambu–Goldstone mode. We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities. To confirm the validity of the low-energy effective Hamiltonians analytically derived by us, the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.

Optical dual-waves to a new dual-mode extension of a third order dispersive nonlinear Schrödinger's equation

The dual-mode equations refer to nonlinear models that elucidate motion of bi-directional waves traveling simultaneously under the influence of enclosed phase velocity. The initial two-mode model was introduced by Korsunsky, who refined the Korteweg-De Vries equation (KDVe) into a second-order form. In this study, we aim to extend nonlinear Schrödinger equation by restructuring it into a dual-mode format, and subsequently examine the geometric assessment of this new model. The extended exponential function expansion scheme, tanh-coth method, and Kudryashov method are utilized to obtain bi-directional explicit solutions. Additionally, we extensively examine impact of phase velocity on the propagation behavior of these paired waves, utilizing 2D and 3D graphs for analysis. The solutions obtained in this study have significant implications for the propagation of solitons in nonlinear optics. As examined model appears in various applications, all the derived solutions can contribute to the interpretation of the underlying mechanisms behind many nonlinear phenomena in different fields, such as, nonlinear optics, plasma physics, Bose-Einstein condensates, and others.

Geometric triangulation uncertainty for sustainable urban underwater localization in presence of malicious virtual node

Sustainability of urban underwater sensor networks (uUWSNs) depends critically on the efficient triangulation during the localization process. There is very limited literature on sustainable range-free localization in uUWSNs. To address this issue, we improve localization method based on triangulation approach through convex optimization with Geometric Dilution of Precision (GDOP). We define “geometric triangulation uncertainty”. A sustainable scheme is proposed for identification of underwater nodesto modify a two-mode Gaussian Mixture Model. The proposed method is then compared to a weighted least square model for different threshold levels of maximum node range and associated triangulation uncertainties. The convex formulation is then solved using semidefinite programming to obtain optimal position of target in presence of a malicious virtual node. Theproposed method is verified using Cramer’s Rao lower bound in terms of RMS errors and cumulative errors. It exhibits close to ideal performance whenever perturbations associated with geometric triangulation uncertainty is bounded. The performance of the proposed method exceeds that of the weighted least squares method, which means that the proposed technique shall find immense application in intelligent computation of urban underwater scenarios, where the amount of sensor information exchange critically depends upon terrain environment and surrounding disturbances.

E-ReMI: Extended Maximal Interaction Two-mode Clustering

In this paper, we present E-ReMI, a new method for studying two-way interaction in row by column (i.e., two-mode) data. E-ReMI is based on a probabilistic two-mode clustering model that yields a two-mode partition of the data with maximal interaction between row and column clusters. The proposed model extends REMAXINT by allowing for unequal cluster sizes for the row clusters, thus introducing more flexibility in the model. In the manuscript, we use a conditional classification likelihood approach to derive the maximum likelihood estimates of the model parameters. We further introduce a test statistic for testing the null hypothesis of no interaction, discuss its properties and propose an algorithm to obtain its distribution under this null hypothesis. Free software to apply the methods described in this paper is developed in the R language. We assess the performance of the new method and compare it with competing methodologies through a simulation study. Finally, we present an application of the methodology using data from a study of person by situation interaction.

Raman-induced mode coupling in temporal waveguides formed by short solitons

We study the propagation of optical pulses trapped inside a temporal waveguide formed by two solitons in a dispersive nonlinear medium such as an optical fiber. The solitons are short enough that they decelerate as their spectra shift continuously toward the red side because of intrapulse Raman scattering. We show that the shape of a probe pulse trapped between the two solitons evolves in a periodic fashion, while its spectrum shifts toward the blue side. We develop a coupled-mode theory showing that such changes occur because of mode coupling induced by the deceleration of the short solitons, resulting in a curved waveguide. A simplified two-mode model is used to introduce a single-parameter governing modal coupling and to find the condition under which coupling becomes weak enough that the probe pulse blueshifts its spectrum without changes in its pulse shape.

Quantum chaos and thermalization in the two-mode Dicke model

We discuss the onset of quantum chaos and thermalization in the two-mode Dicke model, which describes the dipolar interaction between an ensemble of spins and two bosonic modes. The two-mode Dicke model exhibits normal to superradiant quantum phase transition with spontaneous breaking either of a discrete or continuous symmetry. We study the behaviour of the fidelity out-of-time-order correlator (FOTOC) derived from the Loschmidt echo signal in the quantum phases of the model. We show that the exponential growth of the FOTOC in the beginning of the time evolution cannot be related to a classical unstable point in the general case. Furthermore, we find that the collective spin observable in the two-mode Dicke model quickly saturates to its long-time average value, and shows very good agreement between its diagonal ensemble average and microcanonical average even for a small number of spins. We show that the temporal fluctuations of the expectation value of the collective spin observable around its average are small and decrease with the effective system size, which leads to thermalization of the spin system.

Observation of topological pumping of a defect state in a Fock photonic lattice

Topological pumping connects the topological features of a modulated system with its transport behavior. It provides a powerful means for robust topological transport between distant nodes even in a one-dimensional chain, which may find applications in wave manipulation and quantum information processing. Here, we experimentally demonstrate an adiabatic pumping scheme, topological pumping of a defect state, by introducing a Fock photonic lattice, which is a classical analog of the Fock-state lattice of the two-mode Jaynes-Cummings model. Since this pumping is always protected by an energy gap even for a large-size system, its pumping efficiency can be enhanced considerably compared with the conventional topological pumping schemes. Moreover, a topologically protected beam splitter is also realized by designing the pumping channels of a defect state. The experimental results agree well with theoretical simulations. Our scheme provides a different route to study topological transport and implement novel photonic devices.

Identifying Combination of Dark–Bright Binary–Soliton and Binary–Periodic Waves for a New Two-Mode Model Derived from the (2 + 1)-Dimensional Nizhnik–Novikov–Veselov Equation

In this paper, we construct a new two-mode model derived from the (2+1)-dimensional Nizhnik–Novikov–Veselov (TMNNV) equation. We generalize the concept of Korsunsky to accommodate the derivation of higher-dimensional two-mode equations. Since the TMNNV is presented here, for the first time, we identify some of its solutions by means of two recent and effective schemes. As a result, the Kudryashov-expansion method exports a combination of bright–dark binary solitons, which simulate many applications in optics, photons, and plasma. The modified rational sine and cosine functions export binary–periodic waves that arise in the field of surface water waves. Moreover, by using 2D and 3D graphs, some physical properties of the TMNNV were investigated by means of studying the effect of the following parameters of the model: nonlinearity, dispersion, and phase–velocity. Finally, we checked the validity of the obtained solutions by verifying the correctness of the original governing model.

Control of the bipolarization emission of an Yb:YAG laser by the orientation of the pump polarization.

We show that the polarized pumping can be used to control the relative powers of two linear, orthogonally polarized, eigenstates in a Yb:YAG laser. The experimental observations are in full agreement with a two-mode rate-equation model, highlighting the roles of both the gain anisotropy and the cross-saturation parameters, whose values are found to be ε=0.08 and β = 0.64, respectively, in a longitudinally pumped continuous-wave microchip laser. The application to dual-polarization frequency combs is discussed.