Quadratic Coupling Research Articles

Cosmology with subdominant Horndeski scalar field

We study the cosmological evolution of a scalar field in Horndeski gravity, assuming that the scalar field is subdominant with respect to the cosmic fluid. We first analyse the most general shift-symmetric action that respects local Lorentz symmetry. We show that the bound on the speed of gravitational waves set by GW170817+GRB170817A imposes a constraint only on the linear coupling between the scalar and the Gauss-Bonnet invariant and this constraint is rather mild. Then, we consider some interesting examples of theories that break shift-symmetry, such as the Damour-Esposito-Far\`ese model of spontaneous scalarization and a theory with a quadratic coupling to the Gauss-Bonnet invariant that can lead to black hole scalarization. In both cases, tuning of cosmological initial conditions is necessary to keep the scalar field dormant during cosmic evolution.

Experimental study on the wave run-up and air-gap response of a three-column semi-submersible platform

The hydrodynamic responses, characterized by 6 degrees of freedom (DOF) motions, wave run-up and air-gap of a three-column semi-submersible platform in random sea are experimentally investigated. Irregular waves representative of a 100-yr typhoon were used as the incident wave field and the actions of wind and current are included. It was found that extremely large slow-drift surge motions occur under irregular waves, while the low-frequency pitch motions are relatively small which were believed to be remarkable for the deep-draft semi-submersible. A wavelet cross bicoherence analysis was applied to investigate the extreme wave run-up responses. The high-frequency components in the extreme wave run-ups were found to be from the quadratic phase coupling between the dominant response frequencies of the incident waves, heave motion, and pitch motion.

Spinning and excited black holes in Einstein-scalar-Gauss–Bonnet theory

We construct rotating black holes in Einstein-scalar-Gauss–Bonnet theory with a quadratic coupling function. We map the domain of existence of the rotating fundamental solutions, we construct radially excited rotating black holes (including their existence lines), and we show that there are angularly excited rotating black holes. The bifurcation points of the radially and angularly excited solutions branching out of the Schwarzschild solution follow a regular pattern.

Quadratic optomechanical coupling in an active-passive-cavity system

We investigate an active-passive-cavity system where a membrane is quadratically coupled to the passive cavity. When the passive cavity is strong coherently driven to enhance the optomechanical coupling, the optical field interacts with the mechanical oscillator through the two-phonon process. By calculating the eigenfrequencies of system in Keldysh framework, we show the significant splitting of exceptional point in the presence of the optomechanical coupling. We also calculate the transmission rate to show how this system responds to an additional weak probe field. We find the gain effect will induce the two-phonon process amplification window. However, the gain effect becomes weak when the photon-tunneling strength increases. Then the transmission rate of the probe field changes from amplification to absorption. These results have potential applications in quantum metrology, quantum information processing, and quantum optical devices.

Relevance of the Quadratic Diamagnetic and Self-Polarization Terms in Cavity Quantum Electrodynamics.

Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light–matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically, we demonstrate their relevance by showing that neglecting these terms leads to the loss of gauge invariance, basis set dependence, disintegration (loss of bound states) of any system in the basis set limit, unphysical radiation of the ground state, and an artificial dependence on the static dipole. Besides providing important guidance for modeling of strongly coupled light–matter systems, the presented results also indicate conditions under which those effects might become accessible.

Artificial oxide heterostructures with non-trivial topology

In the quest for topological insulators with large band gaps, heterostructures with Rashba spin–orbit interactions come into play. Transition metal oxides with heavy ions are especially interesting in this respect. We discuss the design principles for stacking oxide Rashba layers. Assuming a single layer with a two-dimensional electron gas (2DEG) on both interfaces as a building block, a two-dimensional topological insulating phase is present when negative coupling between the 2DEGs exists. When stacking multiple building blocks, a two-dimensional or three-dimensional topological insulator is artificially created, depending on the intra- and interlayer coupling strengths and the number of building blocks. We show that the three-dimensional topological insulator is protected by reflection symmetry, and can therefore be classified as a topological crystalline insulator. In order to isolate the topological states from bulk states, the intralayer coupling term needs to be quadratic in momentum. It is described how such a quadratic coupling could potentially be realized by taking buckling within the layers into account. The buckling, thereby, brings the idea of stacked Rashba system very close to the alternative approach of realizing the buckled honeycomb lattice in [111]-oriented perovskite oxides.

Understanding the suppression of structure formation from dark matter-dark energy momentum coupling

Models in which scalar field dark energy interacts with dark matter via a pure momentum coupling have previously been found to potentially ease the structure formation tension between early- and late-universe observations. In this article we explore the physical mechanism underlying this feature. We argue analytically that the perturbation growth equations imply the suppression of structure growth, illustrating our discussion with numerical calculations. Then we generalise the previously studied quadratic coupling between the dark energy and dark matter to a more general power law case, also allowing for the slope of the dark energy exponential potential to vary. We find that the structure growth suppression is a generic feature of power law couplings and it can, for a range of parameter values, be larger than previously found.

An improved method for bispectral analysis of nonlinear wave interaction system

Digital bispectral analysis is an effective means to study nonlinear system such as random sea-wave and edge plasma turbulence. In this paper, an improved digital bispectral method, the complete iterative method, is proposed to solve the three-wave coupling equation. The detailed comparisons are made between the previous estimation methods, Ritz’s iterative method (Ritz and Powers 1986 Physica D 20 320) and Kim’s method (Kim et al 1996 Phys. Plasmas 3 3998), and the complete iterative method. The results suggest that, employing the complete iterative method to compute the linear and quadratic nonlinear transfer functions, and linear and quadratic coupling coefficients, the resultant calculations are shown to be more accurate than those reconstructed by the first two methods. And different from the previous two methods, the complete iterative method is demonstrated to be more suitable for the study of ordinary ‘black-box’ fluctuating systems or turbulence system with ‘ideal’ power spectrum, i.e., all the output signals are limited to have the same power spectra as input signals. Finally, some further discussions are made briefly that address on the applications of the complete iterative method in the study of some specific nonlinear systems.

Prospects of reinforcement learning for the simultaneous damping of many mechanical modes

We apply adaptive feedback for the partial refrigeration of a mechanical resonator, i.e. with the aim to simultaneously cool the classical thermal motion of more than one vibrational degree of freedom. The feedback is obtained from a neural network parametrized policy trained via a reinforcement learning strategy to choose the correct sequence of actions from a finite set in order to simultaneously reduce the energy of many modes of vibration. The actions are realized either as optical modulations of the spring constants in the so-called quadratic optomechanical coupling regime or as radiation pressure induced momentum kicks in the linear coupling regime. As a proof of principle we numerically illustrate efficient simultaneous cooling of four independent modes with an overall strong reduction of the total system temperature.

Bicoherence Interpretation in EEG Requires Signal to Noise Ratio Quantification: An Application to Sensorimotor Rhythms

In the electroencephalogram (EEG) the quadratic phase coupling (QPC) phenomenon indicates the presence of non-linear interactions among brain rhythms that could affect the interpretation of their physiological meaning. We propose the use of the bicoherence as a QPC quantification method to understand the nature of brain rhythm interplay. We firstly provide a simulation study to show under which condition of signal to noise ratio (SNR) the bicoherence is a reliable QPC quantifier and how to interpret the results. Secondly, in the light of the simulation results, we applied the bicoherence analysis to real EEG data acquired on thirteen volunteers during a cue-paced reaching motor task to quantify coupling and decoupling between mu and beta rhythms. An inter-trial averaging procedure was adopted in order to allow the correct calculation of the bicoherence during a motor task. Simulations demonstrated that SNR has a strong impact on the correct quantification of bicoherence and that a reliable detection of QPC is possible when the SNR is favorable (>-5dB). Results from EEG data demonstrated a QPC between mu and beta rhythms during the resting state and its fading during movement planning and execution, providing valuable information for the interpretation of their dynamics. The bicoherence was proven to be an effective tool for the investigation of coupling between the sensorimotor rhythms during all the phases of a motor task. This was assessed in relation to the physiological changing of the SNR characterizing the frequency components of interest.

Photon-assisted entanglement and squeezing generation and decoherence suppression via a quadratic optomechanical coupling.

Entanglement and quantum squeezing have wide applications in quantum technologies due to their non-classical characteristics. Here we study entanglement and quantum squeezing in an open spin-optomechanical system, in which a Rabi model (a spin coupled to the mechanical oscillator) is coupled to an ancillary cavity field via a quadratic optomechanical coupling. We find that their performances can be significantly modulated via the photon of the ancillary cavity, which comes from photon-dependent spin-oscillator coupling and detuning. Specifically, a fully switchable spin-oscillator entanglement can be achieved, meanwhile a strong mechanical squeezing is also realized. Moreover, we study the environment-induced decoherence and dissipation, and find that they can be mitigated by increasing the number of photons. This work provides an effective way to manipulate entanglement and quantum squeezing and to suppress decoherence in the cavity quantum electrodynamics with a quadratic optomechanics.

Force sensing beyond standard quantum limit with optomechanical "soft" mode induced by nonlinear interaction.

We consider an optomechanical (OM) system that consists of a mechanical and an optical mode interacting through linear and quadratic OM dispersive couplings. The system is operated in unresolved sideband limit with a high quality factor mechanical resonator. Such a system acts as a parametrically driven oscillator, giving access to an intensity-assisted tunability of the spring constant. This enables the operation of the OM system in its "soft mode," wherein the mechanical spring softens and responds with a lower resonance frequency. We show that this soft mode can be exploited to nonlinearize backaction noise, which yields higher force sensitivity beyond the conventional standard quantum limit.

The role of vibronic coupling in the electronic spectroscopy of maleimide: a multi-mode and multi-state quantum dynamics study.

The first two excitation bands below 7 eV in the electronic absorption spectrum of maleimide are investigated using a model Hamiltonian including four low-lying singlet excited states within the manifold of 24 vibrational modes. The role of non-adiabatic effects is studied and shines light on both the broad, inter-state coupling-dominated spectral band as well as the fine-structured, not-so-strong coupled band. Calculations have been performed using the Multiconfigurational Time-Dependent Hartree (MCTDH) wavepacket propagation method as well as its multilayer version (ML-MCTDH) using a quadratic vibronic coupling (QVC) Hamiltonian model where parameters are obtained from fitting adiabatic potential energy surfaces computed by ab initio methods. The quantum dynamics calculations provide information on the relaxation dynamics and the vibrational modes involved. Already with a low-order vibronic coupling model and only a few modes being considered, a quantitative agreement with the experimental spectrum is obtained. However, it is found that all modes need to be considered to get a full picture of the photo-excited relaxation dynamics of this molecule.

Temperature dependence of nitrogen-vacancy optical center in diamond

Diamond, a wide band gap semiconductor material, has been attracting interest in several fields from electrics and optics to biomedicine and quantum computing due to its outstanding properties. These properties of diamond are related to its unique lattice and optically active defect centers. In this paper, the dependence of nitrogen-vacancy (NV) center on measurement temperature is studied by using the low-temperature photoluminescence (PL) spectroscopy in a temperature range of 80–200 K. The results show that with the increase of the measurement temperature, the zero phonon lines of NV defects are red-shifted, its intensity decreases and its full width at half maximum increases. These results are attributed to the synergetic process of the lattice expansion and quadratic electron-phonon coupling. The NV<sup>—</sup> and NV<sup>0</sup> centers have similar values in the quenching activation energy and the thermal softening coefficient, resulting from their similar structures. The small differences may be associated with the electron-phonon coupling. The broadening mechanism of the NV centers is carefully distinguished by <inline-formula><tex-math id="Z-20200615115616-1">\begin{document}$T^3,\; T^5,\; T^7$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200395_Z-20200615115616-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200395_Z-20200615115616-1.png"/></alternatives></inline-formula> Voigt function fitting with the relation. These results show that the full width at half maximum of the Gaussian component of NV<sup>—</sup> and NV<sup>0</sup> centers are randomly distributed near 0.1 meV and 2.1 meV, respectively, while the full width at half maximum of the Lorentz component of NV<sup>—</sup> and NV<sup>0</sup> centers increase with measurement temperature increasing. The full width at half maximum of Lorentz of NV<sup>—</sup> and NV<sup>0</sup> centers conform to the <inline-formula><tex-math id="Z-20200615115631-1">\begin{document}$ T^3 $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200395_Z-20200615115631-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="12-20200395_Z-20200615115631-1.png"/></alternatives></inline-formula> relationship. It can be proved that under the action of the fluctuating field, the zero phonon lines of the NV defects exhibit an obvious homogeneous widening mechanism.

Decaying localized structures beyond Turing space in an activator–inhibitor system

We perform numerical simulations beyond Turing space in an activator–inhibitor system involving quadratic and cubic nonlinearities . We show that while all the three fixed points of the system are stable nodes, it exhibits spatially stable patterns as diverse as labyrinths, worms, negatons, and combination of them. The transition among the patterns is found to be dependent on the relative strength (h) of quadratic and cubic couplings. The labyrinths and worms are formed for small values of h while stable negatons are obtained for $$0.0891\le h\le 0.1106$$. The negatons start showing decaying behavior for $$h\ge 0.1135$$ and, finally they vanish at random positions by emitting remnant solitary waves, yielding a pattern of stable concentric rings. The spatial extension of the concentric rings is found to depend on the initial concentration profile of the decaying negatons. The resulting concentric rings do not decay further due to limitation of numerical precision. We also find that the transient period for each pattern also depends on h.

Normal-mode splitting in a linear and quadratic optomechanical system with an ensemble of two-level atoms

We theoretically calculate normal-mode splitting (NMS) in a linear and quadratic optomechanical system (OMS) with an ensemble of two-level atoms, where the interaction between the mechanical membrane and the optical cavity includes linear optomechanical coupling and quadratic optomechanical coupling (QOC). In the presence of atomic ensemble, a negative QOC strength is instrumental for generating NMS, while the positive QOC restricts NMS, and eventually it disappears. Further, for the hybrid OMS assisted with the atomic ensemble, the displacement spectrum of the mechanical resonator displays three peaks, where the middle peak results from the effective coupling strength between the cavity field and the atomic ensemble. Here the negative QOC strength and the effective ensemble-field coupling can provide an efficient control of the amplitude and position of the three peaks.

Floquet spinor Bose gases

We introduce a Floquet spinor Bose-Einstein condensate induced by a periodically driven quadratic Zeeman coupling whose frequency is larger than any other energy scales. By examining a spin-1 system available in ultracold atomic gases, we demonstrate that such an external driving field has great effect on the condensate through emergence of a unique spin-exchange interaction. We uncover that the ferromagnetic condensate has several unconventional stationary states and thus exhibits rich continuous phase transitions. On the other hand, the antiferromagnetic condensate is found to possess a nontrivial metastable region, which supports unusual elementary excitations and hysteresis phenomena.

Tunable transparency and amplification in a hybrid optomechanical system with quadratic coupling

We theoretically study the optical response of a hybrid optomechanical system with quadratic coupling, where an optomechanical cavity with a movable membrane in the middle is coupled to an auxiliary cavity with a tunable gain rate. We show that the optical transmission of the system can be controlled by a variety of parameters, including power of the control field, coupling strength between the two cavities, the gain rate of the auxiliary cavity, reflectivity of the membrane, and the temperature of the environment. In particular, tunable transparency and amplification can be realized by modifying the gain rate of the auxiliary cavity. Under the condition of two-phonon resonance, we find that (i) for the no-loss-gain cavity, a broad transparency window appears in the probe transmission due to the coupling between the two cavities; (ii) for the passive cavity, an extremely narrow transparency window occurs within a broad transmission window due to quadratic optomechanical coupling; (iii) for the active cavity, the probe field can be amplified in a wide frequency regime. Our proposal provides a new platform to control the propagation of light.

Spin-orbit vibronic coupling in Π4 states of linear triatomic molecules.

The Renner vibronic-coupling problem in 4Π electronic states of linear molecules is analyzed with rigorous and systematic inclusion of spin-orbit (SO) coupling. The 8 × 8 Hamiltonian matrix of a 4Π state in the diabatic electronic representation has been constructed by a Taylor expansion in the bending normal mode up to second order. As previously found for 2Π states and 3Π states, SO-induced vibronic-coupling terms that are linear in the bending amplitude exist in addition to the quadratic electrostatic Renner coupling. The effects of the linear and quadratic Renner coupling on the four Kramers-degenerate potential energy surfaces of the 4Π state are discussed. The spectroscopic effects of the linear SO-vibronic-coupling mechanism have been analyzed by numerical calculations of vibronic spectra.

Complementary Techniques for the Accelerometric Environment Characterization of Thermodiffusion Experiments on the ISS

The accelerometric environment of IVIDIL and DCMIX experiments were successively monitored not only to identify the main disturbances that could affect the experiments but as well to ensure the correct interpretation of the experimental results. To do so, the conventional techniques used by NASA have been complemented by new tools developed and adapted to help the surveillance of the runs. A summary of these main new techniques is presented further. To show the potentiality of all these techniques, moderate and strong disturbance episodes such as berthings, dockings and reboostings were analyzed by using acceleration signals that came from three different sensors located in the Destiny, Columbus and JEM/Kibo modules, respectively. The first technique proposed is based on the Shannon entropy concept in both time (TEN) and frequency (SEN) domains. It has been found, that SEN technique is a fast and easy tool to detect the different disturbances registered throughout the experiments. The second technique suggested by the authors is based on the one-third octave frequency band RMS values and is called RMS warning map. It is a visual tool which was demonstrated to be very efficient in detecting the range of the frequencies that surpasses the ISS limits requirements, especially when a sudden disturbance occurs. Finally, in order to identify nonlinearities in the frequency domain within a signal, bispectrum and trispectrum functions have been applied. Quadratic and cubic phase couplings have been detected with these techniques only between high frequencies and especially for the signals coming from JEM/Kibo module.