Long-lived Resonances Research Articles

High‐harmonic generation with plasmonics: feasible or unphysical?

High-harmonic generation (HHG) provides for efficient and coherent XUV generation for a wide range of spectroscopic applications, enabling attosecond spectroscopy, ultrafast photo-emission spectroscopy, or ultrahigh spatial resolution imaging [1]. Conventionally HHG is based on the use of high power amplified femtosecond laser pulses, special phase matching techniques, or intra-cavity field enhancement. As a compelling alternative, resonant plasmonic field enhancement in metallic nanostructures has been proposed to achieve the necessary peak intensity for HHG. Using nJ pulses from a Ti:S oscillator, XUV generation attributed to plasmon-enhanced HHG was reported in 2008 by the group of Seung-Woo Kim from KAIST in Daejeon, Korea, first in Ar [2] and later

Long-Lived Scattering Resonances and Bragg Structures

We consider a system governed by the wave equation with index of refraction $n({\bf x})$, taken to be variable within a bounded region $\Omega\subset \mathbb R^d$ and constant in $\mathbb R^d \setminus \Omega$. The solution of the time-dependent wave equation with initial data, which is localized in $\Omega$, spreads and decays with advancing time. This rate of decay can be measured (for $d=1,3$, and more generally, $d$ odd) in terms of the eigenvalues of the scattering resonance problem, a non--self-adjoint eigenvalue problem governing the time-harmonic solutions of the wave (Helmholtz) equation which are outgoing at $\infty$. Specifically, the rate of energy escape from $\Omega$ is governed by the complex scattering eigenfrequency, which is closest to the real axis. We study the structural design problem: Find a refractive index profile $n_\star({\bf x})$ within an admissible class which has a scattering frequency with minimal imaginary part. The admissible class is defined in terms of the compact support of $n({\bf x})-1$ and pointwise upper and lower (material) bounds on $n({\bf x})$ for ${\bf x} \in \Omega$, i.e., $0 < n_- \le n({\bf x}) \le n_+ < \infty$. We formulate this problem as a constrained optimization problem and prove that an optimal structure, $n_\star({\bf x})$, exists. Furthermore, $n_\star({\bf x})$ is piecewise constant and achieves the material bounds, i.e., $n_\star({\bf x})\in\{n_-, n_+ \} $. In one dimension, we establish a connection between $n_\star(x)$ and the well-known class of Bragg structures, where $n(x)$ is constant on intervals whose length is one quarter of the effective wavelength.

Resonant regimes in the Fock-space coherence of multilevel quantum dots

The coherence between quantum states with different particle numbers --- the Fock-space coherence --- qualitatively differs from the more common Hilbert-space coherence between states with equal particle numbers. For a quantum dot with multiple channels available for transport, we find the conditions for decoupling the dynamics of the Fock-space coherence from both the Hilbert-space coherence as well as the population dynamics. We further find specific energy and coupling regimes where a long-lived resonance in the Fock-space coherence of the system is realized, even where no resonances are found either in the populations or Hilbert-space coherence. Numerical calculations show this resonance remains robust in the presence of both boson-mediated relaxation and transport through the quantum dot.

Channeling Chaotic Rays into Waveguides for Efficient Collection of Microcavity Emission

We demonstrate a robust and generic mechanism, which we term "chaos-assisted channeling," to achieve unidirectional output from wave-chaotic microcavities with long-lived resonances. It utilizes the coexistence of regular and chaotic ray dynamics in most deformed microcavities. Long-lived resonances are formed by total internal reflection on classical periodic orbits, and their leakage into the chaotic region of the phase space is efficiently channeled into an attached waveguide without additional loss. We explain this behavior using a ray dynamics analysis which is confirmed via numerical simulations and experimental demonstration.

State-resolved spectroscopy of high vibrational levels of water up to the dissociative continuum

We summarize here our experimental studies of the high rovibrational energy levels of water. The use of double-resonance vibrational overtone excitation followed by energy-selective photofragmentation and laser-induced fluorescence detection of OH fragments allowed us to measure previously inaccessible rovibrational energies above the seventh OH-stretch overtone. Extension of the experimental approach to triple-resonance excitation provides access to rovibrational levels via transitions with significant transition dipole moments (mainly OH-stretch overtones) up to the dissociation threshold of the O-H bond. A collisionally assisted excitation scheme enables us to probe vibrations that are not readily accessible via pure laser excitation. Observation of the continuous absorption onset yields a precise value for the O-H bond dissociation threshold, 41 145.94 ± 0.15 cm(-1). Finally, we detect long-lived resonances as sharp peaks in spectra above the dissociation threshold.

State-to-state photodissociation dynamics of triatomic molecules: H2O in the B band

State-to-state photodissociation dynamics of H(2)O in its B band has been investigated quantum mechanically on a new set of non-adiabatically coupled potential energy surfaces for the lowest two (1)A' states of H(2)O, which are developed at the internally contracted multi-reference configuration interaction level with the aug-cc-pVQZ basis set. Quantum dynamical calculations carried out using the Chebyshev propagator yield absorption spectra, product state distributions, branching ratios, and differential cross sections, which are in reasonably good agreement with the latest experimental results. Particular focus is placed here on the dependence of various dynamical observables on the photon energy. Detailed analyses of the dynamics have assigned the diffuse structure in absorption spectrum to short-time recurring dynamics near the HOH conical intersection. The non-adiabatic dissociation to the ground state OH product via the HOH conical intersection is facile, direct, fast, and produces rotationally hot OH(X̃) products. On the other hand, the adiabatic channel on the excited state leading to the OH(Ã) product is dominated by long-lived resonances, which depend sensitively on the potential energy surfaces.

On relativistic shifts of negative-ion resonances

Results from a Dirac approach to electron- (neutral) atom resonance calculations are compared with those from nonrelativistic ones. A recently developed amplitude-phase method for the Dirac equations that is valid also in the non-relativistic limit is applied. The main conclusion is that significant energy differences are expected for long-lived resonances.

Toward a microscopic reaction description based on energy-density-functional structure models

A microscopic calculation of reaction cross sections for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all particle-hole excitations in the target and one-nucleon pickup channels. The particle-hole states may be regarded as doorway states through which the flux flows to more complicated configurations, and subsequently to long-lived compound nucleus resonances. Target excitations for ${}^{40,48}$Ca, ${}^{58}$Ni, ${}^{90}$Zr, and ${}^{144}$Sm were described in a random-phase framework using a Skyrme functional. Reaction cross sections obtained agree very well with experimental data and predictions of a state-of-the-art fitted optical potential. Couplings between inelastic states were found to be negligible, while the pickup channels contribute significantly. The effect of resonances from higher-order channels was assessed. Elastic angular distributions were also calculated within the same method, achieving good agreement with experimental data. Observed absorptions are completely accounted for by explicit channel coupling, for incident energies between 10 and 70 MeV, with consistent angular distribution results.

Spectral behavior of contractive noise

We study the behavior of the spectra corresponding to quantum systems subjected to a contractive noise, i.e., the environment reduces the accessible phase space of the system, but the total probability is conserved. We find that the number of long-lived resonances grows as a power law in h, but surprisingly there is no relationship between the exponent of this power law and the fractal dimension of the corresponding classical attractor. This is in disagreement with the predictions of the fractal Weyl law which has been established for open systems, where the probability is lost under the effect of a projective opening.

Pion-proton correlations and asymmetry measurement in Au + Au collisions at √s NN = 200 GeV data

Correlations between non-identical particles at small relative velocity probe asymmetries in the average space-time emission points at freeze-out. The origin of such asymmetries may be from long-lived resonances, bulk collective effects, or differences in the freeze-out scenario for the different particle species. STAR has extracted pion-proton correlation functions from a dataset of Au+Au collisions at √sNN = 200 GeV. We present correlation functions in the spherical harmonic decomposition representation, for different centralities and for different combinations of pions and (anti-)protons.

Spectral problems in open quantum chaos

We present an overview of mathematical results and methods relevant for the spectral study of semiclassical Schrödinger (or wave) operators of scattering systems, in cases where the corresponding classical dynamics is chaotic; more precisely, we assume that in some energy range, the classical Hamiltonian flow admits a fractal set of trapped trajectories, which hosts chaotic (hyperbolic) dynamics. The aim is then to connect the information on this trapped set with the distribution of quantum resonances in the semiclassical limit.Our study encompasses several models sharing these dynamical characteristics: free motion outside a union of convex hard obstacles, scattering by certain families of compactly supported potentials, geometric scattering on manifolds with (constant or variable) negative curvature. We also consider the toy model of open quantum maps, and sketch the construction of quantum monodromy operators associated with a Poincaré section for a scattering flow.The semiclassical density of long-living resonances exhibits a fractal Weyl law, related to the fact that the corresponding metastable states are ‘supported’ by the fractal trapped set (and its outgoing tail). We also describe a classical condition for the presence of a gap in the resonance spectrum, equivalently a uniform lower bound on the quantum decay rates, and present a proof of this gap in a rather general situation, using quantum monodromy operators.

State-to-state quantum dynamics of the N(4S) + OH(X 2Π) → H(2S) + NO(X 2Π) reaction

Quantum state-to-state dynamics for the N((4)S) + OH(X( 2)Π) → H((2)S) + NO(X( 2)Π) reaction is reported on an accurate ab initio potential energy surface of the lowest triplet electronic state (a(3)A(")) of HNO∕HON. It was found that the reaction is dominated by long-lived resonances supported by the HNO and HON wells. Significant non-reactive scattering was observed, indicating substantial deviations from the statistical limit. Due to the large exothermicity of the reaction, the NO product has hot internal state distributions: its rotational state distribution is inverted and peaks near the highest accessible rotational level; and its vibrational state distribution extends to υ = 10 and decays monotonically with the vibrational quantum number. In particular, the predicted product vibrational distribution is in reasonably good agreement with experiment. The calculated differential cross section is dominated by scattering in both the forward and backward directions, consistent with the formation of reaction intermediates.

Reaction cross-section predictions for nucleon induced reactions

A microscopic calculation of the optical potential for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all the particle-hole (p-h) excitation states in the target and to all relevant pickup channels. These p-h states may be regarded as doorway states through which the flux flows to more complicated configurations, and to long-lived compound nucleus resonances. We calculated the reaction cross sections for the nucleon induced reactions on the targets 40,48Ca, 58Ni, 90Zr and 144Sm using the QRPA description of target excitations, coupling to all inelastic open channels, and coupling to all transfer channels corresponding to the formation of a deuteron. The results of such calculations were compared to predictions of a well-established optical potential and with experimental data, reaching very good agreement. The inclusion of couplings to pickup channels was an important contribution to the absorption. For the first time, calculations of excitations account for all of the observed reaction cross-sections, at least for incident energies above 10 MeV.

Nonadiabatic quantum dynamics of C(1D)+H2→CH+H: Coupled-channel calculations including Renner-Teller and Coriolis terms

The Renner-Teller (RT) coupled-channel dynamics for the C((1)D)+H(2)(X(1)Σ(g) (+))→CH(X(2)Π)+H((2)S) reaction has been investigated for the first time, considering the first two singlet states ã̃(1)A' and b(1)A'' of CH(2) dissociating into the products and RT couplings, evaluated through the ab initio matrix elements of the electronic angular momentum. We have obtained initial-state-resolved probabilities, cross sections and thermal rate constants via the real wavepacket method for both coupled electronic states. In contrast to the N((2)D)+H(2)(X(1)Σ(g)(+)) system, RT effects tend to reduce probabilities, cross sections, and rate constants in the low energy range compared to Born-Oppenheimer (BO) ones, due to the presence of a repulsive RT barrier in the effective potentials and to long-lived resonances. Furthermore, contrary to BO results, the rate constants have a positive temperature dependence in the 100-400 K range. The two-state RT rate constant at 300 K, lower than the BO one, remains inside the error bars of the experimental value.

Meson-baryon femtoscopy in Au+Au collisions at 200 GeV measured by STAR experiment

Correlations between non-identical particles at small relative velocity probe asymmetries in the average space-time emission points at freezeout [1]. Such asymmetries may arise from long-lived resonances, bulk collective effects, or differences in the freezeout scenario for the different particle species. STAR has extracted pion-proton correlation functions from a high-statistics dataset of Au+Au collisions at \(\sqrt {s_{NN} } \) = 200 GeV. We present a femtoscopic analysis of this data for all combinations of charged pions and (anti-) protons, for collisions of different centrality. The measurements are compared with calculations of a simple Blast-wave model, in which asymmetries are driven only by collective flow, as well as with Therminator [2], which also accounts fully for resonance effects.

Elastic scattering of slow electrons from Y, Ru, Pd, Ag and Pt atoms: search for nanocatalysts

Electron elastic scattering total cross sections (TCSs) for Y, Ru, Pd, Ag and Pt atoms are investigated in the electron impact energy range 0 ⩽ E ⩽ 7.0 eV. The complex angular momentum method that incorporates the electron–electron correlations and core-polarization interactions, crucial for the existence and stability of most negative ions, is used for the calculations. The TCSs for these atoms are found to be characterized by shape resonances (short-lived resonances), Ramsauer–Townsend minima and very sharp resonances (long-lived resonances) that correspond to the existence of stable bound states of the negative ions formed during the collision as Regge resonances. Using the configuration of the negative-ion resonances and Ramsauer–Townsend minima in the Au TCS as the benchmark for nanocatalysts, we conclude that the Y, Ru, Pd, Ag and Pt atoms represent excellent candidates for nanocatalysts individually or in various combinations. Calculated electron elastic TCSs for Y, Ru, Pd, Ag and Pt atoms are presented as illustrations.

Trace formula for a dielectric microdisk with a point scatterer

Two-dimensional dielectric microcavities are of widespread use in microoptics applications. Recently, a trace formula has been established for dielectric cavities which relates their resonance spectrum to the periodic rays inside the cavity. In this paper, we extend this trace formula to a dielectric disk with a small scatterer. This system has been introduced for microlaser applications, because it has long-lived resonances with strongly directional far field. We show that its resonance spectrum contains signatures not only of periodic rays but also of diffractive rays that occur in Keller's geometrical theory of diffraction. We compare our results with those for a closed cavity with Dirichlet boundary conditions.

Low-energy electron elastic collision cross sections for ground and excited Tm, Lu and Hf atoms

Low-energy 0 ⩽ E ⩽ 1.0 eV electron elastic scattering from ground and excited Tm, Lu and Hf atoms has been investigated. Both total and differential cross sections have been calculated; the latter at the scattering angles θ = 0°, 90° and 180°. The recent Regge-pole methodology has been used for the calculations. In the method the crucial electron–electron correlation effects are accounted for through the Mulholland formula. We find that the total cross sections are characterized generally by shape resonances, Ramsauer-Townsend minima and dramatically sharp long-lived resonances from which we extract the binding energies of the negative ions. Our extracted binding energy of the Hf − negative ion from the total cross section is compared with that of Pan and Beck [14].

Optimization of Optoelectronic Plasmonic Structures

We discuss the interplay between surface plasmon polaritons (SPPs) and localized shape resonances (LSRs) in a plasmonic structure working as a photo-coupler for a GaAs quantum well photodetector. For a targeted electronic inter-subband transition inside the quantum well, maximum photon absorption is found by compromising two effects: the mode overlapping with incident light and the lifetime of the resonant photons. Under the optimal conditions, the LSR mediates the coupling between the incident light and plasmonic structure while the SPP provides long-lived resonance which is limited ultimately by metal loss. The present work provides insight to the design of plasmonic photo-couplers in semiconductor optoelectronic applications.

Highly directional output from long-lived resonances in optical microcavity

We report a simple and robust mechanism that can result in highly directional emission from long-lived resonances in microcavities. By placing a nanoparticle (NP) into the evanescent wave region of microcavities, highly directional outputs with divergence angle ~1.9°-10° can be obtained in single or double directions. The perturbation of NP on evanescent waves preserves the high-quality (Q) factors, and the collimation of microcavities generates the highly directional outputs. Our numerical simulations show that this mechanism is very robust to the size of NP and the refractive index/separation distance/size of microcavities.