Odd Angular Momentum Research Articles

Collinear scattering and long-lived excitations in two-dimensional electron fluids

For a long time, it has been thought that 2D Fermi gases could support long-lived excitations, thanks to the collinear quasiparticle scattering controlled by phase space constraints at a 2D Fermi surface. We present a direct calculation that reveals such excitations. The excitation lifetimes are found to exceed the fundamental bound set by Landau Fermi-liquid theory by a factor as large as $(T_F/T)^\alpha$ with $\alpha \approx 2$. These excitations represent Fermi-surface modulations of an odd parity, one per each odd angular momentum. To explain this surprising behavior, we employ a connection between the linearized quantum kinetic equation and the dynamics of a fictitious quantum particle moving in a 1D reflectionless ${\rm sech^2}$ potential. In this framework, we identify the long-lived excitations in Fermi gases as zero modes that arise from supersymmetry.

Large-scale simulations of particle-hole-symmetric Pfaffian trial wave functions

We introduce a family of paired-composite-fermion trial wave functions for any odd Cooper-pair angular momentum. These wave functions are parameter-free and can be efficiently projected into the lowest Landau level. We use large-scale Monte Carlo simulations to study three cases: Firstly, the Moore-Read phase, which serves us as a benchmark. Secondly, we explore the pairing associated with the anti-Pfaffian and the particle-hole-symmetric Pfaffian. Specifically, we assess whether their trial states feature exponentially decaying correlations and thus represent gapped phases of matter. For Moore-Read and anti-Pfaffian we find decay lengths of $\xi_\text{Moore-Read}=1.30(5)$ and $\xi_\text{anti-Pfaffian}=1.38(14)$, in units of the magnetic length. By contrast, for the case of PH-Pfaffian, we find no evidence of a finite length scale for up to $56$ particles.

Brightening odd-parity excitons in transition-metal dichalcogenides: Rashba spin-orbit interaction, skyrmions, and cavity polaritons

Odd-angular momentum exciton states are dark to light in monolayers of transition-metal dichalcogenides and can be addressed only by two-photon probes. Besides, $2p$ excitons states are expected to show a fine splitting that arises from the peculiar electronic band structure of the material, characterized by a finite Berry curvature around each valley. In this work we study in detail the coupling of photons to $p$ exciton states and we find that the Rashba spin-orbit interaction or a Skyrmion in the transition-metal dichalcogenide substrate can be exploited to engineer finite optical selection rules. The basis mechanism relies on a matching of the exciton angular momentum with the winding of the Rashba spin-orbit interaction or the Skyrmion topological charge. In a photonic cavity, the coupling is enhanced due to photon confinement and the resulting polaritonic branches acquire a mixing with $2p^\pm$ excitons, thus providing a useful tool to detect exciton fine-splitting and and enable novel uses of odd-parity dark excitons.

Moments of angular distribution and beam asymmetries in ηπ0 photoproduction at GlueX

In the search for exotic mesons, the GlueX collaboration will soon extract moments of the $\eta\pi^0$ angular distribution. In the perspective of these results, we generalize the formalism of moment extraction to the case in which the two mesons are produced with a linearly polarized beam, and build a model for the reaction $\vec \gamma p \to \eta \pi^0 p$. The model includes resonant $S$-, $P$-, $D$-waves in $\eta\pi^0$, produced by natural exchanges. Moments of the $\eta\pi^0$ angular distribution are computed with and without the $P$-wave, to illustrate the sensitivity to exotic resonances. Although little sensitivity to the $P$-wave is found in moments of even angular momentum, moments of odd angular momentum are proportional to the interference between the $P$-wave and the dominant $S$- and $D$-waves. We also generalize the definition of the beam asymmetry for two mesons photoproduction and show that, when the meson momenta are perpendicular to the reaction plane, the beam asymmetry enhances the sensitivity to the exotic $P$-wave.

Mark and Marshak boundary conditions in surface harmonics method

In the surface harmonics method (SHM) as a boundary condition it can be used a link of even angular momentum vector of the neutron distribution with odd momentum vector to obtain a finite difference equations. On the border with the vacuum such boundary conditions are called Mark or Marshak boundary conditions. Instead of odd angular momenta the SHM uses their linear combinations (so called neutron levels), so in this paper it is obtained the matrix of connection between odd angular momentum vector and the neutron levels vector (such as Marshak boundary conditions) and matrices of connection between odd angular momentum vector and the neutron levels vector(such as Mark boundary conditions). In present article connection matrix is used in SHM and for computation of the reference neutron distributions in PN - approximation (up to N = 97).

Chirp and carrier-envelope-phase effects in the multiphoton regime: measurements and analytical modeling of strong-field ionization of sodium

We investigate the influence of chirp on carrier-envelope-phase (CEP)-dependent strong-field few-cycle laser-induced photoelectron spectra of sodium, well within the multiphoton regime. Our measurements and analytical model of this process reveal a simple chirp-dependence, which has the potential to be utilized as an online monitor of laser chirp. Moreover, this effect could extend single-shot measurements of the CEP using above-threshold ionization to longer, chirped pulses, and significantly lower the required pulse energies. Specifically, at a wavelength of 775 nm and an intensity of the CEP- and energy-dependent left-right asymmetries of emitted electrons are measured in a time-of-flight spectrometer. In these asymmetry maps, inclined stripe-like structures emerge, where the inclination is tunable with the chirp of the pulse. We report a simple analytical model, explaining the effect as the interference of electrons with even and odd angular momenta, located at energies in between adjacent above-threshold ionization peaks. As we demonstrate, the analytical model is in good agreement with the measurement, as well as with solutions of the three-dimensional time-dependent Schrödinger equation. Further, the analytical model, which can easily be extended to other atoms, allows us to derive an equation, describing the relation between the slope of the inclined stripes and the chirp of the laser.

Intrinsic ac anomalous Hall effect of nonsymmorphic chiral superconductors with an application to UPt3

We identify an intrinsic mechanism of the anomalous Hall effect for non-symmorphic chiral superconductors. This mechanism relies on both a nontrivial multi-band chiral superconducting order parameter, which is a mixture of pairings of even and odd angular momentum channels, and a complex normal state inter-sublattice hopping, both of which are consequences of the nonsymmorphic group symmetry of the underlying lattice. We apply this mechanism to the putative chiral superconducting phase of the heavy-fermion superconductor $\mathrm{UPt_3}$ and calculate the anomalous ac Hall conductivity in a simplified two-band model. From the ac Hall conductivity and optical data we estimate the polar Kerr rotation angle and compare it to the measured results for $\mathrm{UPt_3}$ [E. R. Schemm \textit{et al.}, Science \textbf{345},190(2014)].

Even exciton series in Cu2O

In $\mathrm{Cu_{2}O}$ parity is a good quantum number and thus the exciton spectrum falls into two parts: The dipole-active exciton states of negative parity and odd angular momentum, which can be observed in one-photon absorption ($\Gamma_4^-$ symmetry) and the exciton states of positive parity and even angular momentum, which can be observed in two-photon absorption ($\Gamma_5^+$ symmetry). The unexpected observation of $D$ excitons in two-photon absorption and of $F$ excitons in one-photon absorption has given evidence that the dispersion properties of the $\Gamma_5^+$ orbital valence band is giving rise to a coupling of the yellow and green exciton series. In this paper we show that the even and odd parity exciton system can be consistently described within the same theoretical approach. However, the Hamiltonian of the even parity system needs, in comparison to the odd exciton case, modifications to account for the very small radius of the $1S$ exciton. In the presented treatment we take special care of the central-cell corrections, which comprise a reduced screening of the Coulomb potential at distances comparable to the polaron radius, the exchange interaction being responsible for the exciton splitting into ortho and para states, and the inclusion of terms in the fourth power of $p$ in the kinetic energy. Since the yellow $1S$ exciton state is coupled to all other states of positive parity, we show how the central-cell corrections affect the whole even exciton series. The close resonance of the $1S$ green exciton with states of the yellow exciton series has a strong impact on the energies and oscillator strengths of all implied states. The consistency between theory and experiment with respect to energies and oscillator strengths for the even and odd exciton system in $\mathrm{Cu_{2}O}$ is a convincing proof for the validity of the applied theory.

Ground-state properties of rare-earth nuclei in the Nilsson mean-field plus extended-pairing model

The Nilsson mean-field plus extended-pairing model for deformed nuclei is applied to describe the ground-state properties of selected rare-earth nuclei. Binding energies, even-odd mass differences, energies of the first pairing excitation states, and moments of inertia for the ground-state band of $^{152\ensuremath{-}164}\mathrm{Er}$, $^{154\ensuremath{-}166}\mathrm{Yb}$, and $^{156\ensuremath{-}168}\mathrm{Hf}$ are calculated systematically in the model employing both proton-proton and neutron-neutron pairing interactions. The pairing interaction strengths are determined as a function of the mass number in the isotopic chains. In comparison with the corresponding experimental data, it is shown that pairing interaction is crucial in elucidating the properties of both the ground state and the first pairing excitation state of these rare-earth nuclei. With model parameters determined by fitting the energies of these states, ground-state occupation probabilities of valence nucleon pairs with angular momentum $J=0,1,\ensuremath{\cdots},12$ for even-even $^{156\ensuremath{-}162}\mathrm{Yb}$ are calculated. It is inferred that the occupation probabilities of valence nucleon pairs with even angular momenta are much higher than those of valence nucleon pairs with odd angular momenta. The results clearly indicate that $S, D$, and $G$ valence nucleon pairs dominate in the ground state of these nuclei.

Fractional angular momentum in cold-atom systems.

The quantum statistics of bosons or fermions are manifest through the even or odd relative angular momentum of a pair. We show theoretically that, under certain conditions, a pair of certain test particles immersed in a fractional quantum Hall state possesses, effectively, a fractional relative angular momentum, which can be interpreted in terms of fractional braid statistics. We propose that the fractionalization of the angular momentum can be detected directly through the measurement of the pair correlation function in rotating ultracold atomic systems in the fractional quantum Hall regime. Such a measurement will also provide direct evidence for the effective magnetic field resulting from Berry phases arising from attached vortices, and of excitations with a fractional particle number, analogous to the fractional charge of the electron fractional quantum Hall effect.

Pairing in half-filled Landau level

Pairing of composite fermions in half-filled Landau level state is reexamined by solving the BCS gap equation with full frequency dependent current–current interactions. Our results show that there can be a continuous transition from the Halperin–Lee–Read state to a chiral odd angular momentum Cooper pair state for short-range contact interaction. This is at odds with the previously established conclusion of first order pairing transition, in which the low frequency effective interaction was assumed for the entire frequency range. We find that even if the low frequency effective interaction is repulsive, it is compensated by the high frequency regime, which is attractive. We construct the phase diagrams and show that ℓ=1 angular momentum channel is quite different from higher angular momenta ℓ≥3. Remarkably, the full frequency dependent analysis applied to the bilayer Hall system with a total filling fraction ν=12+12 is quantitatively changed from the previously established results but not qualitatively.

A theoretical study on the strong-field ionization of the lithium atom

We apply a recently developed momentum space method (Jiang et al 2012 Phys. Rev. E 86 066702) to investigate the experimental results of strong-field ionization of the lithium atom (Schuricke et al 2011 Phys. Rev. A 83 023413). By splitting the photoelectron into groups of even and odd angular momenta and by using the states’ population history, we can analyse the ionization mechanism in further detail. The lower energy double-peak structure, shown experimentally, of the photoelectron is attributed to the three-level Λ-coupling effect. The spectral difference of 10 and 30 fs pulses at a typical intensity is demonstrated. We explain why the strong-field ionization fluctuates at intensities of 6 and 10 fs, but not for a 30 fs pulse. The change of fan-like photoelectron angular distribution with intensity in direction parallel to polarization is explained. Use of the Keldysh parameter to classify the tunnelling and multiphoton ionization is not meaningful for the lithium atom, because the ground state is mostly depleted before reaching peak intensity.

NUCLEAR ALTERNATING-PARITY BANDS AND TRANSITION RATES IN A MODEL OF COHERENT QUADRUPOLE–OCTUPOLE MOTION

A further extension of a model of coherent quadrupole–octupole vibrations and rotations and its application to alternating-parity spectra in heavy even–even nuclei is presented. Within the model the yrast alternating-parity sequence includes the ground state band and the lowest negative parity levels with odd angular momenta, while the non-yrast sequences include excited β-bands and higher negative-parity levels. Electric transition operators reflecting the complex shape characteristics associated with the quadrupole–octupole vibration modes are introduced. By using them B(E1), B(E2) and B(E3) reduced transition probabilities within and between the different energy sequences are calculated. It is shown that the model successfully reproduces yrast and non-yrast alternating-parity bands together with the attendant B(E1)–B(E3) transition rates in the nuclei 154 Sm , 156 Gd and 100 Mo .

Non-yrast nuclear spectra in a model of coherent quadrupole-octupole motion

A model assuming coherent quadrupole-octupole vibrations and rotations is applied to describe non-yrast energy sequences with alternating parity in several even-even nuclei from different regions, namely $^{152,154}$Sm, $^{154,156,158}$Gd, $^{236}$U and $^{100}$Mo. Within the model scheme the yrast alternating-parity band is composed by the members of the ground-state band and the lowest negative-parity levels with odd angular momenta. The non-yrast alternating-parity sequences unite levels of $\beta$-bands with higher negative-parity levels. The model description reproduces the structure of the considered alternating-parity spectra together with the observed B(E1), B(E2) and B(E3) transition probabilities within and between the different level-sequences. B(E1) and B(E3) reduced probabilities for transitions connecting states with opposite parity in the non-yrast alternating-parity bands are predicted. The implemented study outlines the limits of the considered band-coupling scheme and provides estimations about the collective energy potential which governs the quadrupole-octupole properties of the considered nuclei.

Non-yrast quadrupole-octupole spectra

A model of strongly coupled quadrupole and octupole vibrations and rotations is applied to de- scribe non-yrast alternating-parity sequences in even-even nuclei and split parity-doublet spectra in odd-mass nuclei. In even-even nuclei the yrast alternating-parity sequence includes the ground-state band and the lowest negative-parity levels with odd angular momenta, while the non-yrast sequences include excited β-bands and higher negative-parity levels. In odd-mass nuclei the yrast levels are described as low-energy rotation-vibration modes coupled to the ground single-particle (s.p.) state, while the non-yrast parity-doublets are obtained as higher-energy rotation-vibration modes coupled to excited s.p. configurations. We show that the extended model scheme describes the yrast and non-yrast quadrupole-octupole spectra in both even-even and odd-A nuclei. The involvement of the reflection-asymmetric deformed shell model to explain the single-particle motion and the Coriolis interaction in odd nuclei is discussed.

ANALYTIC WAVE FUNCTIONS FOR THE HALF-FILLED LOWEST LANDAU LEVEL

We consider a two-dimensional strongly correlated electronic system in a strong perpendicular magnetic field at half-filling of the lowest Landau level (LLL). We seek to build a wave function that, by construction, lies entirely in the Hilbert space of the LLL. Quite generally, a wave function of this nature can be built as a linear combination of all possible Slater determinants formed by using the complete set of single-electron states that belong to the LLL. However, due to the vast number of Slater determinant states required to form such basis functions, the expansion is impractical for any but the smallest systems. Thus, in practice, the expansion must be truncated to a small number of Slater determinants. Among many possible LLL Slater determinant states, we note a particular special class of such wave functions in which electrons occupy either only even, or only odd angular momentum states. We focus on such a class of wave functions and obtain analytic expressions for various quantities of interest. Results seem to suggest that these special wave functions, while interesting and physically appealing, are unlikely to be a very good approximation for the exact ground state at half-filling factor. The overall quality of the description can be improved by including other additional LLL Slater determinant states. It is during this process that we identify another special family of suitable LLL Slater determinant states to be used in an enlarged expansion.

Serber symmetry, largeNc, and Yukawa-like one-boson exchange potentials

The Serber force has relative orbital parity symmetry and requires vanishing $\mathit{NN}$ interactions in partial waves with odd angular momentum. We illustrate how this property is well fulfilled for spin triplet states with odd angular momentum and violated for odd singlet states for realistic potentials but fails for chiral potentials. The analysis is carried out in terms of partial wave sum rules for $\mathit{NN}$ phase shifts, $r$-space potentials at long distances, and ${V}_{\mathrm{low} k}$ potentials. We analyze how Serber symmetry can be accommodated within a large-${N}_{c}$ perspective when interpreted as a long-distance symmetry. A prerequisite for this is the numerical similarity of the scalar and vector meson resonance masses. The conditions under which the resonance exchange potential can be approximated by a Yukawa form are also discussed. Although these masses arise as poles on the second Riemann in $\ensuremath{\pi}\ensuremath{\pi}$ scattering, we find that within the large-${N}_{c}$ expansion the corresponding Yukawa masses correspond instead to a well-defined large-${N}_{c}$ approximation to the pole that cannot be distinguished from their location as Breit-Wigner resonances.

Fluorescence of low-lying doubly photoexcited states in helium

In this work we investigate fluorescence decay of low-lying $(n<~8)$ resonances with odd parity and total angular momentum $J=1$ below the $N=2$ threshold of helium. After discussing the photoabsorption cross section for creation of such states, we estimate the probability for the primary fluorescence transition to $1snl$ states below the first ionization threshold. The subsequent fluorescence cascade decay brings helium into the ground state or into one of the two long lived $1s2s{}^{1,3}S$ states. We discuss the time scale of the cascade and combine all the calculated transition probabilities to determine branching ratios for singlet and triplet metastable production. Finally, we estimate the angular distribution of the emitted uv photons and perform a comparison with the recent experimental data of Penent et al. [Phys. Rev. Lett. 86, 2758 (2001)].

Degeneracies whenT=0two body matrix elements are set equal to zero and Regge’s6jsymmetry relations

The effects of setting all T=0 two body interaction matrix elements equal to a constant (or zero) in shell model calculations (designated as $<T=0>=0$) are investigated. Despite the apparent severity of such a procedure, one gets fairly reasonable spectra. We find that using $<T=0>=0$ in single j shell calculations degeneracies appear e.g. the $I={1/2} ^{-}$ and ${13/2}^{-}$ states in $^{43}$Sc are at the same excitation energies; likewise the I=$3_{2}^{+}$,$7_{2}^{+}$,9$^{+}_{1}$ and 10$^{+}_{1}$ states in $^{44}$Ti. The above degeneracies involve the vanishing of certain 6j and 9j symbols. The symmetry relations of Regge are used to explain why these vanishings are not accidental. Thus for these states the actual deviation from degeneracy are good indicators of the effects of the T=0 matrix elements. A further indicator of the effects of the T=0 interaction in an even - even nucleus is to compare the energies of states with odd angular momentum with those that are even.

Laser excitation of angular Rydberg wavepackets

We consider the dynamics of the formation of high angular momentum Rydberg states in a hydrogen by laser excitation. The Schrödinger equation is solved by expanding the wavefunction in spherical |n,l,m states. Results obtained by expansions over a large and a small number of basis functions are compared in order to identify the main excitation dynamics. The final population is studied by simpler models and the survival of only odd angular momentum in the long-time limit states can be explained within an analytical model. From this model it is shown that the survival of odd high-l states originates from symmetry properties of the time development operator and that the population of even l states may occur with ultra-short laser pulses.