Momentum Matching Research Articles

Momentum matching in the tunneling between 2-dimensional and 0-dimensional electron systems

We investigate the tunneling rates from a 2-dimensional electron gas (2DEG) into the ground state of self-assembled InGaAs quantum dots. These rates are strongly affected by a magnetic field perpendicular to the tunneling direction. Surprisingly, we find an increase in the rates for fields up to 4 T before they decrease again. This can be explained by a mismatch between the characteristic momentum of the quantum dot ground state and the Fermi momentum kF of the 2DEG. Calculations of the tunneling probability can account for the experimental data and allow us to determine the dot geometry as well as kF.

Intermediate-energy inverse-kinematics one-proton pickup reactions on neutron-deficientfp-shell nuclei

Background: Thick-target-induced nucleon-adding transfer reactions onto energetic rare-isotope beams are an emerging spectroscopic tool. Their sensitivity to single-particle structure complements one-nucleon removal reaction capabilities in the quest to reveal the evolution of nuclear shell structure in very exotic nuclei. Purpose: To add intermediate-energy, carbon-target-induced one-proton pickup reactions to the arsenal of $\gamma$-ray tagged direct reactions applicable in the regime of low beam intensities and to apply these for the first time to $fp$-shell nuclei. Methods: Inclusive and partial cross sections were measured for the $\nuc{12}{C}(\nuc{48}{Cr},\nuc{49}{Mn}+\gamma)$X and $\nuc{12}{C}(\nuc{50}{Fe},\nuc{51}{Co}+\gamma)$X proton pickup reactions at 56.7 and 61.2 MeV/nucleon, respectively, using coincident particle-$\gamma$ spectroscopy at the NSCL. The results are compared to reaction theory calculations using $fp$-shell-model nuclear structure input. For comparison with our previous work, the same reactions were measured on \nuc{9}{Be} targets. Results: The measured partial cross sections confirm the specific population pattern predicted by theory, with pickup into high-$\ell$ orbitals being strongly favored; driven by linear and angular momentum matching. Conclusion: Carbon target-induced pickup reactions are well-suited, in the regime of modest beam intensity, to study the evolution of nuclear structure, with specific sensitivities that are well described by theory.

Double Ionization and Coulomb Explosion of the Formic Acid Dimer by Intense Near-Infrared Femtosecond Laser Pulses

Ionization and fragmentation of formic acid dimers (HCOOH)(2) and (DCOOD)(2) by irradiation of femtosecond laser pulses (100 fs, 800 nm, ~1 × 10(14) W/cm(2)) were investigated by time-of-flight (TOF) mass spectrometry. In the TOF spectra, we observed fragment ions (HCOOH)H(+), (HCOOH)HCOO(+), and H(3)O(+), which were produced via the dissociative ionization of (HCOOH)(2). In addition, we found that the TOF signals of COO(+), HCOO(+), and HCOOH(+) have small but clear side peaks, indicating fragmentation with large kinetic energy release caused by Coulomb explosion. On the basis of the momentum matching among pairs of the side peaks, a Coulomb explosion pathway of the dimer dication, (HCOOH)(2)(2+) → HCOOH(+) + HCOOH(+), was identified with the total kinetic energy release of 3.6 eV. Quantum chemical calculations for energies of (HCOOH)(2)(2+) were also performed, and the kinetic energy release of the metastable dication was estimated to be 3.40 eV, showing good agreement with the observation. COO(+) and HCOO(+) signals with kinetic energies of 1.4 eV were tentatively assigned to be fragment ions through Coulomb explosion occurring after the elimination of a hydrogen atom or molecule from (HCOOH)(2)(2+). The present observation demonstrated that the formic acid dimer could be doubly ionized prior to hydrogen bond breaking by intense femtosecond laser fields.

Conductance through Multilayer Graphene Films

The ballistic conductance through junctions between multilayer graphene films and several different metals is studied using ab initio calculations within the local density approximation. The system consists of films of up to four graphene layers (Bernal stacking) between metallic electrodes, assuming reasonable metal-graphene epitaxial relationships. For some metals, the conductance decays exponentially with increasing number of layers, while for others the conductance saturates with film thickness. This difference in asymptotic behavior stems from the crystal momentum (mis)match between the bulk Fermi-level states in the electrode and those in the film. In contrast, for sufficiently thin films the bonding between the metal and the adjacent graphene layer dominates, giving a metal dependence for graphene similar to that seen experimentally for single-wall carbon nanotubes. Among the metals considered here, we find Pd to be the best for electrodes to films with up to 4 graphene layers.

Spectral analysis of enhanced third harmonic generation from plasmonic excitations

We experimentally achieved enhanced third harmonic generation (THG) from hole-array in gold film. The surface plasmon polarition excitations, considered as the major contribution to this THG enhancement, are elaborately studied by a spectrum-resolved femto-second laser system. The momentum matching conditions between the fundamental and harmonic waves are well established, giving results of a series of clear THG beam spots with respect to different excitation wavelengths. This efficient THG beaming from the pure metallic structure would considerably broaden the research in the field of nonlinear plasmonics.

Modifying an Infrared Microscope To Characterize Propagating Surface Plasmon Polariton-Mediated Resonances

Metal films with periodic arrays of subwavelength holes (meshes) show extraordinary transmission resonances using ordinary, benchtop Fourier transform infrared (FTIR) spectrometers. However, the infrared study of single, wavelength-scale particles with an FTIR microscope typically involves an instrument with a large range of angles that will disperse surface plasmon polariton (SPP) resonances. This work shows how to add an aperture and mesh to a commercial FTIR microscope system to obtain well-defined and identifiable SPP transmission-mediated resonances using a dispersion geometry that is convenient to a microscope, that is, rotation of the mesh in the focal plane of the microscope about the microscope’s optical axis. Momentum matching equations are derived that identify the resonances and model the measured dispersion of each resonance. These equations effectively model the data and cover the parts of momentum space that fall between better-known, high symmetry geometric arrangements, which are often called ΓX and ΓM in the reciprocal space of a square lattice. Both a region of extensive overlapping of many resonances and a very narrow and isolated resonance were discovered that may be particularly useful for SPP studies.

Effects of the intermediate SiO2 layer on polarized output of a light-emitting diode with surface plasmon coupling

The variation behaviors of the output intensity and polarization ratio of InGaN/GaN quantum well (QW) light-emitting diodes (LEDs) with surface plasmon (SP) coupling by inserting SiO2 intermediate layers between the p-GaN layers and surface Ag grating structures are demonstrated. The insertion of the SiO2 layer is expected to reduce the metal dissipation of SP energy and extend the near-field distribution range of the induced SP for generating more favored SP-QW coupling effects. The Ag grating period for optimizing SP-QW coupling is increased when a SiO2 layer is added to the device, which is consistent with the simulation results of the momentum matching of SP polariton and the resonance behavior of localized SP. The almost unpolarized outputs from other LED samples fabricated with an epitaxial structure of thicker p-GaN layer, which leads to weak SP-QW coupling, indicate that the observed polarization ratios are due to near-field SP-QW coupling, instead of far-field diffraction.

Photodissociation of heptane isomers and relative ionization efficiencies of butyl and propyl radicals at 157 nm

We report an ion imaging and time-of-flight mass spectroscopy study of the photodissociation of a variety of heptane isomers using 157 nm dissociation and ionization. Time-of-flight mass spectra show that C(3)H(7) + C(4)H(9) is the dominant detected product channel following one-color 157 nm dissociation/ionization of heptanes. The results further allow determination of the relative ionization efficiencies of 1- and 2-butyl and propyl radicals at 157 nm. Momentum matching for the two radical products indicates that, for the C3-C4 products, neutral dissociation followed by ionization is the main source of the detected signals. The images show isotropic angular distributions and the translational energy distributions peak at very low energy, with only approximately 0.3 eV or 8% of the available energy appearing in translation. This is consistent with dissociation from the ground state or low-lying triplet states following non-radiative electronic relaxation.

Surface Plasmon Resonance Enhanced Transmission of Light through Gold-Coated Diffraction Gratings

Narrow peaks are observed in the transmission spectra of p-polarized light passing through a thin gold film that is coated on the surface of a transparent diffraction grating. The spectral position and intensity of these peaks can be tuned over a wide range of wavelengths by simple rotation of the grating. The wavelengths where these transmission peaks are observed correspond to conditions where surface plasmon resonance occurs at the gold-air interface. Light diffracted by the grating couples with surface plasmons in the metal film to satisfy the resonant condition, resulting in enhanced light transmission through the film. Notably, this phenomenon is not observed at flat, gold-coated surfaces or uncoated gratings, where coupling to surface plasmons does not occur. The nature of the coupling and, thus, the details of light transmission are governed by the momentum matching conditions between the diffracted light and the surface plasmons. In the presence of bound analytes or surface films, the enhanced transmission peaks are red-shifted, making a simple, yet highly responsive sensing platform. The utility of this platform is demonstrated for ex situ sensing by analyzing thin films of various thicknesses and detecting a model immunoreaction between bovine serum albumin and anti-bovine serum albumin. This grating-based transmission surface plasmonic device represents a simple and sensitive platform, which can be readily tuned to enhance performance and be used in the study of a variety of surface adsorption processes or analysis of biomolecular interactions.

Temperature dependence of the surface plasmon coupling with an InGaN∕GaN quantum well

The authors demonstrate the temperature-dependent behavior of the surface plasmon (SP) coupling with two InGaN∕GaN quantum-well (QW) structures of different internal quantum efficiencies. The SP modes are generated at the interface between the QW structures and Ag thin films coated on their tops. It is observed that the SP-QW coupling rate increases with temperature. Such a trend may rely on several factors, including the availability of carriers with sufficient momenta for transferring the energy and momentum into the SP modes and possibly the variation of the SP density of state with temperature. Although the required momentum matching condition only needs the thermal energy corresponding to a few tens of Kelvins, the carrier delocalization process results in a significantly higher probability of SP-carrier momentum matching and hence SP-QW coupling.

Apex-enhanced second-harmonic generation by using double-hole arrays in a gold film

The enhancement of second harmonic generation (SHG) from arrays of subwavelength double holes in a gold film is studied. Each overlapping double hole, which is created in a straightforward manner by approaching two individual holes, has apexes that are responsible for nanoscale focusing of the electric field. A 14 times enhancement of SHG is measured when compared to the circular hole shape. The angular dependence of the SHG is explained by momentum matching and by symmetry breaking required for SHG. By varying the periodicity of the arrays, the Bragg resonances are tuned and modify the SHG signal. The SHG is shown to be enhanced by a resonance at the second harmonic wavelength. The local enhancement of the electric field presented in this work shows that the double-hole structure is a good candidate for applications such as surface-enhanced Raman spectroscopy and nonlinear optics.

Photodissociation of Cyclobutyl Bromide at 234 nm Studied Using Velocity Map Imaging

This study investigates the 234 nm photodissociation dynamics of cyclobutyl bromide using a two-dimensional photofragment velocity imaging technique. The spin-orbit ground- and excited-state Br(2P) atoms are state-selectively detected via [2+1] resonance enhanced multiphoton ionization (REMPI), whereas the cyclobutyl radicals are ionized using 157 nm laser light. The Br(2P(3/2)) and the Br(2P(1/2)) atoms and their c-C4H7 radical cofragments evidence a single-peaked, Gaussian-shaped translational energy distribution ranging from approximately 14 to approximately 39 kcal/mol and angular distributions with significant parallel character. The Br(2P(1/2))/ Br(2P(3/2)) spin-orbit branching ratio is determined to be 0.11 +/- 0.07 by momentum match between the Br(2P) photofragments and the recoiling c-C4H7 fragments, assuming a uniform photoionization probability of the c-C4H7 radicals with an internal energy range of 10-35 kcal/mol. The REMPI line strength ratio for the detection of Br(2P(3/2)) and Br(2P(1/2)) atoms at 233.681 and 234.021 nm, respectively, is therefore derived to be 0.10 +/- 0.07. The measured recoil kinetic energies of the c-C4H7 radicals, and the resulting distribution of internal energies, indicates some of the radicals are formed with total internal energies above the barrier to isomerization and subsequent dissociation, but our analysis indicates they may be stable due to the substantial fraction of the internal energy which is partitioned to rotational energy of the radicals.

Dispersion Study of the Infrared Transmission Resonances of Freestanding Ni Microarrays

Nickel films (several-micrometer thickness, with 5.2-μm square holes in a square lattice array with 12.7-μm hole-to-hole spacing) exhibit Ebbesen's extraordinary transmission effect in the infrared; that is, they transmit a higher fraction of incident infrared light than the fractional open area of the holes. The role of surface plasmons (SPs) in this phenomenon is much debated, so we have obtained a data set whereby this idea and others can be tested against empirically determined dispersion curves. Unpolarized, zero-order transmission spectra have been recorded by rotating the mesh (from −2° to 60° in 1° steps) relative to the spectrometer's incident beam about an axis along the mesh's nearest hole-to-hole spacing in order to create the dispersion diagram. The data are numerically analyzed for peak centers that are then projected outside of the light line (by SP momentum matching equations) to two SP dispersion curves that are spaced in frequency by a splitting. With this caveat, all of the observed structure is accounted for by a simple SP model.

Velocity Imaging Studies on Ion-Pair Dissociation of CH3Br + hνVUV → CH3+ + Br- as a Function of Wavelength

The ion-pair dissociation dynamics of CH3Br + hνVUV → CH3+ + Br- as a function of vacuum ultraviolet (VUV) wavelength have been studied by means of velocity imaging. Photofragment excitation (PHOFEX) spectra as well as images for both the cation and the anion products have been collected, which confirm the dissociation occurs through the ion-pair channel from the momentum matching of both products. The wavelength region for the PHOFEX covers a small portion (from 121.4 to 122.7 nm) of the absorption spectrum where transitions from the ground state to both ns and np Rydberg states as well as to the underlying continuum states are all present. Images were taken at selected wavelengths both on the peaks and in the valleys of the PHOFEX spectrum, as well as at 118.22 nm. The PHOFEX spectra closely resemble the absorption spectra of CH3Br, and the images taken at peaks and continuum wavelengths in PHOFEX show no marked differences with respect to the product energy and angular distributions. These observations prompt us to conclude that the ion-pair state is directly populated by the VUV photons and the ion-pair dissociation is one of the major exit channels for the excited states in the energy region just below the ionization energy of the parent molecule, although large uncertainties in wavelength in the absorption spectra make the proposed mechanisms less conclusive.

High spin two-neutron-hole states via the208Pb(p,t)206Pbreaction at 120 MeV

Cross sections and analyzing powers were obtained for the reaction ${}^{208}\mathrm{Pb}(p,t){ }^{206}\mathrm{Pb}$ at ${T}_{p}=120\mathrm{MeV},$ up to an excitation energy of 6.5 MeV, and with an energy resolution of 25--40 keV. Momentum matching considerations strongly favor the population of two-neutron-hole states with $J>~6.$ Making use of cross section and analyzing power angular distributions, 14 natural parity states were identified with $J=6$ to 12, including all of the states with $J>~9$ expected in the $N=5$ shell model space. The data were analyzed using the local zero-range distorted-wave Born approximation. Theory was normalized to experiment by making use of the sum rules for two-nucleon transfer reactions. Enhancement factors (ratio of experiment to normalized theory) were obtained, both for single, pure-configuration, and mixed configuration two-particle amplitudes from the shell model calculations of Kuo and Herling. Some of the details of the observed distribution of strengths were better accounted for by the shell model calculations, but, overall, the pure-configuration assumption accounted for the enhancement factors and energies about as well.

Ring opening dissociation of d6-benzene

The photodissociation of jet-cooled d6-benzene at 193 nm was studied. Photofragment translational energy distributions were measured by multimass ion imaging techniques. In addition to the major channel of D atom elimination from one-photon excitation, elimination of two D atoms and two ring opening dissociation channels, C6D6→CD3+C5D3 and C6D6→C2D3+C4D3, resulting from two-photon dissociation was observed. These ring opening channels were confirmed by the momentum match between the two fragments in each channel.

Coulomb explosion dynamics of N 2 in intense laser field by mass-resolved momentum imaging

The Coulomb explosion reactions of N 2, N 2 ( p+ q)+ → N p+ +N q+ , caused by the irradiation of intense laser light (0.73–6.9 PW/cm 2) were investigated by high-resolution time-of-flight (TOF) mass spectroscopy and by the mass-resolved two-dimensional momentum imaging (MRMI) method. Six explosion pathways ( p, q)=(1, 1), (1, 2), (1, 3), (2, 2), (2, 3) and (3, 3) in addition to (0, 1), (0, 2) dissociation pathways were identified, whose assignments were securely performed both from the momentum matching between the fragment pair and their correlation with the laser-field intensity dependence. The MRMI method, which visualizes the radial and angular momentum distributions of mass-selected fragment ions on a two-dimensional momentum plane, was used to correlate ion fragments produced after the Coulomb explosion. By examining theoretically synthesized MRMI maps, it was found that the momentum distributions of the fragment ions in a wide momentum range can be extracted by the MRMI technique. The relative yields of the explosion pathways at six different laser-field intensities were evaluated from the three-dimensional integration of the MRMI maps, and the intensity dependence of the formation of singly and multiply charged parent N 2 ( p+ q)+ ions prior to the fragmentation was derived.

Universal crossed molecular beams apparatus with synchrotron photoionization mass spectrometric product detection

Vacuum ultraviolet radiation was generated from an undulator at the Advanced Light Source Synchrotron facility and used for photoionization detection of reaction products in a new universal crossed molecular beams machine. A description of the machine and its performance is presented. Initial experiments on the photodissociation of methylamine (CH3 NH2), ozone (O3), oxalyl chloride [ (OCCl)2] as well as the reactive scattering of Cl with C3 H8 show many of the advantages of photoionization in comparison to electron impact ionization, which has been exclusively used in such instruments in the past. “Momentum matching” of reaction products is much more easily accomplished than in electron impact studies due to suppression of dissociative ionization. The tunability of the vacuum ultraviolet radiation can be used to suppress background from residual gases especially when it is desired to detect free radical reaction products. Even when the tunability cannot be used to suppress background, the fact that little heat is generated by the ionizing beam allows background to be substantially suppressed by cryogenic pumping. The energy resolution of the apparatus is comparable to instruments that have previously been designed with electron impact ionization which have more than twice as long a flight path. This new instrument provides outstanding performance for fundamental studies of chemical dynamics.

Photoluminescence from dye molecules on silver gratings

Excited dye molecules on metallic gratings can relax by generating surface plasmon polaritons (SPPs). These non-radiative modes can scatter from the grating emitting light in well-defined direction and with a characteristic polarisation. This paper presents an experimental study of the emission properties of a thin layer of laser dye on a silver grating. It is found that the emission is dominated by light re-radiated by SPPs. The direction and the polarisation of the emission are found to depend on the azimuthal angle between the emitted light and the grating grooves. The experimental results are explained in terms of the momentum matching conditions that govern the coupling between photons and SPPs.

Current-current operator evolution in the chiral limit

We consider the strong interaction corrections to current-current hadronic operators in the chiral limit. High-momentum contributions are computed in perturbative QCD with massless quarks while low-momentum contributions are estimated in a truncated non-linear σ-model for massless pseudoscalars. In the large- N approximation, the ambiguity on the momentum matching around the confining scale is removed by using the effective color-singlet gauge boson exchanged between the two currents as a universal probe.