Quadratic Coupling Research Articles

Effects of quadratic coupling on optical response of a hybrid optomechanical cavity assisted by Kerr non-linear medium

We theoretically investigate the effect of non-linearity on the optical response of a hybrid optomechanical system. The optical cavity consists of a Kerr non-linear medium. We study how the presence of quadratic optomechanical coupling and Kerr nonlinearity in the conventional optomechanical system affects the system’s stability. It is shown that the presence of all the non-linearities in the system leads to seven real roots in the optical bistability. However, if any of the two non-linearities (quadratic optomechanical coupling or Kerr non-linearity) decreases, the roots in the optical bistability also decrease. Hence, quadratic optomechanical coupling and Kerr nonlinearity can be used as handles to control the optical bistability of the system. Therefore, we propose this system to be used as an all-optical switch in quantum information devices.

Formulation of temperature dependent effective Hartree potential incorporating quadratic over linear molecular DOFs-surface modes couplings and its effect on quantum dynamics of D2 (v = 0, j = 0)/D2 (v = 0, j = 2) on Cu(111) metal surface

The effect of surface temperature on the scattering and dissociation processes of D2 (v = 0, j = 0)/D2 (v = 0, j = 2) on Cu(111) metal plane is investigated by formulating a time and temperature dependent effective Hamiltonian within mean-field approach, where the molecular degrees of freedom and surface mode vibrations are assumed to be weakly coupled with each other. While constructing such effective Hamiltonian with a Hartree product type wavefunction, we incorporate: (i) an operator algebra method to circumscribe higher order-quadratic (anharmonic) molecular DOFs-surface modes couplings over the linear coupling case implemented previously [Adhikari and coworkers, J. Chem. Phys. 154, 104103 (2021)]; (ii) surface temperature by considering Bose–Einstein or Maxwell–Boltzmann probability factors for the initial state distribution of the surface vibrational modes. Finally, a six-dimensional (6D) quantum dynamical (QD) calculation is performed with such newly formulated effective Hartree potential and calculated transition/dissociation probabilities at various surface temperature situations. The quadratic (anharmonic) molecular DOFs-surface modes couplings modify the reaction and transition probabilities substantially with change of surface temperature, which indicates the crucial role of surface mode vibrations on the molecule-surface scattering phenomena.

The environment dependent dilaton in the laboratory and the solar system

We consider the environment-dependent dilaton in the laboratory and the solar system and derive approximate analytical solutions to the field theory equations of motion in the presence of a one or two mirror system or a sphere. The solutions obtained herein can be applied to qBOUNCE experiments, neutron interferometry and for the calculation of the dilaton field induced “Casimir force” in the Cannex experiment as well as for Lunar Laser Ranging. They are typical of the Damour–Polyakov screening mechanism whereby deviations from General Relativity are suppressed by a vanishingly small direct coupling of the dilaton to matter in dense environments. We specifically focus on dilaton models which are compatible with the late time acceleration of the expansion of the Universe, i.e. the cosmological dilaton. We show how future laboratory experiments will essentially test a region of parameter space with A_2simeq lambda ^2 where A_2 is the quadratic coupling strength of the dilaton to matter and lambda is the steepness of the exponential runaway potential. Current constraints favour the large A_2 regime implying that the environment-dependent dilaton satisfies two of the swampland conjectures, i.e. the distance conjecture whereby the field excursion should not exceed the Planck scale and the de Sitter conjecture specifying that the running dilaton potential should be steep enough with a large lambda .

Theory of superconductivity due to Ngai's mechanism in lightly doped SrTiO3

We develop a theory of superconducting pairing in low-density strontium titanate due to the quadratic coupling of electron density to soft transverse optical phonons first proposed by Ngai [Phys. Rev. Lett. 32, 215 (1974)]. This leads to a static attractive potential between electrons with decay length ${l}_{\mathrm{eff}}$ that scales inversely with soft optical gap ${\ensuremath{\omega}}_{T}$. For low electron densities $n\ensuremath{\le}{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, attraction between electrons is static and local in space; thus the transition temperature ${T}_{c}$ was found using known results for low-density electron gas. The ${T}_{c}(n)$ dependence for low doping was calculated and found to be in agreement with experimental data. In addition, we show that suppression of ${T}_{c}$ by hydrostatic pressure and strong increase in ${T}_{c}$ due to isotope substitution $^{16}\mathrm{O}{\ensuremath{\rightarrow}}^{18}\mathrm{O}$ observed experimentally also can be explained within our theory.

Majorized iPADMM for Nonseparable Convex Minimization Models with Quadratic Coupling Terms

In this paper, we consider nonseparable convex minimization models with quadratic coupling terms arised in many practical applications. We use a majorized indefinite proximal alternating direction method of multipliers (iPADMM) to solve this model. The indefiniteness of proximal matrices allows the function we actually solved to be no longer the majorization of the original function in each subproblem. While the convergence still can be guaranteed and larger stepsize is permitted which can speed up convergence. For this model, we analyze the global convergence of majorized iPADMM with two different techniques and the sublinear convergence rate in the nonergodic sense. Numerical experiments illustrate the advantages of the indefinite proximal matrices over the positive definite or the semi-definite proximal matrices.

An Improved Imaging Algorithm for Multi-Receiver SAS System with Wide-Bandwidth Signal

When the multi-receiver synthetic aperture sonar (SAS) works with a wide-bandwidth signal, the performance of the range-Doppler (R-D) algorithm is seriously affected by two approximation errors, i.e., point target reference spectrum (PTRS) error and residual quadratic coupling error. The former is generated by approximating the PTRS with the second-order term in terms of the instantaneous frequency. The latter is caused by neglecting the cross-track variance of secondary range compression (SRC). In order to improve the imaging performance in the case of wide-bandwidth signals, an improved R-D algorithm is proposed in this paper. With our method, the multi-receiver SAS data is first preprocessed based on the phase center approximation (PCA) method, and the monostatic equivalent data are obtained. Then several sub-blocks are generated in the cross-track dimension. Within each sub-block, the PTRS error and residual quadratic coupling error based on the center range of each sub-block are compensated. After this operation, all sub-blocks are coerced into a new signal, which is free of both approximation errors. Consequently, this new data is used as the input of the traditional R-D algorithm. The processing results of simulated data and real data show that the traditional R-D algorithm is just suitable for an SAS system with a narrow-bandwidth signal. The imaging performance would be seriously distorted when it is applied to an SAS system with a wide-bandwidth signal. Based on the presented method, the SAS data in both cases can be well processed. The imaging performance of the presented method is nearly identical to that of the back-projection (BP) algorithm.

Magnetic transitions in two novel mixed-valence iron(II)–iron(III) metal formate frameworks: Two sublattice model

We study the two-sublattice model in the mean field theory by expanding the Gibbs free energy in terms of the magnetizations M1 (Mup) and M2 (Mdown) with the quadratic coupling M12M22 (quadrupolar interactions) for the order–disorder transition in the two mixed-valence iron (II)-iron (III) metal formate frameworks, C2H5NH3FeIIFeIIIHCOO6 and C2H52NH2FeIIFeIIIHCOO6. Expressions derived from the Gibbs free energy for the temperature dependence of the magnetizations M1 and M2, are fitted to the observed data (H=100Oe) from the literature for the two mixed-valence iron (II) – iron (III) system. The inverse susceptibilities (χ1-1 and χ2-1) are predicted as a function of temperature (H=100Oe) from the two-sublattice model. Additionally, the field dependence of the total magnetization (M=M1+M2) is analyzed using the literature data for the compounds studied.We find that the two-sublattice model with the quadrupolar interactions, is satisfactory to describe the order–disorder transition in the two mixed-valence iron (II) – iron (III) metal formate frameworks as studied here. It indicates that the two-sublattice model can also be applied to some other multiferroic mixed materials.

Fluctuation Results for Multi-species Sherrington-Kirkpatrick Model in the Replica Symmetric Regime

We study the Replica Symmetric region of general multi-species Sherrington-Kirkpatrick (MSK) Model and answer some of the questions raised in Ann. Probab. 43 (2015), no. 6, 3494–3513, where the author proved the Parisi formula under positive-definite assumption on the disorder covariance matrix $$\Delta ^2$$ . First, we prove exponential overlap concentration at high temperature for both indefinite and positive-definite $$\Delta ^2$$ MSK model. We also prove a central limit theorem for the free energy using overlap concentration. Furthermore, in the zero external field case, we use a quadratic coupling argument to prove overlap concentration up to $$\beta _c$$ , which is expected to be the critical inverse temperature. The argument holds for both positive-definite and emphindefinite $$\Delta ^2$$ , and $$\beta _c$$ has the same expression in two different cases. Second, we develop a species-wise cavity approach to study the overlap fluctuation, and the asymptotic variance-covariance matrix of overlap is obtained as the solution to a matrix-valued linear system. The asymptotic variance also suggests the de Almeida–Thouless (AT) line condition from the Replica Symmetry (RS) side. Our species-wise cavity approach does not require the positive-definiteness of $$\Delta ^2$$ . However, it seems that the AT line conditions in positive-definite and indefinite cases are different. Finally, in the case of positive-definite $$\Delta ^2$$ , we prove that above the AT line, the MSK model is in Replica Symmetry Breaking phase under some natural assumption. This generalizes the results of J. Stat. Phys. 174 (2019), no. 2, 333–350, from 2-species to general species.

Spin-wave growth via Shapiro resonances in a spinor Bose-Einstein condensate

We theoretically study the resonant phenomenon in a spin-1 Bose-Einstein condensate periodically driven by a quadratic Zeeman coupling. This phenomenon is closely related to the Shapiro steps in superconducting Josephson junctions, and the previous experimental work [Evrard $et al.,$ Phys. Rev. A 100, 023604 (2019)] for a spin-1 bosonic system observed the resonant dynamics and then called it Shapiro resonance. In this work, using the spin-1 Gross-Pitaevskii equation, we study the Shapiro resonance beyond the single-mode approximation used in the previous work, which assumes that all components of the spinor wavefunction have the same spatial configuration. Considering resonant dynamics starting from a polar state, we analytically calculate the Floquet-Lyapunov exponents featuring an onset of the resonance under a linear analysis and find that spin waves with finite wavenumbers can be excited. This kind of non-uniform excitation cannot be described by the single-mode approximation. Furthermore, to study the long-time resonant dynamics beyond the linear analysis, we numerically solve the one-dimensional spin-1 Gross-Pitaevskii equation, finding that the nonresonant hydrodynamic variables also grow at wavelengths of even multiples of the resonant one due to the nonlinear effect.

Exploring multi-Higgs models with softly broken large discrete symmetry groups

We develop methods to study the scalar sector of multi-Higgs models with large discrete symmetry groups that are softly broken. While in the exact symmetry limit, the model has very few parameters and can be studied analytically, proliferation of quadratic couplings in the most general softly broken case makes the analysis cumbersome. We identify two sets of soft breaking terms which play different roles: those which preserve the symmetric vacuum expectation value alignment, and the remaining terms which shift it. Focusing on alignment preserving terms, we check which structural features of the symmetric parent model are conserved and which are modified. We find remarkable examples of structural features which are inherited from the parent symmetric model and which persist even when no exact symmetry is left. The general procedure is illustrated with the example of the three-Higgs-doublet model with the softly broken symmetry group Sigma (36).

Acousto-optic cavity coupling in 2D phoxonic crystal with combined convex and concave holes

A two-dimensional cross-like phoxonic crystal (PxC) model is proposed, which exhibits simultaneously large complete photonic crystal (PtC) and phononic crystal (PnC) bandgaps. The most salient trait of the structure is the wide range of geometrical parameters compatible with large complete bandgaps. After geometrical optimization, photonic and phononic bandgaps with gap-to-midgap ratios of 11.5% and 90.7% are obtained, respectively. These values are close to the best topology-optimized reported values but are obtained with simple shapes compatible with nanoscale fabrication technology. These characteristics make the convex–concave topology a promising candidate for PxC devices. A cavity is then introduced by filling up one cross-like hole in the 7 × 7 super-cell. PtC and PnC bands with defects appear in the respective large complete bandgaps, confining phonons and photons in the same cavity. Acousto-optic (AO) coupling between photonic and phononic defect modes is further investigated by the finite element method, taking both photoelastic and moving interface mechanisms into consideration. The symmetries of both photonic and phononic modes play a dominant role in the coupling strength. Results show that the strongest linear coupling between a photonic transverse magnetic mode and phononic breathing mode is obtained due to the in-phase superposition in the x and y directions. A quadratic nonlinear coupling is observed when photonic modes are coupled with the phononic stretching mode due to the inverse superposition of x and y directions. Finally, the optomechanical coupling rates relative to zero-point motion are estimated.

Optomechanical isolation with tunable center frequency

Optomechanical (OM) isolators have the ability to stop the optical field for one direction and to pass the field in the opposite direction. Thus they work as bandstop filter in one direction and bandpass filter in the opposite direction. The maximum isolation happens when the frequency of the field becomes equal to that of the mechanical membrane inside the isolator. This frequency, called the isolation (or center) frequency, however is restricted by the fact that the fundamental frequency of the membrane depends upon its physical parameters (such as mass and length), which are fixed during fabrication of the membrane. We propose a dynamical way of tuning this center frequency, by using a mechanical drive attached to a membrane with quadratic OM coupling in a membrane-in-the-middle setup. This provides a way for future applications where tunable filtering is required.

Quantum estimation of coupling strengths in driven-dissipative optomechanics

We exploit local quantum estimation theory to investigate the measurement of linear and quadratic coupling strengths in a driven-dissipative optomechanical system. For experimentally realistic values of the model parameters, we find that the linear coupling strength is considerably easier to estimate than the quadratic one. Our analysis also reveals that the majority of information about these parameters is encoded in the reduced state of the mechanical element, and that the best estimation strategy for both coupling parameters is well approximated by a direct measurement of the mechanical position quadrature. Interestingly, we also show that temperature does not always have a detrimental effect on the estimation precision, and that the effects of temperature are more pronounced in the case of the quadratic coupling parameter.

Nonequilibrium thermal transport and photon squeezing in a quadratic qubit-resonator system

We investigate steady-state thermal transport and photon statistics in a nonequilibrium hybrid quantum system, in which a qubit shows longitudinal and quadratic coupling with an optical resonator. Our calculations are conducted with the method of the quantum dressed master equation combined with full counting statistics. The effect of negative differential thermal conductance is unravelled at finite temperature bias, which stems from the suppression of cyclic heat transitions and large mismatch of two squeezed photon modes at weak and strong qubit-resonator hybridizations, respectively. The giant thermal rectification is also exhibited at large temperature bias. It is found that the asymmetric composition of the hybrid system by spin and boson roles and negative differential thermal conductance show the cooperative contribution. Noise power and skewness, as typical current fluctuations, exhibit global maximum with strong hybridization at small and large temperature bias limits, respectively. Moreover, the effect of photon quadrature squeezing is discovered in the strong hybridization and low-temperature regime, which shows asymmetric response to two bath temperatures. These results would provide some insight to thermal functional design and photon manipulation in qubit-resonator hybrid quantum systems.

Landau phenomenological model for the α-INC (incommensurate)-β transition in quartz

ABSTRACT The temperature dependence of the order parameters η (α-phase) and ξ (INC – incommensurate phase) are calculated in the presence of the electric field for the α-INC-β transition in quartz by the Landau mean field theory. Landau phenomenological model with the linear () and quadratic () coupling is introduced to investigate mainly the nature of the INC phase between α (ordered) and β (disordered) phases in quartz. The temperature dependence of the inverse susceptibilities ( and ) of the order parameter is also predicted at constant electric fields studied for the α-INC-β transition in quartz. Additionally, the E−T phase diagram for the transitions of the α-INC and INC-β in quartz is constructed from the Landau phenomenological model by using the literature data. Our predictions for the order parameters (η and ξ) and the inverse susceptibilities ( and ) can be compared with the experimental measurements for the α-INC-β transition in quartz.

Quantum simulation of tunable and ultrastrong mixed-optomechanics.

We propose a reliable scheme to simulate tunable and ultrastrong mixed (first-order and quadratic optomechanical couplings coexisting) optomechanical interactions in a coupled two-mode bosonic system, in which the two modes are coupled by a cross-Kerr interaction and one of the two modes is driven through both the single- and two-excitation processes. We show that the mixed-optomechanical interactions can enter the single-photon strong-coupling and even ultrastrong-coupling regimes. The strengths of both the first-order and quadratic optomechanical couplings can be controlled on demand, and hence first-order, quadratic, and mixed optomechanical models can be realized. In particular, the thermal noise of the driven mode can be suppressed totally by introducing a proper squeezed vacuum bath. We also study how to generate the superposition of coherent squeezed state and vacuum state based on the simulated interactions. The quantum coherence effect in the generated states is characterized by calculating the Wigner function in both the closed- and open-system cases. This work will pave the way to the observation and application of ultrastrong optomechanical effects in quantum simulators.

Evolution of turbulent kinetic energy during the entire sandstorm process

Abstract. An adaptive segmented stationary method for non-stationary signal is proposed to reveal the turbulent kinetic energy evolution during the entire sandstorm process observed at the Qingtu Lake Observation Array. Sandstorm which is a common natural disaster is mechanically characterized by a particle-laden two-phase flow experiencing wall turbulence, with an extremely high Reynolds number and significant turbulent kinetic energy. Turbulence energy transfer is important to the understanding of sandstorm dynamics. This study indicates that large-/very-large-scale coherent structures originally exist in the rising stage of sandstorms with a streamwise kinetic energy of 75 % rather than gradually forming. In addition to carrying a substantial portion of energy, the very-large-scale-motions are active structures with strong nonlinear energy transfer. These structures gain energy from strong nonlinear interaction. As sandstorm evolves, these large structures are gradually broken by quadratic phase coupling, with the energy fraction reducing to 40 % in the declining stage. The nonlinear process in the steady and declining stages weakens and maintains a balanced budget of energy. The systematic bispectrum results provide a new perspective for further insight of sandstorms.

Rotating scalarized black holes in scalar couplings to two topological terms

The tachyonic instability of the Kerr black holes is analyzed in the Einstein-scalar theory with the quadratic scalar couplings to two topological terms which are parity-even Gauss-Bonnet and parity-odd Chern-Simons terms. For positive coupling α, we use the (2+1)-dimensional hyperboloidal foliation method to derive the threshold curve which is the boundary between stable and unstable Kerr black holes by considering a spherically symmetric scalar-mode perturbation. In case of negative coupling, a newly bound of a≥0.26 with a the rotation parameter is found for unstable Kerr black holes and its threshold curve is derived.

Locomotive Gear Fault Diagnosis Based on Wavelet Bispectrum of Motor Current

The motor current signature analysis (MCSA) provides a nondestructive method for gear fault detection. The motor current in the faulty gear system not only involves the frequency information related to the fault but also the electric supply frequency and gear meshing-related frequency, which not only contaminates the fault characteristics but also increases the difficulty of fault extraction. To extract the fault characteristic frequency effectively, an innovative method based on the wavelet bispectrum (WB) is proposed. Bispectrum is an effective tool for identifying the fault-related quadratic phase coupling (QPC). However, it requires a large amount of data averaging, which is not suitable for short data analysis. In this paper, the wavelet bispectrum is introduced to motor current analysis and the problem of QPC extraction under variable speed conditions is preliminarily solved. Furthermore, a fault diagnostic approach for locomotive gears using the wavelet bispectrum and wavelet bispectral entropy is suggested. The presented method was effectively applied to the locomotive online running operations, and faults of the drive gear were successfully diagnosed.

Age-dependent cross frequency coupling features from children to adults during general anesthesia

BackgroundThe frequency coupling characteristics in electroencephalogram (EEG) induced by anesthetics have been well studied in adults, but the investigation of the age-dependent cross frequency coupling features from children to adults is still lacking. MethodsWe analyzed EEG signals recorded from pediatric to adult patients (n = 131), separated into six age groups: <1 year (n = 15), 1–3 years (n = 23), 3–6 years (n = 19), 6–12 years (n = 18), 12–18 years (n = 16), and 18–45 years (n = 40). Age related EEG power and cross frequency coupling analysis (phase amplitude coupling (PAC) and quadratic phase coupling) of data from maintenance of a surgical state of anesthesia (MOSSA) was conducted. Also, for patients of ages less than 6 years, we analyzed the performance of cross frequency coupling derived indices in distinguishing the states of wakefulness, MOSSA, and recovery of consciousness (ROC). Results(1) During MOSSA, EEG power substantially increased with age from infancy to 3–6 years then decreased with age in the theta-gamma frequency bands. The infant group (<1 year) had the highest slow oscillation (SO) power among all age groups. (2) The distinct PAC pattern is absent in patients less than 1 year of age both in SO-alpha and delta-alpha frequency band coupling during propofol induced unconsciousness. The modulation index between delta and alpha oscillations in MOSSA increased with age. (3) Wavelet bicoherence derived indices reach their peaks in the 3–6 years group and then decrease with age growth. (4) The Diag_En index (normalized entropy of the diagonal bicoherence entries of the bicoherence matrix) performed the best at distinguishing different states for ages less than 6 years (p<0.05). ConclusionsThe combination of propofol induction and sevoflurane maintenance exhibited age-dependent EEG power spectra, PAC, and bicoherence, likely related to brain development. These observations suggest new rules for infant and child brain state monitoring during general anesthesia are needed.