Single-mode Approximation Research Articles

Resolution of superluminal signalling in non-perturbative cavity quantum electrodynamics

Recent technological developments have made it increasingly easy to access the non-perturbative regimes of cavity quantum electrodynamics known as ultrastrong or deep strong coupling, where the light–matter coupling becomes comparable to the bare modal frequencies. In this work, we address the adequacy of the broadly used single-mode cavity approximation to describe such regimes. We demonstrate that, in the non-perturbative light–matter coupling regimes, the single-mode models become unphysical, allowing for superluminal signalling. Moreover, considering the specific example of the quantum Rabi model, we show that the multi-mode description of the electromagnetic field, necessary to account for light propagation at finite speed, yields physical observables that differ radically from their single-mode counterparts already for moderate values of the coupling. Our multi-mode analysis also reveals phenomena of fundamental interest on the dynamics of the intracavity electric field, where a free photonic wavefront and a bound state of virtual photons are shown to coexist.

Fractional quantum Hall systems near nematicity: Bimetric theory, composite fermions, and Dirac brackets

We perform a detailed comparison of the Dirac composite fermion and the recently proposed bimetric theory for a quantum Hall Jain states near half filling. By tuning the composite Fermi liquid to the vicinity of a nematic phase transition, we find that the two theories are equivalent to each other. We verify that the single mode approximation for the response functions and the static structure factor becomes reliable near the phase transition. We show that the dispersion relation of the nematic mode near the phase transition can be obtained from the Dirac brackets between the components of the nematic order parameter. The dispersion is quadratic at low momenta and has a magnetoroton minimum at a finite momentum, which is not related to any nearby inhomogeneous phase.

Frequency lock-in during vortex induced vibration of a rotating blade

The vortex-induced vibration (VIV) of a rotating blade is studied in this paper. Uniform Euler–Bernoulli cantilever beam equation is used to model the rotating blade, while the nonlinear oscillator satisfying Van der Pol equation is used to represent the vortex shedding. The fluctuating lift force on the blade due to the wake dynamics is expressed such that it is proportional to the square of the magnitude of the relative velocity at which the blade interacts with the fluid. An unsteady lift due to vortex shedding acts on the blade, where as the blade is coupled with the fluid through a linear inertial coupling, resulting in a fluid–structure interaction problem. The coupled equations are discretized by using modal functions which satisfy the Eigenvalue problem. The work attempts to understand the interaction between the blade modes and the wake modes. The influence of the mass ratio and the reduced flow velocity on the coupling of the modes is explored. It is concluded form the study that the first mode is dominant and the effect of higher modes is less significant. Therefore, the single mode approximation is considered to study the instabilities associated with the frequency lock-in phenomenon of a rotating blade. The influence of fluid and blade damping, mass ratio and the coupling parameter on the lock-in phenomenon is investigated in this study.

Light, matter, and quantum randomness generation: A relativistic quantum information perspective

We study how quantum randomness generation based on unbiased measurements on a hydrogen-like atom can get compromised by the unavoidable coupling of the atom with the electromagnetic field. We improve on previous literature by analyzing the light–atom interaction in 3+1 dimensions with no single-mode or rotating-wave approximations and taking into account the non-pointlike nature of the atom, its orbital structure, and the exchanges of angular momentum between atom and field. We show that preparing the atom in the ground state in the presence of no field excitations is not universally the safest state to generate randomness.

Cavity-QED interactions of two correlated atoms

We consider the resonant van der Waals (vdW) interaction between two correlated identical two-level atoms (at least one of which being excited) within the framework of macroscopic cavity quantum electrodynamics in linear, dispersing and absorbing media. The interaction of both atoms with the body-assisted electromagnetic field of the cavity is assumed to be strong. Our time-independent evaluation is based on an extended Jaynes–Cummings model. For a system prepared in a superposition of its dressed states, we derive the general form of the vdW forces, using a Lorentzian single-mode approximation. We demonstrate the applicability of this approach by considering the case of a planar cavity and showing the position dependence of Rabi oscillations. We also show that in the limiting case of weak coupling, our results reproduce the perturbative ones for the case where the field is initially in vacuum state while the atomic state is in a superposition of two correlated states sharing one excitation.

Universal scaling of transverse wave attenuation in polycrystals

A single mode approximation for the transverse attenuation coefficient in polycrystals is obtained from the far field approximation model (Rokhlin et al., 2015). The model is applicable in all frequency ranges to polycrystals with ellipsoidal grains of triclinic symmetry and is shown to be in favorable agreement with other second order models. In the frame of this model, the transverse wave attenuation coefficient depends on a single elastic scattering factor only (it solely encompasses dependence on the crystallite elastic moduli and the elastic covariance). Therefore in this approximation the attenuation coefficient can be scaled with this factor (normalized), obtaining the universal (master) curve. The admissibility of scaling is supported by the use of the second order model (the type of Stanke-Kino) for a large number of material systems with different grain anisotropies. Within the second order model, the behavior of the scaled transverse wave attenuation coefficient versus frequency is nearly independent of the material system and is a function of the grain geometrical characteristics only. The scaling of the transverse wave attenuation coefficient is tested on the measurements for Ti alloy samples performed in this work and a large set of experimental data obtained for different material systems available in the literature. The results confirm the scaled coefficient independence of the material and good agreement between the data and the universal attenuation curve.

Probing quantum entanglement in the Schwarzschild space-time beyond the single-mode approximation

In this paper, we deduce the vacuum structure for Dirac fields in the background of Schwarzschild space-time beyond the single-mode approximation and discuss the performance of quantum entanglement between particle and antiparticle modes of a Dirac field with Hawking effect. It is shown that Hawking radiation does not always destroy the physically accessible entanglement, and entanglement amplification may happen in some cases. This striking result is different from that of the single-mode approximation, which holds that the Hawking radiation can only destroy entanglement. Lastly, we analyze the physically accessible entanglement relation outside the event horizon and demonstrate that the monogamy inequality is constantly established regardless of the choice of given parameters.

Analytical modeling of nonlinear flexural-extensional vibration of flexure beams with an interconnected compliant element

The constraint behavior of compliant mechanisms can be improved via strengthening the stiffness of their constitutive beams using intermediate elements. This interior element may be assumed to be perfectly rigid or one can consider its compliance as a design parameter. While modeling the static behavior of such systems is state of art, the nonlinear dynamic of such systems have been remained un-investigated. So the objective of this paper is to suggest an analytical framework for modeling nonlinear free and forced vibrations of a simple flexure beam strengthened via a compliant intermediate element. The equations of motion of the system are derived using Hamilton's principle. Based on a single mode approximation, the partial differential equations of motion are transformed into two temporal equations. Employing multiple time-scales perturbation techniques, free vibration time histories and forced vibration response due to base excitation is derived analytically. Different parametric studies are carried out to recognize the effect of the intermediate compliant element on the vibrational behavior of the flexure beam. The results of this paper are expected to develop a new approach in modeling and investigation of load-displacement behavior of compliant mechanisms.

Quantum coherence behaviors of fermionic system in non-inertial frame

In this paper, we analyze the quantum coherence behaviors of a single qubit in the relativistic regime beyond the single-mode approximation. Firstly, we investigate the freezing condition of quantum coherence in fermionic system. We also study the quantum coherence tradeoff between particle and antiparticle sector. It is found that there exists quantum coherence transfer between particle and antiparticle sector, but the coherence lost in particle sector is not entirely compensated by the coherence generation of antiparticle sector. Besides, we emphatically discuss the cohering power and decohering power of Unruh channel with respect to the computational basis. It is shown that cohering power is vanishing and decohering power is dependent of the choice of Unruh mode and acceleration. Finally, we compare the behaviors of quantum coherence with geometric quantum discord and entanglement in relativistic setup. Our results show that this quantifiers in two region converge at infinite acceleration limit, which implies that this measures become independent of Unruh modes beyond the single-mode approximations. It is also demonstrated that the robustness of quantum coherence and geometric quantum discord are better than entanglement under the influence of acceleration, since entanglement undergoes sudden death.

Electromagnetic Control of Nonlinear Behavior of an Excited Cantilever Beam in a Single Mode Approximation

The effects of combined DC and fast AC electromagnetic actuations on the dynamic behavior of an excited cantilever beam is studied considering a single mode approximation. Analytical investigation is performed to extract the equation of motion describing the slow dynamic of the system. The influence of the fast AC actuation and the air gap on the nonlinear behavior of the system is examined. It is shown that the nonlinear characteristic of the system can be controlled by appropriately tuning the AC actuation or the air gap. This can be useful in certain engineering applications where the operating frequency range includes one or several critical frequencies that should be avoided.

Ultrahigh lattice thermal conductivity in topological semimetal TaN caused by a large acoustic-optical gap

Topological semimetals may have potential applications such as in topological qubits, spintronics and quantum computations. Efficient heat dissipation is a key factor for the reliability and stability of topological semimetal-based nano-electronics devices, which is closely related to high thermal conductivity. In this work, the elastic properties and lattice thermal conductivity of TaN are investigated using first-principles calculations and the linearized phonon Boltzmann equation within the single-mode relaxation time approximation. According to the calculated bulk modulus, shear modulus and C44, TaN can be regarded as a potential incompressible and hard material. The room-temperature lattice thermal conductivity is predicted to be 838.62 along the a axis and 1080.40 along the c axis, showing very strong anisotropy. It is found that the lattice thermal conductivity of TaN is several tens of times higher than other topological semimetals, such as TaAs, MoP and ZrTe, which is due to the very longer phonon lifetimes for TaN than other topological semimetals. The very different atomic masses of Ta and N atoms lead to a very large acoustic-optical band gap, and then prohibit the scattering between acoustic and optical phonon modes, which gives rise to very long phonon lifetimes. Calculated results show that isotope scattering has little effect on lattice thermal conductivity, and that phonons with mean free paths larger than 20 (80) along the c direction at 300 K have little contribution to the total lattice thermal conductivity. This work implies that TaN-based nano-electronics devices may be more stable and reliable due to efficient heat dissipation, and motivates further experimental works to study lattice thermal conductivity of TaN.

On natural modes in moonpools and gaps in finite depth

In this paper an extension of the theoretical model of Molin (J. Fluid Mech., vol. 430, 2001, pp. 27–50) is proposed, where the assumptions of infinite depth and infinite horizontal extent of the support are released. The fluid domain is decomposed into two subdomains: the moonpool (or the gap) and a lower subdomain bounded by the seafloor and by an outer cylinder where the linearized velocity potential is assumed to be nil. Eigenfunction expansions are used to describe the velocity potential in both subdomains. Garrett’s method is then applied to match the velocity potentials at the common boundary and an eigenvalue problem is formulated and solved, yielding the natural frequencies and associated modal shapes of the free surface. Applications are made, first in the case of a circular moonpool, then in the rectangular gap and moonpool cases. Based on so-called single-mode approximations, simple formulas are proposed that give the resonant frequencies.

Comprehensive Analytical Approximations of the Pull-In Characteristics of an Electrostatically Actuated Nanobeam under the Influences of Intermolecular Forces

In this paper, analytical closed-form expressions to accurately estimate the pull-in characteristics of an electrostatically-actuated doubly-clamped nanobeam are derived and examined. In this regard, a coupled electro-mechanical problem for the nano-actuator is first presented assuming a single mode approximation while taking into account all the possible structural, electrical and nanoscale effects: the fringing of the electrical actuating force, the geometric mid-plane stretching and intermolecular (van der Walls and Casimir) forces. The complicated nonlinear resultant equations are numerically approximated in order to derive the closed-form expressions for the important nano-actuator pull-in characteristics: i.e., the detachment length, the minimum reachable gap size before the collapse and the respective pull-in voltage. The resulting closed-form expressions are first quantitatively validated with other previously published results, and comparisons showed an acceptable agreement. Unlike the reported expressions in the literature, the proposed closed-form expressions in this work are proper approximations, fairly accurate and, more importantly, provide a quick estimate of the critical design pull-in parameters of the nano-actuator. In addition, the analysis of these expressions demonstrated that the consideration of the intermolecular forces together with the fringe effect tends to significantly reduce the threshold pull-in voltage, whereas the mid-plane stretching parameter tends to the contrary to increase the voltage at the pull-in collapse. The derived expressions of these analytical/approximate solutions could hopefully be appropriately used by NEMS engineers as simple/quick procedures for successful design and fabrication of electrostatically-actuated nano-devices.

First principles study of the structural, stability properties and lattice thermal conductivity of bulk ReSe2

Thermoelectric devices can convert heat into an electric current and have immense potential for efficient use of the available energy. This includes converting heat energy from internal combustion engines, conventional power plants and solar cells into usable energy. Research into finding efficient thermoelectric materials has intensified over the past decade. One of the desired features of efficient thermoelectric materials is a low lattice thermal conductivity. In other words, the thermal energy transported by the motion of the atoms in thermoelectric materials should be small. Recent research suggests that some layered materials may possess this property. In this study we used first-principles calculations to investigate the structural, mechanical, and vibrational properties of bulk ReSe2, a layered material. The lattice thermal conductivity was calculated by using a single-mode relaxation-time approximation in the linearized phonon Boltzmann equation from first-principles an-harmonic lattice dynamics calculations. We find that the lattice thermal conductivity of ReSe2 is non-isotropic, with the highest value of 18.58W(mK)-1 along the a-axis and lowest one of 0.69W(mK)-1 along the c-axis at room temperature. These values make this an interesting material as a potential active component in a thermoelectric device.

On the use of continuous spectrum and discrete-mode differential models to predict contraction-flow pressure drops for Boger fluids

Over recent years, there has been slow but steady progress towards the qualitative numerical prediction of observed behaviour when highly elastic Boger fluids flow in contraction geometries. This has led to an obvious desire to seek quantitative agreement between prediction and experiment, a subject which is addressed in the current paper. We conclude that constitutive models of non-trivial complexity are required to make headway in this regard. However, we suggest that the desire to move from qualitative to quantitative agreement between theory and experiment is making real progress. In the present case with differential models, this has involved the introduction of a generalized continuous spectrum model. This is based on direct data input from material functions and rheometrical measurements. The class of such models assumes functional separability across shear and extensional deformation, through two master functions, governing independently material-time and viscous-response. The consequences of such a continuous spectrum representation are compared and contrasted against discrete-mode alternatives, via an averaged single-mode approximation and a multi-modal approximation. The effectiveness of each chosen form is gauged by the quality of match to complex flow response and experimental measurement. Here, this is interpreted in circular contraction-type flows with Boger fluids, where large experimental pressure-drop data are available and wide disparity between different fluid responses has been recorded in the past. Findings are then back-correlated to base-material response from ideal viscometric flow.

An analytical approach for modeling nonlinear vibration of doubly clamped functionally graded Timoshenko microbeams using strain gradient theory

In the current study, the nonlinear free and forced vibration of functionally graded strain gradient Timoshenko microbeam are analytically investigated. The nonlinear equations governing the motion of the microbeam and the corresponded boundary conditions are derived using variational approach. A novel analytical approach is proposed to derive closed-form expressions for the mode shapes of the system. The analytical mode shapes are then closely verified via numerical simulations and the effect of different parameters on the fundamental natural frequency of the beam is studied. Multiple time scales (MTS) perturbation technique is employed to model nonlinear free vibration of the system based on a single mode approximation. The accuracy of the time history results are confirmed by numerical calculations. The nonlinear forced vibration of the Timoshenko beam is also simulated using MTS. More specifically, the primary resonance and the frequency responses of the system are derived analytically and the effect of different design parameters on their behavior is studied in detail. The results and approaches presented in this paper can be further employed for suggesting analytical predictions in more complex micro structures.

Squeezed relic photons beyond the horizon

Owing to the analogy with the ordinary photons in the visible range of the electromagnetic spectrum, the Glauber theory is generalized to address the quantum coherence of the gauge field fluctuations parametrically amplified during an inflationary stage of expansion. The first and second degrees of quantum coherence of relic photons are then computed beyond the effective horizon defined by the evolution of the susceptibility. In the zero-delay limit the Hanbury Brown-Twiss correlations exhibit a super-Poissonian statistics which is however different from the conventional results of the single-mode approximation customarily employed, in quantum optics, to classify the coherence properties of visible light. While in the case of large-scale curvature perturbations the degrees of quantum coherence coincide with the naive expectation of the single-mode approximation, the net degree of second-order coherence computed for the relic photons diminishes thanks to the effect of the polarizations. We suggest that the Hanbury Brown-twiss correlations are probably the only tool to assess the quantum or classical origin of the large-scale magnetic fluctuations and of the corresponding curvature perturbations.

Quantum coherence of cosmological perturbations

In this paper, the degrees of quantum coherence of cosmological perturbations of different spins are computed in the large-scale limit and compared with the standard results holding for a single mode of the electromagnetic field in an optical cavity. The degree of second-order coherence of curvature inhomogeneities (and, more generally, of the scalar modes of the geometry) reproduces faithfully the optical limit. For the vector and tensor fluctuations, the numerical values of the normalized degrees of second-order coherence in the zero time-delay limit are always larger than unity (which is the Poisson benchmark value) but differ from the corresponding expressions obtainable in the framework of the single-mode approximation. General lessons are drawn on the quantum coherence of large-scale cosmological fluctuations.

Direct-exchange duality of the Coulomb interaction and collective excitations in graphene in a magnetic field

In a magnetic field two-dimensional (2D) electron systems host, with quenched kinetic energy, a variety of many-body correlation phenomena, such as interaction-driven new states and associated collective excitations over them. In a magnetic field, the two-body operators pertinent to the 2D Coulomb interaction obey a crossing relation, with which the Coulomb interaction is also cast into the form of manifest exchange interaction. It is shown that active use of this direct/exchange duality of the interaction allows one to develop, within the framework of the single-mode approximation, a new efficient algorithm for handling a wide class of collective excitations. The utility of our algorithm is demonstrated by studying some examples of inter- and intra-Landau-level collective excitations in graphene and in conventional electron systems.

Anisotropic lattice thermal conductivity in three-fold degeneracy topological semimetal MoP: a first-principles study

Recently, three-component new fermions in topological semimetal MoP are experimentally observed (2017 Nature 546 627), which may have potential applications like topological qubits, low-power electronics and spintronics. These are closely related to thermal transport properties of MoP. In this work, the phonon transport of MoP is investigated by solving the linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA). The calculated room-temperature lattice thermal conductivity is 18.41 and 34.71 along the in- and cross-plane directions, exhibiting very strong anisotropy. The isotope and size effects on the lattice thermal conductivity are also considered. It is found that isotope scattering produces little effect, and phonon has little contribution to the lattice thermal conductivity, when phonon mean free path (MFP) is larger than 0.15 at 300 K. It is noted that average room-temperature lattice thermal conductivity of MoP is lower than that of representative Weyl semimetal TaAs, which is due to smaller group velocities and larger Grüneisen parameters. Our works provide valuable informations for the thermal management of MoP-based nano-electronics devices, and motivate further experimental works to study thermal transport of MoP.