Electronic Angular Momentum Research Articles

Oriented O(3P2), Ne(3P2), and He(3S1) atoms emerging from a bent magnetic guide

ABSTRACTWe describe our observation of strongly oriented total electronic angular momentum J in O(3P2), Ne(3P2), and He(3S1) atoms emerging from a bent magnetic multipole guide, as measured by resonant multiphoton ionisation. This was contrary to our expectation because no additional (uniform) magnetic fields were applied to orient the atoms behind the exit of the guide. Two- and three-photon ionisation techniques were employed to determine the degree of J polarisation, from which we infer that atoms become oriented as a result of a combination of weak fringe fields, possible stray fields, and the fact that molecular beam packets do not oscillate around the geometric center of the bent multipole guide. We conclude that similar effects may exist in other, related experiments and that a detailed characterisation of the degree of orientation is required prior to any study of chemical dynamics or spectroscopy. This paper should serve as a warning for anybody using similar devices not to assume isotropic angular momentum distributions of atoms and molecules emerging from a magnetic guide or a decelerator, particularly when it is bent; whenever possible, the possibility for a J anisotropy should be experimentally checked.

Mid-infrared signatures of hydroxyl containing water clusters: Infrared laser Stark spectroscopy of OH-H2O and OH(D2O)n (n = 1-3).

Small water clusters containing a single hydroxyl radical are synthesized in liquid helium droplets. The OH-H2O and OH(D2O)n clusters (n = 1-3) are probed with infrared laser spectroscopy in the vicinity of the hydroxyl radical OH stretch vibration. Experimental band origins are qualitatively consistent with ab initio calculations of the global minimum structures; however, frequency shifts from isolated OH are significantly over-predicted by both B3LYP and MP2 methods. An effective Hamiltonian that accounts for partial quenching of electronic angular momentum is used to analyze Stark spectra of the OH-H2O and OH-D2O binary complexes, revealing a 3.70(5) D permanent electric dipole moment. Computations of the dipole moment are in good agreement with experiment when large-amplitude vibrational averaging is taken into account. Polarization spectroscopy is employed to characterize two vibrational bands assigned to OH(D2O)2, revealing two nearly isoenergetic cyclic isomers that differ in the orientation of the non-hydrogen-bonded deuterium atoms relative to the plane of the three oxygen atoms. The dipole moments for these clusters are determined to be approximately 2.5 and 1.8 D for "up-up" and "up-down" structures, respectively. Hydroxyl stretching bands of larger clusters containing three or more D2O molecules are observed shifted approximately 300 cm(-1) to the red of the isolated OH radical. Pressure dependence studies and ab initio calculations imply the presence of multiple cyclic isomers of OH(D2O)3.

Electronic structure of alkali-metal/alkaline-earth-metal fluorine beryllium borate NaSr3Be3B3O9F4 single crystal: DFT approach

The electronic band structure, total and angular momentum resolved projected density of states for NaSr3Be3B3O9F4 are calculated using the all-electron full potential linearized augmented plane wave plus local orbitals (FP-LAPW+lo) method. The calculations are performed within four exchange correlations namely; local density approximation (LDA), general gradient approximation (PBE-GGA), Engel–Vosko generalized gradient approximation (EVGGA) and the recently modified Becke–Johnson potential (mBJ). Calculations suggest that NaSr3Be3B3O9F4 is a direct wide band gap semiconductor. The exchange correlations potentials exhibit significant influence on the value of the energy gap being about 4.82eV (LDA), 5.16eV (GGA), 6.20 (EVGGA) and 7.20eV (mBJ). The mBJ approach succeed by large amount in bringing the calculated energy gap closer to the experimental one (7.28eV). The angular momentum resolved projected density of states shows the existence of a strong hybridization between the various orbitals. In additional we have calculated the electronic charge density distribution in two crystallographic planes namely (101) and (00−1) to visualized the chemical bonding characters.

Quenching of dynamic nuclear polarization by spin–orbit coupling in GaAs quantum dots

The central-spin problem is a widely studied model of quantum decoherence. Dynamic nuclear polarization occurs in central-spin systems when electronic angular momentum is transferred to nuclear spins and is exploited in quantum information processing for coherent spin manipulation. However, the mechanisms limiting this process remain only partially understood. Here we show that spin–orbit coupling can quench dynamic nuclear polarization in a GaAs quantum dot, because spin conservation is violated in the electron–nuclear system, despite weak spin–orbit coupling in GaAs. Using Landau–Zener sweeps to measure static and dynamic properties of the electron spin–flip probability, we observe that the size of the spin–orbit and hyperfine interactions depends on the magnitude and direction of applied magnetic field. We find that dynamic nuclear polarization is quenched when the spin–orbit contribution exceeds the hyperfine, in agreement with a theoretical model. Our results shed light on the surprisingly strong effect of spin–orbit coupling in central-spin systems.

On the Stark effect in open shell complexes exhibiting partially quenched electronic angular momentum: Infrared laser Stark spectroscopy of OH–C2H2, OH–C2H4, and OH–H2O

The Stark effect is considered for polyatomic open shell complexes that exhibit partially quenched electronic angular momentum. Matrix elements of the Stark Hamiltonian represented in a parity conserving Hund’s case (a) basis are derived for the most general case, in which the permanent dipole moment has projections on all three inertial axes of the system. Transition intensities are derived, again for the most general case, in which the laser polarization has projections onto axes parallel and perpendicular to the Stark electric field, and the transition dipole moment vector is projected onto all three inertial axes in the molecular frame. Simulations derived from this model are compared to experimental rovibrational Stark spectra of OH–C2H2, OH–C2H4, and OH–H2O complexes formed in helium nanodroplets.

Berry curvature and orbital angular momentum of electrons in angle-resolved photoemission spectroscopy

Berry curvature and orbital angular momentum of electrons in angle-resolved photoemission spectroscopy

Developing a field independent frequency reference

We show that by averaging over transitions to multiple hyperfine levels, quadrupole shifts and dominant Zeeman effects exactly cancel whenever the nuclear spin, I, is at least as large as the total electronic angular momentum, J. The average frequency thus defines a frequency reference which is inherently independent of external magnetic fields and electric field gradients. We use to illustrate the method although the approach could be readily adapted to other atomic species. This approach practically eliminates the quadrupole and Zeeman shift considerations for many potential clock transitions.

Symmetry-breaking effects on spin and electronic transport in graphene

The decoration of graphene samples with adatoms or nanoparticles leads to the enhancement of spin-orbit interactions as well as to the introduction of symmetry-breaking effects that could have drastic effects on spin and electronic transport phenomena. We present an analysis based on symmetry considerations and examine the impact on the scattering matrix for graphene systems containing defects that enhance spin-orbit interactions, while conserving the electronic total angular momentum. We show that the appearance and dominance of skew scattering, and the related observation of valley and/or spin Hall effect in decorated graphene samples, suggests the set of symmetries that adatom perturbations should satisfy. We further show that detailed measurements of the transport and elastic times as a function of carrier concentration make it possible to not only extract the strength of the spin-orbit interaction, as suggested before, but also obtain the amplitude of the symmetry-breaking terms introduced. To examine how different terms would affect measurements, we also present calculations for typical random distributions of impurities with different perturbations, illustrating the detailed energy dependence of different observables

The calculated rovibronic spectrum of scandium hydride, ScH

The electronic structure of six low-lying electronic states of scandium hydride, X 1Σ+, a 3Δ, b 3Π, A 1Δ, c 3Σ+ and B 1Π, is studied using multi-reference configuration interaction as a function of bond length. Diagonal and off-diagonal dipole moment, spin–orbit coupling and electronic angular momentum curves are also computed. The results are benchmarked against experimental measurements and calculations on atomic scandium. The resulting curves are used to compute a line list of molecular rovibronic transitions for 45ScH.

Infrared rovibrational spectroscopy of OH-C2H2 in (4)He nanodroplets: Parity splitting due to partially quenched electronic angular momentum.

The T-shaped OH-C2H2 complex is formed in helium droplets via the sequential pick-up and solvation of the monomer fragments. Rovibrational spectra of the a-type OH stretch and b-type antisymmetric CH stretch vibrations contain resolved parity splitting that reveals the extent to which electronic angular momentum of the OH moiety is quenched upon complex formation. The energy difference between the spin-orbit coupled (2)B1 (A″) and (2)B2 (A') electronic states is determined spectroscopically to be 216 cm(-1) in helium droplets, which is 13 cm(-1) larger than in the gas phase [Marshall et al., J. Chem. Phys. 121, 5845 (2004)]. The effect of the helium is rationalized as a difference in the solvation free energies of the two electronic states. This interpretation is motivated by the separation between the Q(3/2) and R(3/2) transitions in the infrared spectrum of the helium-solvated (2)Π3/2 OH radical. Despite the expectation of a reduced rotational constant, the observed Q(3/2) to R(3/2) splitting is larger than in the gas phase by ≈0.3 cm(-1). This observation can be accounted for quantitatively by assuming the energetic separation between (2)Π3/2 and (2)Π1/2 manifolds is increased by ≈40 cm(-1) upon helium solvation.

Stern-Gerlach Experiments on Fe@Sn12: Magnetic Response of a Jahn–Teller Distorted Endohedrally Doped Molecular Cage Cluster

The magnetic response of the Fe@Sn12 cluster is investigated by magnetic beam deflection experiments. In contrast to Mn@Sn12, the molecular beam of this cluster is deflected almost exclusively toward increasing field, also at low temperatures, supposable due to Jahn–Teller induced distortions of the tin cage. The magnitude of the magnetic dipole moment is extracted from the shift of the beam profile and provides evidence for a (partially quenched) contribution of electronic orbital angular momentum to the magnetic dipole moment.

Calibration of Recoil-In-Vacuum attenuations from first principles: comparison with recent experimental data on Fe isotopes

Precession of aligned nuclear spin systems in ions recoiling from the target into vacuum (RIV) with consequent attenuation of angular distributions of emitted radiation is, in principle, a versatile method for measurement of g-factors of nuclear excited states of lifetimes in the pico-second range (Stone et al., Phys. Rev. Lett., 94, 192501, 2005 and Stuchbery and Stone, Phys. Rev. C, 76, 034307, 2007). Calibration of the observed attenuations has been achieved in favourable cases through comparison with measurements on states having previously known g-factors and lifetimes. The general lack of suitable states with known g-factors has limited application of the RIV method. This paper concerns the present status of efforts to describe the states of excited ions recoiling into vacuum in detail so that the average interaction can be estimated with useful precision from a-priori theory. The calculations use the GRASP2K package (Froese-Fischer et al. 1997 and Jonsson, Comp. Phys. Comm., 177, 597, 2007 & 184, 2197, 2013) to obtain, for each recoiling ion change state, the individual possible electronic states, their configurations, lifetimes and hyperfine interactions. It is assumed that all possible ionic states are produced, up to a chosen excitation energy. This energy is selected to approximate the energy at which all states have lifetimes far shorter than the nuclear state of interest. It is further assumed that the ionic state total electron angular momenta are randomly oriented in space. The first estimates of the average attenuation of emission distributions, as a function of the product g τ of the nuclear state g-factor and mean lifetime, used an averaged precession frequency obtained neglecting transitions between electronic states. Improved calculations, which include such transitions, are described.

Method for the production of highly charged ions with polarized nuclei and zero total electron angular momentum

The capture of polarized electrons by H-like ions provides a method for polarizing the nuclei of He-like heavy ions with zero total electron angular momentum in storage rings for high-energy ions. A detailed analysis for $_{63}^{151}\mathrm{Eu}$ ions with nuclear spin $I=5/2$ predicts a nuclear polarization degree of about $47%$ already after one passage through a target containing $100%$ polarized electrons. Almost $50%$ of the polarized He-like ions are predicted to be in states with zero total electron angular momentum. Such ions were recently considered as the most promising candidates in experiments at storage rings for the search for violations of the fundamental symmetries and for a nuclear and an electron electric dipole moment.

The effects of weak magnetic fields on radical pairs.

It is proposed that radical concentrations can be modified by combinations of weak, steady and alternating magnetic fields that modify the population distribution of the nuclear and electronic spin state, the energy levels and the alignment of the magnetic moments of the components of the radical pairs. In low external magnetic fields, the electronic and nuclear angular momentum vectors are coupled by internal forces that outweigh the external fields' interactions and are characterized in the Hamiltonian by the total quantum number F. Radical pairs form with their unpaired electrons in singlet (S) or triplet (T) states with respect to each other. At frequencies corresponding to the energy separation between the various states in the external magnetic fields, transitions can occur that change the populations of both electron and nuclear states. In addition, the coupling between the nuclei, nuclei and electrons, and Zeeman shifts in the electron and nuclear energy levels can lead to transitions with resonances spanning frequencies from a few Hertz into the megahertz region. For nuclear energy levels with narrow absorption line widths, this can lead to amplitude and frequency windows. Changes in the pair recombination rates can change radical concentrations and modify biological processes. The overall conclusion is that the application of magnetic fields at frequencies ranging from a few Hertz to microwaves at the absorption frequencies observed in electron and nuclear resonance spectroscopy for radicals can lead to changes in free radical concentrations and have the potential to lead to biologically significant changes.

Specific features of electronic structures and nonlinear optical susceptibilities of superhard metallic diamond-like t-B2CN compound

The geometry of diamond-like t-B2CN was relaxed by minimizing the forces acting on each atom using an all-electron full potential linearized augmented plane wave within general gradient approximation (PBE-GGA). Using the relaxed geometry, the electronic band structure's dispersion, total and angular momentum resolved projected density of states, anthropomorphic shape of Fermi surface, electronic charge density distribution, and linear and nonlinear optical responses were performed within the local density approximation (CA-LDA), PBE-GGA, Engel–Vosko generalized gradient approximation (EV-GGA) and the modified Becke–Johnson potential (mBJ). Calculations showed that t-B2CN is metallic with two bands overlapping around the Fermi level. The density of states at the Fermi level N(EF) and the electronic specific heat coefficient (γ) were obtained. The electronic charge density showed that there are only two type of bonds (B–C and B–N). The Fermi surface is formed by two bands; the shape of the Fermi surface consists of empty areas representing holes and shaded areas corresponding to electrons. The linear optical response confirmed that there exists a lossless region between 5.0 eV and 7.5 eV, and the existence of a considerable anisotropy favors enhanced phase matching conditions for the second harmonic generation (SHG). The nonlinear optical susceptibilities exhibited that χ(2)113(ω) is the dominant component, with values of about 5.5 pm V−1 at static limit and 8.8 pm V−1 at λ = 1064 nm. This suggests that the t-B2CN single crystal is a promising nonlinear crystal in comparison with the well-known KTiOPO4 nonlinear optical single crystal.

Muonic–electronic quasi molecules based on a fully stripped multicharged ion

In our previous paper (Can. J. Phys. 91, 715 (2013) doi: 10.1139/cjp-2013-0077 ) we studied a system consisting of a proton, a muon, and an electron; the muon and the electron being in circular states. The study was motivated by numerous applications of muonic atoms and molecules, where one of the electrons is substituted by the heavier lepton μ–. We demonstrated that in such a μpe quasi molecule, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem — a result that may seem counterintuitive. In other words, the muon rapidly revolves in a circular orbit about the axis connecting the proton and electron while this axis slowly rotates following a relatively slow electronic motion. We showed that the spectral lines, emitted by the muon in the quasi molecule, μpe, experience a red shift compared to the corresponding spectral lines that would have been emitted by the muon in a muonic hydrogen atom. In the present paper we generalize this study by replacing the proton in the μpe quasi molecule by a fully stripped ion of nuclear charge Z > 1. We show that in this case, just as in the previously studied case of Z = 1, the muonic motion can represent a rapid subsystem while the electronic motion can represent a slow subsystem. For this to be valid, the ratio of the muonic and electronic angular momenta should be slightly greater than in the case of Z = 1. We demonstrate that the binding energies of the muon for Z > 1 are much greater than for Z = 1 at any finite value of the nucleus–electron distance. Finally we show that the red shift of the spectral lines emitted by the muon (compared to the spectral lines of the corresponding muonic hydrogen-like ion of nuclear charge Z) decreases as Z increases. However, the relative red shift remains within the spectral resolution of available spectrometers at least up to Z = 5. Observing this red shift should be one of the ways to detect the formation of the quasi molecules, μZe.

Laser induced rovibrational cooling of the linear polyatomic ion C2H2(+).

The laser-induced blackbody-assisted rotational cooling of a linear polyatomic ion, C2H2(+), in its (2)Π ground electronic state in the presence of the blackbody radiation field at 300 K and 77 K is investigated theoretically using a rate-equations model. Although pure rotational transitions are forbidden in this non-polar species, the ν5 cis-bending mode is infrared active and the (1-0) band of this mode strongly overlaps the 300 K blackbody spectrum. Hence the lifetimes of state-selected rotational levels are found to be short compared to the typical timescale of ion trapping experiments. The ν5 (1-0) transition is split by the Renner-Teller coupling of vibrational and electronic angular momentum, and by the spin-orbit coupling, into six principal components and these effects are included in the calculations. In this paper, a rotational-cooling scheme is proposed that involves simultaneous pumping of a set of closely spaced Q-branch transitions on the (2)Δ5/2 - (2)Π3/2 band together with two Q-branch lines in the (2)Σ(+) - (2)Π1/2 band. It is shown that this should lead to >70% of total population in the lowest rotational level at 300 K and over 99% at 77 K. In principle, the multiple Q-branch lines could be pumped with just two broad-band (∼Δν = 0.4-3 cm(-1)) infrared lasers.

Electronic orbital angular momentum and magnetism of graphene

Orbital angular momentum (OAM) of graphene electrons in a perpendicular magnetic field is calculated and corresponding magnetic moment is used to investigate the magnetism of perfect graphene. Variation in magnetization demonstrates its decrease with carrier-doping, plateaus in a large field, and de Haas–van Alphen oscillation. Regulation of graphene׳s magnetism by a parallel electric field is presented. The OAM originates from atomic-scale electronic motion in graphene lattice, and vector hopping interaction between carbon atomic orbitals is the building element. A comparison between OAM of graphene electrons, OAM of Dirac fermions, and total angular momentum of the latter demonstrates their different roles in graphene׳s magnetism. Applicability and relation to experiments of the results are discussed.

Direct generation of optical vortices

A detailed scheme is established for the direct generation of optical vortices, signifying light endowed with orbital angular momentum. In contrast to common techniques based on the tailored conversion of the wave front in a conventional beam, this method provides for the direct spontaneous emission of photons with the requisite field structure. This form of optical emission results directly from the electronic relaxation of a delocalized exciton state that is supported by a ringlike array of three or more nanoscale chromophores. An analysis of the conditions leads to a general formulation revealing a requirement for the array structure to adhere to one of a restricted set of permissible symmetry groups. It is shown that the coupling between chromophores within each array leads to an energy level splitting of the exciton structure, thus providing for a specific linking of exciton phase and emission wavelength. For emission, arrays conforming to one of the given point-group families' doubly degenerate excitons exhibit the specific phase characteristics necessary to support vortex emission. The highest order of exciton symmetry, corresponding to the maximum magnitude of electronic orbital angular momentum supported by the ring, provides for the most favored emission. The phase properties of the emission produced by the relaxation of such excitons are exhibited on plots which reveal the azimuthal phase progression around the ring, consistent with vortex emission. It is proven that emission of this kind produces electromagnetic fields that map with complete fidelity onto the phase structure of a Laguerre-Gaussian optical mode with the corresponding topological charge. The prospect of direct generation paves the way for practicable devices that need no longer rely on the modification of a conventional laser beam by a secondary optical element. Moreover, these principles hold promise for the development of a vortex laser, also based on nanoscale exciton decay, enabling the production of coherent radiation with a tailor-made helical wave front.

Observation of low-field Fano-Feshbach resonances in ultracold gases of dysprosium

We report the observation of resonance-like loss in the trap population of ultracold dysprosium as a function of magnetic field, which we attribute to anisotropy-induced Fano-Feshbach resonances arising from Dy's large magnetic dipole moment and nonzero electronic orbital angular momentum. We recorded these resonances for four different isotopes, three bosonic and one fermionic, over a field range of 0-6 G and show that the number of resonances changes significantly as a function of temperature, even in the nK regime. Most of the observed resonances are of very narrow width. The fermionic isotope, unlike its bosonic counterparts, possesses nonzero nuclear spin and exhibits a much higher density of resonances.