Near-resonant Interactions Research Articles

The high-resolution infrared spectrum of the ν3 + ν8 combination band of jet-cooled propyne

The high-resolution infrared spectrum of the ν3+ν8 combination band of propyne (CH3CCH) is presented for the first time. Continuous-wave cavity ring-down spectroscopy is used to measure this weak infrared band in the 3175cm−1 region using a supersonic free jet. The rotational analysis of the experimental spectrum results in accurate spectroscopic parameters for the ν3+ν8 combination vibrational state. Severe perturbations are found for K=3 and 4 rotational levels that are likely due to near-resonant or non-resonant interactions between the ν3+ν8 and other vibrational states. Moreover three parallel-transition type subbands are observed and their analysis is presented as well.

Vibronic origin of sulfur mass-independent isotope effect in photoexcitation of SO2and the implications to the early earth’s atmosphere

Signatures of mass-independent isotope fractionation (MIF) are found in the oxygen ((16)O,(17)O,(18)O) and sulfur ((32)S, (33)S, (34)S, (36)S) isotope systems and serve as important tracers of past and present atmospheric processes. These unique isotope signatures signify the breakdown of the traditional theory of isotope fractionation, but the physical chemistry of these isotope effects remains poorly understood. We report the production of large sulfur isotope MIF, with Δ(33)S up to 78‰ and Δ(36)S up to 110‰, from the broadband excitation of SO2 in the 250-350-nm absorption region. Acetylene is used to selectively trap the triplet-state SO2 ( (3)B1), which results from intersystem crossing from the excited singlet ( (1)A2/ (1)B1) states. The observed MIF signature differs considerably from that predicted by isotopologue-specific absorption cross-sections of SO2 and is insensitive to the wavelength region of excitation (above or below 300 nm), suggesting that the MIF originates not from the initial excitation of SO2 to the singlet states but from an isotope selective spin-orbit interaction between the singlet ( (1)A2/ (1)B1) and triplet ( (3)B1) manifolds. Calculations based on high-level potential energy surfaces of the multiple excited states show a considerable lifetime anomaly for (33)SO2 and (36)SO2 for the low vibrational levels of the (1)A2 state. These results demonstrate that the isotope selectivity of accidental near-resonance interactions between states is of critical importance in understanding the origin of MIF in photochemical systems.

Phase-averaged equation for water waves

AbstractWe investigate phase-averaged equations describing the spectral evolution of dispersive water waves subject to weakly nonlinear quartet interactions. In contrast to Hasselmann’s kinetic equation, we include the effects of near-resonant quartet interaction, leading to spectral evolution on the ‘fast’ $O({\epsilon }^{- 2} )$ time scale, where $\epsilon $ is the wave steepness. Such a phase-averaged equation was proposed by Annenkov & Shrira (J. Fluid Mech., vol. 561, 2006b, pp. 181–207). In this paper we rederive their equation taking some additional higher-order effects related to the Stokes correction of the frequencies into account. We also derive invariants of motion for the phase-averaged equation. A numerical solver for the phase-averaged equation is developed and successfully tested with respect to convergence and conservation of invariants. Numerical simulations of one- and two-dimensional spectral evolution are performed. It is shown that the phase-averaged equation describes the ‘fast’ evolution of a spectrum on the $O({\epsilon }^{- 2} )$ time scale well, in good agreement with Monte-Carlo simulations using the Zakharov equation and in qualitative agreement with known features of one- and two-dimensional spectral evolution. We suggest that the phase-averaged equation may be a suitable replacement for the kinetic equation during the initial part of the evolution of a wave field, and in situations where ‘fast’ field evolution takes place.

Quadripartite cluster and Greenberger–Horne–Zeilinger entangled light via cascade interactions with separated atomic ensembles

It has been known that two-mode entangled light can possibly be generated by employing near-resonant interaction with an ensemble of two-level atoms. The responsible mechanism is the absorption of two photons from the strong driving field and the emission of two new photons into the cavity field. Here, we generalize such a mechanism to three separated atomic ensembles and establish cascade interactions for four nondegenerate fields. It is shown that the quadripartite cluster and Greenberger–Horne–Zeilinger entangled states occur for continuous variables. The advantage of the present scheme for the multipartite entanglement lies in that the coupling strengths are much larger due to the near resonances than for far-off-resonance-based parametric processes.

Photofragmentations, state interactions, and energetics of Rydberg and ion-pair states: Two-dimensional resonance enhanced multiphoton ionization of HBr via singlet-, triplet-, Ω = 0 and 2 states

Mass spectra were recorded for one-colour resonance enhanced multiphoton ionization (REMPI) of H(i)Br (i = 79, 81) for the two-photon resonance excitation region 79,040-80,300 cm(-1) to obtain two-dimensional REMPI data. The data were analysed in terms of rotational line positions, intensities, and line-widths. Quantitative analysis of the data relevant to near-resonance interactions between the F(1)Δ(2)(v' = 1) and V(1)Σ(+)(v' = m + 7) states gives interaction strengths, fractional state mixing, and parameters relevant to dissociation of the F state. Qualitative analysis further reveals the nature of state interactions between ion-pair states and the E(1)Σ(+) (v' = 1) and H(1)Σ(+)(v' = 0) Rydberg states in terms of relative strengths and J' dependences. Large variety in line-widths, depending on electronic states and J' quantum numbers, is indicative of number of different predissociation channels. The relationship between line-widths, line-shifts, and signal intensities reveals dissociation mechanisms involving ion-pair to Rydberg state interactions prior to direct or indirect predissociations of Rydberg states. Quantum interference effects are found to be important. Moreover, observed bromine atom (2 + 1) REMPI signals support the importance of Rydberg state predissociation channels. A band system, not previously observed in REMPI, was observed and assigned to the k(3)Π(0)(v' = 0) ←← X transition with band origin 80,038 cm(-1) and rotational parameter B(v('))=7.238 cm(-1).

Resonant and Near-Resonant Internal Wave Interactions

Abstract The spectral energy density of the internal waves in the open ocean is considered. The Garrett and Munk spectrum and the resonant kinetic equation are used as the main tools of the study. Evaluations of a resonant kinetic equation that suggest the slow time evolution of the Garrett and Munk spectrum is not in fact slow are reported. Instead, nonlinear transfers lead to evolution time scales that are smaller than one wave period at high vertical wavenumber. Such values of the transfer rates are inconsistent with the viewpoint expressed in papers by C. H. McComas and P. Müller, and by P. Müller et al., which regards the Garrett and Munk spectrum as an approximate stationary state of the resonant kinetic equation. It also puts the self-consistency of a resonant kinetic equation at a serious risk. The possible reasons for and resolutions of this paradox are explored. Inclusion of near-resonant interactions decreases the rate at which the spectrum evolves. Consequently, this inclusion shows a tendency of improving of self-consistency of the kinetic equation approach.

Spectral energy transfer of atmospheric gravity waves through sum and difference nonlinear interactions

Abstract. Nonlinear interactions of gravity waves are studied with a two-dimensional, fully nonlinear model. The energy exchanges among resonant and near-resonant triads are examined in order to understand the spectral energy transfer through interactions. The results show that in both resonant and near-resonant interactions, the energy exchange between two high frequency waves is strong, but the energy transfer from large to small vertical scale waves is rather weak. This suggests that the energy cascade toward large vertical wavenumbers through nonlinear interaction is inefficient, which is different from the rapid turbulence cascade. Because of considerable energy exchange, nonlinear interactions can effectively spread high frequency spectrum, and play a significant role in limiting wave amplitude growth and transferring energy into higher altitudes. In resonant interaction, the interacting waves obey the resonant matching conditions, and resonant excitation is reversible, while near-resonant excitation is not so. Although near-resonant interaction shows the complexity of match relation, numerical experiments show an interesting result that when sum and difference near-resonant interactions occur between high and low frequency waves, the wave vectors tend to approximately match in horizontal direction, and the frequency of the excited waves is also close to the matching value.

Attenuation of short surface waves by the sea floor via nonlinear sub-harmonic interaction

AbstractWe consider the indirect mechanism for dissipation of short surface waves through their near-resonant interactions with long sub-harmonic waves that are dissipated by the bottom. Using direct perturbation analysis and an energy argument, we obtain analytic predictions of the evolution of the amplitudes of two short primary waves and the long sub-harmonic wave which form a near-resonant triad, elucidating the energy transfer, from the short waves to the long wave, which may be significant over time. We obtain expressions for the rate of total energy loss of the system and show that this rate has an extremum corresponding to a specific value of the (bottom) damping coefficient (for a given pair of short wavelengths relative to water depth). These analytic results agree very well with direct numerical simulations developed for the general nonlinear wave–wave and wave–bottom interaction problem.

Resonant-wave signature of an oscillating and translating disturbance in a two-layer density stratified fluid

We investigate the nonlinear wave signature of a translating and oscillating disturbance under the influence of ambient waves in a two-layer fluid. The main interests are the generation and features of the far-field waves due to nonlinear wave resonances. We show, using perturbation theory, that free waves on the surface and/or interface can be produced by triad-resonant interactions, a mechanism not obtained in a homogeneous fluid. These occur among the radiated waves due to the disturbance motion (disturbance waves); and between the disturbance waves and free ocean waves (ambient waves). Such resonance-generated waves can appear upstream or downstream, and may propagate away from or towards the disturbance. In realistic situations where ambient waves and disturbance oscillations contain multiple frequencies, numerous resonant and near-resonant interactions at second and higher orders may occur, making the theoretical analysis of the problem intractable. For this purpose, we develop a direct simulation capability using a high-order spectral method, which provides independent validation of the theoretical predictions. Our investigations show that, under specific but realistic conditions, resonance interactions may lead to significant far-field short waves that are more amenable to remote sensing. If the characteristics of the disturbance are known, we illustrate how nonlinear wave resonances provide a mechanism for more precise estimation of ocean stratification properties using surface wave measurements. Finally we show that when a moving disturbance oscillates at multiple frequencies, ensuing multiple resonances may lead to energy spreading across a broader spectrum, resulting in the loss of information about the body motion.

Interaction of light with a single atom in the strong focusing regime

We consider the near-resonant interaction between a single atom and a focused light mode, where the single atom localized at the focus of a lens can scatter a significant fraction of light. Complementary to previous experiments on extinction and phase shift effects of a single atom, here we report on the measurement of coherently backscattered light. The strength of the observed effect suggests combining strong focusing with a cavity to further enhance the field at the location of the atom. This could make scaling up to a network of several atom + cavity nodes more realistic due to significant technical simplification of the atom–light interface. We consider theoretically a nearly concentric cavity, which has a strongly focused optical mode. Simple estimates show that in such a case one can expect a significant single photon Rabi frequency.

Long-range collisional energy transfer between charge-transfer (ion-pair) states of I2, induced by H2O and I2(X)

Long-range (resonant) energy transfer, between g/u charge-transfer states of molecular iodine [i.e., f0(g) (+)((3)P(0))-->F0(u)(+)((3)P(0)) and E0(g)(+)((3)P(2))-->D0(u) (+)((3)P(2))], induced by collisions with H(2)O and I(2)(X) via multipole coupling, has been observed. Large rate constants, up to 5 x 10(-9) molecules(-1) cm(3) s(-1), for collisional transfer between a range of vibrational levels of the f0(g)(+)((3)P(0)) and F0(u)(+)((3)P(0)) ion-pair states of I(2), by H(2)O, are reported. Some previously reported studies on E0(g)(+)((3)P(2))-->D0(u)(+)((3)P(2)) and f0(g)(+)((3)P(0))-->F0(u)(+)((3)P(0)) collisional transfer, induced by I(2)(X), have been repeated and revised rate data are presented; the range of initially excited vibrational states studied has also been extended. Much smaller rate constants for quenching by I(2)(X), compared to H(2)O, are found and it is proposed that H(2)O desorbed from the walls of the sample cell could have significantly affected much larger rate data previously reported in the literature. For both collision partners, a model is proposed in which long-range, near-resonant interactions can occur when there is close matching of the change in energy in the ion-pair states with the change in energy that accompanies the rotational transition undergone by the collision partner.

Two-dimensional (2+n) resonance enhanced multiphoton ionization of HCl: State interactions and photorupture channels via low-energy triplet Rydberg states

Mass spectra were recorded for (2+n) resonance enhanced multiphoton ionization (REMPI) of HCl as a function of resonance excitation energy in the 81,710-82,870 cm(-1) region to obtain two-dimensional REMPI data. Small but significant fragmentations and H(+), Cl(+), as well as HCl(+) formations are found to occur after resonance excitations to the triplet Rydberg states f (3)Delta(2)(v(') = 0), f (3)Delta(1)(v(') = 0), and g (3)Sigma(+)(1)(v(') = 0). Whereas insignificant rotational line shifts could be observed, alterations in relative ion signal intensities, due to perturbations, clearly could be seen, making such data ideal for detecting and analyzing weak state interactions. Model analysis of relative ion signal intensities, taking account of the major ion formation channels following excitations to Rydberg states, its near-resonance interactions with ion-pair states as well as dissociations and/or photodissociations were performed. These allowed verification of the existence of all these major channels as well as quantifications of the relative weights of the channels and estimates of state interaction strengths. The proposed mechanisms were supported by ion signal power dependence studies.

Diurnal thermocline oscillations driven by tidal flow around an island in the Middle Adriatic

Oceanographic data collected between February and September 2006 have been examined in order to detect and interpret different physical processes in the Adriatic shelf break area. One of the main objectives was to gain more information on internal tides. The work comprised thermistor measurements carried out at the islands of Biševo, Sušac and Lastovo at 10 equidistant depths, between 4 and 40 m, on submarine cliffs opened to the southeast. Significant diurnal temperature oscillations were detected at Lastovo. The strongest variations were driven by the sea/land breezes (middle of July 2006). However, during several episodes between June and August 2006 diurnal wind forcing was not significant, whereas barotropic currents at an ADCP station close to Lastovo, as well as sea levels at Split and Dubrovnik, contained a pronounced diurnal signal. The wind and tidal influences on the temperature variability were separated by applying a multiple cross-wavelet spectral analysis with the hourly pseudo wind stress and sea level (or barotropic current) data treated as the inputs and the isotherm heights at Lastovo considered as the output. The analysis confirmed that significant correlation between tides and thermocline oscillations existed at the end of June, at the end of July and in August 2006. Diurnal internal tidal observations were consistent with simple theoretical near-resonant interaction of tidal flow with the island of Lastovo under stratified conditions, resulting in the generation of baroclinic island-trapped waves. This study revealed that even in a shallow area of high bathymetric complexity subjected to micro-tides, large amplitude internal waves at diurnal tidal frequency could be generated.

Discreteness and resolution effects in rapidly rotating turbulence

Rotating turbulence is characterized by the nondimensional Rossby number Ro, which is a measure of the strength of the Coriolis term relative to that of the nonlinear term. For rapid rotation (Ro-->0) , nonlinear interactions between inertial waves are weak, and the theoretical approaches used for other weak (wave) turbulence problems can be applied. The important interactions in rotating turbulence at small Ro become those between modes satisfying the resonant and near-resonant conditions. Often, discussions comparing theoretical results and numerical simulations are questioned because of a speculated problem regarding the discreteness of the modes in finite numerical domains versus continuous modes in unbounded continuous theoretical domains. This argument finds its origin in a previous study of capillary waves, for which resonant interactions have a very particular property that is not shared by inertial waves. This possible restriction on numerical simulations of rotating turbulence to moderate Ro has never been quantified. In this paper, we inquire whether the discreteness effects observed in capillary wave turbulence are also present in inertial wave turbulence at small Ro. We investigate how the discreteness effects can affect the setup and interpretation of studies of rapidly rotating turbulence in finite domains. In addition, we investigate how the resolution of finite numerical domains can affect the different types of nonlinear interactions relevant for rotating inertial wave turbulence theories. We focus on Rossby numbers ranging from 0 to 1 and on periodic domains due to their relevance to direct numerical simulations of turbulence. We find that discreteness effects are present for the system of inertial waves for Rossby numbers comfortably smaller than those used in the most recent numerical simulations of rotating turbulence. We use a kinematic model of the cascade of energy via selected types of resonant and near-resonant interactions to determine the threshold of Ro below which discreteness effects become important enough to render an energy cascade impossible.

Two-dimensional (2+n) resonance enhanced multiphoton ionization of HCl: Photorupture channels via the FΔ21 Rydberg state and ab initio spectra

Mass spectra were recorded for (2+n) resonance enhanced multiphoton ionization (REMPI) of HCl as a function of resonance excitation energy in the 82 600-88 100 cm(-1) region to obtain two-dimensional REMPI data. Analysis of ion-mass signal intensities for excitations via the F (1)Delta(2)(v(')=0-2) and the V (1)Sigma(+)(v(')) states as a function of rotational quantum numbers in the intermediate states either revealed near-resonance interactions or no significant coupling between the F (1)Delta(2) and the V (1)Sigma(+) states, depending on quantum levels. Ion-signal intensities and power dependence measurements allowed us to propose photoionization mechanisms in terms of intermediate state involvement. Based on relative ion-signal intensities and rotational line positions we quantified the contributions of Rydberg and valence intermediate states to the photoionization product formation and evaluated coupling strengths for state mixing. Time-dependent density functional theory (TD-DFT), equation-of-motion coupled cluster (EOM-CC), and completely renormalized EOM-CC calculations with various basis sets were performed to derive singlet state potential energy curves, relevant spectroscopic parameters, and to calculate spectra. Experimentally observed spectra and older calculations are compared with the reported ab initio results.

On generation of dark solitons by gravitational waves in a strongly magnetized pulsar plasma

In this paper, the propagation of gravitational wave perpendicular to a superstrong magnetic field immersed in an electron-positron pulsar plasma is considered. On the basis of the Einstein–Maxwell system of magnetohydrodynamic equations, both the linear and nonlinear interactions of the wave with plasma are investigated. In near-resonant interaction, a relation between gravitation perturbations to electromagnetic field perturbations shows that the field perturbations are directly proportional to the product of ambient magnetic field and the gravitational wave perturbation. Thus, a weak gravitational wave may resonate an effective field perturbation in the strongly magnetized plasma in an astrophysical context. A coupled system of equations describing the nonlinear interaction between gravitational wave and field perturbations in the magnetized plasma is obtained. The equations are solved in resonant approximation, and it is found that a linearly polarized electric field is generated with a frequency close to the plasma frequency. For nonresonant interaction, the solution shows that both electric and magnetic field perturbations in the plasma are produced. Density perturbation and field intensity variation in the plasma lead to a nonlinear frequency shift and the slowly varying field amplitude obeys the nonlinear Schrödinger equation. The solution of the equation is the dark soliton, the amplitude of which may be very significant in the case of a superstrong magnetic field in the pulsar plasma.

On the formation of geophysical and planetary zonal flows by near-resonant wave interactions

Numerical simulations on a β-plane are used to further understand the formation of zonal flows from small-scale fluctuations. The dynamics of ‘reduced models’ are computed by restricting the nonlinear term to include a subset of triad interactions in Fourier space. Reduced models of near-resonant triads are considered, as well as the complement set of non-resonant triads. At moderately small values of the Rhines number, near-resonant triad interactions are shown to be responsible for the generation of large-scale zonal flows from small-scale random forcing. Without large-scale drag, both the full system and the reduced model of near resonances produce asymmetry between eastward and westward jets, in favour of stronger westward jets. When large-scale drag is included, the long-time asymmetry is reversed in the full system, with eastward jets that are thinner and stronger than westward jets. Then the reduced model of near resonances exhibits a weaker asymmetry, but there are nevertheless more eastward jets stronger than a threshold value.

Role of non-resonant interactions in the evolution of nonlinear random water wave fields

We present the results of direct numerical simulations (DNS) of the evolution of nonlinear random water wave fields. The aim of the work is to validate the hypotheses underlying the statistical theory of nonlinear dispersive waves and to clarify the role of exactly resonant, nearly resonant and non-resonant wave interactions. These basic questions are addressed by examining relatively simple wave systems consisting of a finite number of wave packets localized in Fourier space. For simulation of the long-term evolution of random water wave fields we employ an efficient DNS approach based on the integrodifferential Zakharov equation. The non-resonant cubic terms in the Hamiltonian are excluded by the canonical transformation. The proposed approach does not use a regular grid of harmonics in Fourier space. Instead, wave packets are represented by clusters of discrete Fourier harmonics. The simulations demonstrate the key importance of near-resonant interactions for the nonlinear evolution of statistical characteristics of wave fields, and show that simulations taking account of only exactly resonant interactions lead to physically meaningless results. Moreover, exact resonances can be excluded without a noticeable effect on the field evolution, provided that near-resonant interactions are retained. The field evolution is shown to be robust with respect to the details of the account taken of near-resonant interactions. For a wave system initially far from equilibrium, or driven out of equilibrium by an abrupt change of external forcing, the evolution occurs on the 'dynamical' time scale, that is with quadratic dependence on nonlinearity s, not on the O(e -4 ) time scale predicted by the standard statistical theory. However, if a wave system is initially close to equilibrium and evolves slowly in the presence of an appropriate forcing, this evolution is in quantitative accordance with the predictions of the kinetic equation. We suggest a modified version of the kinetic equation able to describe all stages of evolution. Although the dynamic time scale of quintet interactions e -3 is smaller than the kinetic time scale e -4 , they are not included in the existing statistical theory, and their effect on the evolution of wave spectra is unknown. We show that these interactions can significantly affect the spectrum evolution, although on a time scale much larger than O(e -4 ). However, for waves of high but still realistic steepness s ∼0.25, the scales of evolution are no longer separated. By tracing the evolution of high statistical moments of the wave field, we directly verify one of the main assumptions used in the derivation of the kinetic equation: the quasi-Gaussianity of the wave holds throughout the evolution, both with and without accounting for quintet interactions. The conclusions are not confined to water waves and are applicable to a generic weakly nonlinear dispersive wave field with prohibited triad interactions.

Controlling polar molecules in optical lattices

We investigate theoretically the interaction of polar molecules with optical lattices and microwave fields. We demonstrate the existence of frequency windows in the optical domain where the complex internal structure of the molecule does not influence the trapping potential of the lattice. In such frequency windows the Franck-Condon factors are so small that near-resonant interaction of vibrational levels of the molecule with the lattice fields have a negligible contribution to the polarizability and light-induced decoherences are kept to a minimum. In addition, we show that microwave fields can induce a tunable dipole-dipole interaction between ground-state rotationally symmetric (J=0) molecules. A combination of a carefully chosen lattice frequency and microwave-controlled interaction between molecules will enable trapping of polar molecules in a lattice and possibly realize molecular quantum logic gates. Our results are based on ab initio relativistic electronic structure calculations of the polar KRb and RbCs molecules combined with calculations of their rovibrational motion.

Inverse Energy Transfer by Near-Resonant Interactions with a Damped-Wave Spectrum

The interaction of long-wavelength anisotropic drift waves with the plasma turbulence of electron density advection is shown to produce the inverse energy transfer that condenses onto zonal modes, despite the expectation of forward transfer on the basis of nonconservation of enstrophy. Wave triads with an unstable wave and two waves of a separate, damped spectrum carry the transfer, provided they satisfy a near-resonance condition dependent on turbulence level and wave number.