Two-mode Coupling Research Articles

Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: Full and hybrid TDMVCC[2

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom.

Effect of initial phase on the ablative Rayleigh–Taylor instability

The effect of initial perturbation phase on the ablative Rayleigh–Taylor instability is investigated by numerical simulations. We aim at the growth of harmonic amplitudes and the formation of spikes and bubbles in single- and two-mode coupling cases, respectively. In the two-mode coupling case, two kinds of simulations are performed: two modes with relatively small linear growth rate difference and two modes with relatively large linear growth rate difference. The initial relative phase between the original two modes has a significant effect on the growth of harmonic amplitudes, and in different initial relative phases, the structures of spikes and bubbles begin to show great differences in the nonlinear stage. Fortunately, the harmonic amplitudes are weakened at a specific initial relative phase. This has a certain enlightening significance for the stabilization of ablative Rayleigh–Taylor instability.

Plexcitonic optical chirality in the chiral plasmonic structure-microcavity-exciton strong coupling system.

Chiral plexcitonic systems exhibit a novel chiroptical phenomenon, which can provide a new route to design chiroptical devices. Reported works focused on the two-mode strong coupling between chiral molecules and nanoparticles, while multiple-mode coupling can provide richer modulation. In this paper, we proposed a three-mode coupling system consisting of a chiral Au helices array, a Fabry-Pérot cavity, and monolayer WSe2, which can provide an extra chiral channel, a more widely tunable region, and more tunable methods compared to two-mode coupled systems. The optical response of this hybrid system was investigated based on the finite element method. Mode splitting observed in the circular dichroism (CD) spectrum demonstrated that the chiroptical response successfully shifted from the resonant position of the chiral structure to three plexcitons through strong coupling, which provided a new route for chiral transfer. Furthermore, we used the coupled oscillator model to obtain the energy and Hopfield coefficients of the plexciton branches to explain the chiroptical phenomenon of the hybrid system. Moreover, the tunability of the hybrid system can be achieved by tuning the temperature and period of the helices array. Our work provides a feasible strategy for chiral sensing and modulation devices.

Synchronization transitions in Kuramoto networks with higher-mode interaction.

Synchronization is an omnipresent collective phenomenon in nature and technology, whose understanding is still elusive for real-world systems in particular. We study the synchronization transition in a phase oscillator system with two nonvanishing Fourier-modes in the interaction function, hence going beyond the Kuramoto paradigm. We show that the transition scenarios crucially depend on the interplay of the two coupling modes. We describe the multistability induced by the presence of a second coupling mode. By extending the collective coordinate approach, we describe the emergence of various states observed in the transition from incoherence to coherence. Remarkably, our analysis suggests that, in essence, the two-mode coupling gives rise to states characterized by two independent but interacting groups of oscillators. We believe that these findings will stimulate future research on dynamical systems, including complex interaction functions beyond the Kuramoto-type.

Coupled model analysis of the ablative Rayleigh–Taylor instability

The weakly nonlinear stage of the ablative Rayleigh–Taylor instability (ARTI) is investigated by expanded hydrodynamic equations in which the third-order corrections of the two-mode perturbations are considered. In the present coupling model, two linear perturbations are simultaneously added near the ablation front at the initial moment, and we have derived the first three coupling harmonics. Furthermore, the coupling model analysis is studied via direct numerical simulation as well. When the original two fundamental modes are always dominant over other modes, the time evolution of the density amplitudes for these modes agrees well with the results of direct numerical simulation. It is found that the harmonics are stabilized by the mode coupling effects, and the long wavelength mode of the fundamental modes tends to dominate the growth of the ARTI. Two-mode coupling is one of the restriction factors for the realization of controlled inertial confinement fusion. Therefore, the coupling harmonics excited by two-mode perturbations have good application potential and are worth further study.

Time-dependent density matrix renormalization group coupled with n-mode representation potentials for the excited state radiationless decay rate: Formalism and application to azulene

We propose a method for calculating the non-radiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface (PES) in the Franck-Condon region. The method combines the n-mode representation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method (TD-DMRG) to simulate quantum dynamics. In addition, in the framework of TD-DMRG, we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process. We use this method to study the internal conversion (IC) process of azulene after taking into account the anharmonicity of the ground state PES. The results show that even for this semi-rigid molecule, the intramode anharmonicity enhances the IC rate significantly, and after considering the two-mode coupling effect, the rate increases even further. The reason is that the anharmonicity enables the C–H vibrations to receive electronic energy while C–H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.

Time-dependent vibrational coupled cluster theory: Theory and implementation at the two-mode coupling level.

Equations are derived for the time evolution of time-dependent vibrational coupled cluster (TDVCC) wave functions covering both the TDVCC ket state and the associated so-called Λ bra state. The equations are implemented in the special case of both the Hamiltonian and the cluster operator containing at most two-mode coupling terms. The nontrivial behavior of the evolution of norm, energy, and expectation values due to the nonunitary time-evolution of the nonvariational TDVCC theory is analyzed theoretically and confirmed in numerical experiments that also include time-dependent Hamiltonians. In the spirit of time-independent size-consistency analysis, the separability of both the coupled cluster and Λ states for noninteracting systems is studied. While the coupled cluster state clearly has the correct behavior, the behavior of the Λ state is more intricate, and the consequence for different properties is shown theoretically and numerically. Overall, the numerical experiments show that TDVCC in incomplete expansions gives higher accuracy than a standard linear variational wave function parameterization with the same number of independent parameters, while equivalent results are obtained for complete expansions. The efficiency of the methodology is illustrated in computations on polycyclic aromatic hydrocarbons with up to 156 modes.

Photonics: Multipolar Conversion Induced Subwavelength High‐Q Kerker Supermodes with Unidirectional Radiations (Laser Photonics Rev. 13(9)/2019)

It is widely known that Q-factors of resonances are inextricably linked to radiation losses, while their connection to angular radiation distributions is largely overlooked. In article number 1900067, Yuntian Chen, Wei Liu, and Weijin Chen revisit arguably the most fundamental model of two-mode coupling, and establish a subtle connection between these two seemingly unrelated properties, revealing the fundamental mechanism of Q-factor enhancement induced by multipolar conversions from lower to higher orders.

Control of Nuclear Dynamics through Conical Intersections and Electronic Coherences.

The effect of nuclear dynamics and conical intersections on electronic coherences is investigated employing a two-state, two-mode linear vibronic coupling model. Exact quantum dynamical calculations are performed using the multiconfiguration time-dependent Hartree method. It is found that the presence of a nonadiabatic coupling close to the Franck-Condon point can preserve electronic coherence to some extent. Additionally, the possibility of steering the nuclear wave packets by imprinting a relative phase between the electronic states during the photoionization process is discussed. It is found that the steering of nuclear wave packets is possible given that a coherent electronic wave packet embodying the phase difference passes through a conical intersection. A conical intersection close to the Franck-Condon point is thus a necessary prerequisite for control, providing a clear path towards attochemistry.

Design of broadband graphene-metamaterial absorbers for permittivity sensing at mid-infrared regions

In this paper, a tunable broadband metamaterial absorber (MA) based on graphene is investigated theoretically and numerically at mid-infrared regions. Compared with the previously reported multiband graphene-based MAs, a broad bandwidth of 11.7 THz with the absorption over 90% is obtained in the proposed MA, which is composed of a Jerusalem cross (JC) metal encrusting into the slot graphene layer in the top layer. The results show that the origin of broadband absorption is caused by coupling effect between metal and graphene, and this effect is explained by the two-mode waveguide coupling theory. The tunability of MA is achieved via changing the external gate voltage to modify the Fermi energy of graphene. Further results show that the proposed MA can be used as the permittivity sensor with a high absorption. This work indicates that the proposed MA has the potential applications with respect to sensors and infrared absorbers.

Nonlinear Energy Cascading in Turbulence during the Internal Reconnection Event at the Sino-United Spherical Tokamak**Supported by the National Basic Research Program of China under Grant No 2012CB934303, the Natural Science Foundation of Shanghai under Grant No 15ZR1403300 and the National Natural Science Foundation of China under Grant No 11275051.

The characteristics of the energy transfer and nonlinear coupling among edge electromagnetic turbulence in thermal quench sub-period of the internal reconnection event (IRE) are studied at the sino-united spherical tokamak device using multiple Langmuir and magnetic probe arrays. The wavelet bispectral analysis and the modified Kim method are applied to investigate linear growth/damping and nonlinear energy transfer rates, along with multi-field turbulence interactions. The results show a multi-field nonlinear energy transfer from electrostatic to magnetic turbulence that results in two-mode coupling in magnetic turbulence, which may play a crucial role to trigger the IRE.

Enhancing the Surface Sensitivity of Metallic Nanostructures Using Oblique-Angle-Induced Fano Resonances.

Surface sensitivity is an important factor that determines the minimum amount of biomolecules detected by surface plasmon resonance (SPR) sensors. We propose the use of oblique-angle-induced Fano resonances caused by two-mode coupling or three-mode coupling between the localized SPR mode and long-range surface plasmon polariton modes to increase the surface sensitivities of silver capped nanoslits. The results indicate that the coupled resonance between the split SPR (−kSPR) and cavity modes (two-mode coupling) has a high wavelength sensitivity for small-angle incidence (2°) due to its short decay length. Additionally, three-mode coupling between the split SPR (−kSPR), substrate (+kSub) and cavity modes has a high intensity sensitivity for large-angle incidence due to its short decay length, large resonance slope and enhanced transmission intensity. Compared to the wavelength measurement, the intensity measurement has a lower detectable (surface) concentration below 1 ng/ml (0.14 pg/mm2) and is reduced by at least 3 orders of magnitude. In addition, based on the calibration curve and current system noise, a theoretical detection limit of 2.73 pg/ml (0.38 fg/mm2) can be achieved. Such a surface concentration is close to that of prism-based SPR with phase measurement (0.1–0.2 fg/mm2 under a phase shift of 5 mdeg).

A strongly coupled Λ-type micromechanical system

We study a classical Λ-type three-level system based on three high-Q micromechanical beam resonators embedded in a gradient electric field. By modulating the strength of the field at the difference frequency between adjacent beam modes, we realize strong dynamic two-mode coupling, via the dielectric force. Driving adjacent pairs simultaneously, we observe the formation of a purely mechanical “dark” state and an all-phononic analog of coherent population trapping—signatures of strong three-mode coupling. The Λ-type micromechanical system is a natural extension of previously demonstrated “two-level” micromechanical systems and adds to the toolbox for engineering of all-phononic micromechanical circuits and arrays.

Harnessing non-Markovian quantum memory by environmental coupling

Controlling the non-Markovian dynamics of open quantum systems is essential in quantum information technology since it plays a crucial role in preserving quantum memory. Albeit in many realistic scenarios the quantum system can simultaneously interact with composite environments, this condition remains little understood, particularly regarding the effect of the coupling between environmental parts. We analyze the non-Markovian behavior of a qubit interacting at the same time with two coupled single-mode cavities which in turn dissipate into memoryless or memory-keeping reservoirs. We show that increasing the control parameter, that is the two-mode coupling, allows for triggering and enhancing a non-Markovian dynamics for the qubit starting from a Markovian one in absence of coupling. Surprisingly, if the qubit dynamics is non-Markovian for zero control parameter, increasing the latter enables multiple transitions from non-Markovian to Markovian regimes. These results hold independently on the nature of the reservoirs. This work highlights that suitably engineering the coupling between parts of a compound environment can efficiently harness the quantum memory, stored in a qubit, based on non-Markovianity.

Excitation of Biomolecules with Incoherent Light: Quantum Yield for the Photoisomerization of Model Retinal

Cis-trans isomerization in retinal, the first step in vision, is often computationally studied from a time-dependent viewpoint. Motivation for such studies lies in coherent pulsed laser experiments that explore the isomerization dynamics. However, such biological processes take place naturally in the presence of incoherent light, which is expected to excite a nonevolving mixture of stationary states. Here the isomerization problem is considered from the latter viewpoint and applied to a standard two-state, two-mode linear vibronic coupling model of retinal that explicitly includes a conical intersection between the ground and first excited electronic states. The calculated quantum yield at 500 nm agrees well with both the previous time-dependent calculations of Hahn and Stock (0.63) [ J. Phys. Chem. B 2000, 104, 1146-1149 ] and with experiment (0.65 ± 0.01), as does its wavelength dependence. Significantly, the effects of environmental relaxation on the quantum yield in this well-established model are found to be negligible. The results make clear the connection of the photoisomerization quantum yield to properties of stationary eigenstates, providing alternate insights into conditions for yield optimization.

Two-mode coupling model in a few mode fiber

A phenomenological two-mode coupling model in few mode fibers (FMF) is developed. It uses a mode coupling coefficient and the differential modal delay as the input parameters and the split-step approach. The model is consistent with the experimental results demonstrating distributed mode coupling effects in FMF and may be used for multipath interference estimation based on statistical analysis of fluctuations.

Two-Mode Coupling Model in a Few Mode Fiber

Two-Mode Coupling Model in a Few Mode Fiber

Influence of shear flow on the linear response of a nematic liquid crystal to external electric fields

We have investigated the linear response of shear stress to ac electric fields under shear flow in a nematic liquid crystal. The experimental results were compared with the theoretical results derived from the Ericksen-Leslie theory. Although close agreement was obtained at low shear rates, discrepancies were observed at high shear rates. By introducing a two-mode coupling model the experimental results were well reproduced for the entire range of shear rates, and nonconservative forces were found to play an important role in determining the fluctuation dynamics, which is a characteristic of nonequilibrium steady states.

Computation of expectation values from vibrational coupled-cluster at the two-mode coupling level

In this work we show how the vibrational coupled-cluster method at the two-mode coupling level can be used to calculate zero-point vibrational averages of properties. A technique is presented, where any expectation value can be calculated using a single set of Lagrangian multipliers computed solving iteratively a single linear set of equations. Sample calculations are presented which show that the resulting algorithm scales only with the third power of the number of modes, therefore making large systems accessible. Moreover, we present applications to water, pyrrole, and para-nitroaniline.

Quasi-harmonic analysis of mode coupling in fluctuating native proteins

Mode coupling and anharmonicity in a native fluctuating protein are investigated in modal space by projecting the motion along the eigenvectors of the fluctuation correlation matrix. The probability distribution of mode fluctuations is expressed in terms of tensorial Hermite polynomials. Molecular dynamics trajectories of Crambin are generated and used to evaluate the terms of the polynomials and to obtain the modal energies. The energies of a few modes exhibit large deviations from the harmonic energy of kT/2 per mode, resulting from coupling to the surroundings, or to another specific mode or to several other modes. Slowest modes have energies that are below that of the harmonic, and a few fast modes have energies significantly larger than the harmonic. Detailed analysis of the coupling of these modes to others is presented in terms of the lowest order two-mode coupling terms. Finally, the effects of mode coupling on conformational properties of the protein are investigated.