Longitudinal Momentum Research Articles

Polarization-dependent high-intensity Kapitza-Dirac effect in strong laser fields

We study the deflection of photoelectrons in intense elliptically polarized standing light waves, known as the high-intensity Kapitza-Dirac effect. In order to compute the longitudinal momentum transfer to the photoelectron in above-threshold ionization, we utilize a complete description of the quantum dynamics in the spatially dependent field of the standing light wave. We propose experimental conditions under which low-energy photoelectrons can be generated with remarkably high longitudinal momenta that can be controlled via the polarization of the standing wave. We expect that future experimental realizations will provide additional insights into the momentum transfer in intense laser-atom interactions.

Novel transverse emittance measurements for electron cooling characterization

The extra low energy antiproton ring (ELENA) finished commissioning before the start of CERN's second long shutdown in December 2018, successfully providing beams to a new experimental zone. In 2021, ELENA will begin distributing cooled 100 keV antiproton beams to all antimatter experiments. To counteract beam blowup due to deceleration, ELENA will employ the use of an electron cooler. Measurements under similar circumstances, such as at the antiproton decelerator at CERN, have shown electron cooling causing non-Gaussian beam profiles. This effect, combined with nonzero dispersion at the location of the scraper in ELENA, presents new challenges in the use of ELENA's scraper to determine the emittance during the deceleration cycle. Two new scraper algorithms have been developed and used to show the first evidence of significant electron cooling in ELENA, at 650 and 100 keV energy plateaus. The algorithms are capable of estimating the longitudinal momentum spread of the beams and accurately determining emittances for non-Gaussian beams in dispersive regions. Additionally, utilizing combinations of measurements from opposing scraper blades, additional information on the beam's evolution is presented, suggesting a correlation between the emittance and longitudinal momentum offset of individual particles. Finally, considerations for further studies in ELENA and similar machines are presented.

Features of the Spatial Localization of Particles in the Coherent Channeling Mode and the Mechanism for the Formation of Controlled Directional Radiation

Features of the spatial evolution of a wave function that describes the motion of fast particles in a planar channel in the coherent channeling mode are considered. It is shown that the interference of eigenstates leads to modulation of the probability density of particle localization in the transverse channel cross section and the longitudinal direction of nonquantized motion if the parametric coupling of longitudinal momentum and the energy of transverse particle motion are taken into account. In the case of a very narrow wave packet, the spatial structure of the probability density is close to the classical particle trajectory. In the case of a particle whose state corresponds to a plane wave before its entrance into the channel, the interference process leads to longitudinal-transverse focusing and the formation of periodically located clusters with a very large probability density. As the entrance angle increases, the position of these clusters approaches the channel walls. In this paper, it is shown that the presence of such clusters leads to the possibility of forming similarly located clusters of excited atoms and nuclei and to a new type of generation of quasicoherent directional radiation.

Measurement of the concurrence of arbitrary two-photon six-qubit hyperentangled state

Hyperentanglement is the quantum system entangled in several degrees of freedom (DOFs), which has attracted extensive attention in quantum communication. In the practical application of hyperentanglement, the key step is to know the information of the hyperentanglement. In this paper, we propose an efficient protocol to measure the concurrence of arbitrary two-photon six-qubit hyperentangled state, which simultaneously entangles in the polarization and double longitudinal momentum DOFs. This protocol requires the weak cross-Kerr nonlinearity and some linear optical elements to construct the quantum nondemolition detection gate. The concurrence in each DOF can be converted into the success probability of distilling some specified states. Our protocol may play an important role in future quantum information processing.

Conversion of the Relativistic Electron Energy into a Single Photon during the Interaction with Periodic Heterogeneities in Crystals

In the channeling model, the interaction between relativistic electrons and crystal axes and planes is described traditionally as the motion in an averaged continuous potential. However, real crystal axes and planes consist of individual atoms arranged periodically. The interaction of an electron with periodic heterogeneities is accompanied by the transfer, to the crystal, of strictly quantized portions of the momentum Δ p|| = 2πnћ/d, where n = 1, 2, 3, … and d is the period of the potential heterogeneity arrangement coinciding with that of the crystal lattice in the case of motion along the axis. A photon with the energy ћω ~ 4πћ$${{E_{1}^{2}} \mathord{\left/ {\vphantom {{E_{1}^{2}} {d{{m}^{2}}{{c}^{3}}}}} \right. \kern-0em} {d{{m}^{2}}{{c}^{3}}}},$$ where E1 is the initial electron energy, is emitted in the case where quantum longitudinal momentum is transferred to the lattice. If E1 ~ 1 GeV or more, a kinetic electron energy of up to 90% transforms into the energy of a single photon during such a process.

Unified Description of Polarized and Unpolarized Quark Distributions in the Proton.

We propose a unified new approach to describe polarized and unpolarized quark distributions in the proton based on the gauge-gravity correspondence, light-front holography, and the generalized Veneziano model. We find that the spin-dependent quark distributions are uniquely determined in terms of the unpolarized distributions by chirality separation without the introduction of additional free parameters. The predictions are consistent with existing experimental data and agree with perturbative QCD constraints at large longitudinal momentum x. In particular, we predict the sign reversal of the polarized down-quark distribution in the proton at x=0.8±0.03, a key property of nucleon substructure which will be tested very soon in upcoming experiments.

Longitudinal photon-momentum transfer in strong-field double ionization of argon atoms

We investigate the longitudinal photon-momentum transfer in nonsequential double ionization of argon atoms exposed to a $2.0\ensuremath{-}\ensuremath{\mu}\mathrm{m}$ linearly polarized strong laser field. The zero momentum of the photoelectron is precisely calibrated using the photoelectron-photoion coincidence spectrum. The sum-longitudinal momentum of two photoelectrons from the double ionization noticeably deflects along the laser propagation direction, which is opposite to and much larger than that of single ionization. By tracking the electron trajectories for double ionization in semiclassical simulations, we find that the Coulomb focusing of the ionic core with the assistance of the Lorentz pushing of the laser field dominates the observed longitudinal momentum deflection. Our results open the possibility to control the photon-momentum transfer by manipulating the waveform of the laser fields and thus the Coulomb and magnetic effects experienced by the photoelectrons.

Hadron-in-jet production at partonic threshold

We consider the longitudinal momentum distribution of hadrons inside jets in proton-proton collisions. At partonic threshold large double logarithmic corrections arise which need to be resummed to all orders. We develop a factorization formalism within SCET that allows for the joint resummation of threshold and jet radius logarithms. We achieve next-to-leading logarithmic NLL′ accuracy by including non-global logarithms in the leading-color approximation. Overall, we find that the threshold resummation leads to a sizable enhancement of the cross section and a reduced QCD scale dependence, suggesting that the all-order resummation can be important for the reliable extraction of fragmentation functions in global analyses when jet substructure data is included.

Deeply virtual Compton scattering off the neutron

The three-dimensional structure of nucleons (protons and neutrons) is embedded in so-called generalized parton distributions, which are accessible from deeply virtual Compton scattering. In this process, a high energy electron is scattered off a nucleon by exchanging a virtual photon. Then, a highly-energetic real photon is emitted from one of the quarks inside the nucleon, which carries information on the quark's transverse position and longitudinal momentum. By measuring the cross-section of deeply virtual Compton scattering, Compton form factors related to the generalized parton distributions can be extracted. Here, we report the observation of unpolarized deeply virtual Compton scattering off a deuterium target. From the measured photon-electroproduction cross-sections, we have extracted the cross-section of a quasi-free neutron and a coherent deuteron. Due to the approximate isospin symmetry of quantum chromodynamics, we can determine the contributions from the different quark flavours to the helicity-conserved Compton form factors by combining our measurements with previous ones probing the proton's internal structure. These results advance our understanding of the description of the nucleon structure, which is important to solve the proton spin puzzle.

Double parton distribution of valence quarks in the pion in chiral quark models

The valence double parton distribution of the pion is analyzed in the framework of chiral quark models, where in the chiral limit factorization between the longitudinal and transverse degrees of freedom occurs. This feature leads, at the quark-model scale, to a particularly simple distribution of the form $D(x_1,x_2, \vec{q}) = \delta(1-x_1-x_2) F(\vec{q})$, where $x_{1,2}$ are the longitudinal momentum fractions carried the valence quark and antiquark and $\vec{q}$ is their relative transverse momentum. For $\vec{q}=\vec{0}$ this result complies immediately to the Gaunt-Sterling sum rules. The DGLAP evolution to higher scales is carried out in terms of the Mellin moments. We then explore its role on the longitudinal correlation quantified with the ratio of the double distribution to the product of single distributions, $D(x_1,x_2, \vec{q}=\vec{0})/D(x_1)D(x_2)$. We point out that the ratios of moments $\langle x_1^n x_2^m \rangle / \langle x_1^n \rangle \langle x_2^m \rangle $ are independent of the evolution, providing particularly suitable measures to be tested in the upcoming lattice simulations. The transverse form factor $F(\vec{q})$ and its Fourier conjugate in the relative transverse coordinate $\vec{b}$ are obtained in variants of the Nambu--Jona-Lasinio model with the spectral and Pauli-Villars regularizations.The results are valid in the soft-momentum domain. Interestingly, with the spectral regularization of the model, the effective cross section for the double parton scattering of pions is exactly equal to the geometric cross section, $\sigma_{\rm eff}=\pi \langle \vec{b}^2 \rangle$ and yields about 20~mb.

Singularities in twist-3 quark distributions

We find in one-loop calculations and spectator models that twist-3 GPDs exhibit discontinuities. In the forward limit these discontinuities grow into Dirac delta functions which are essential to satisfy the sum rules involving twist-3 PDFs. We calculate twist-3 quasi-PDFs as a function of longitudinal momentum and identify the Dirac delta function terms with momentum components in the nucleon state that do not scale as the nucleon is boosted to the infinite momentum frame.

A Theoretical Approach to Study J/Ψ Suppression in Relativistic Heavy Ion Collisions with Ellipsoidal Evolution

With a view to understanding J/$\Psi$ suppression in relativistic heavy ion collisions, we compute the suppression rate within the framework of hydrodynamical evolution model. For this, we consider an ellipsoidal flow and use an ansatz for temperature profile function which accounts for time and the three dimensional space evolution of the quark-gluon plasma. We have calculated the survival probability separately as the function of transverse and longitudinal momentum. We have shown that previous calculations are special cases of this model.

State-selective single electron capture in slow O 6+-He collisions

SynopsisThe state-selective single-electron capture processes were measured by cold-target recoil-ion momentum spectroscopy in O 6+-He collisions between 18keV and 96keV. From the longitudinal momentum spectrum of recoil ions, the single electron captured into n=3 states of projectile ion is predominant and n=4 states have a small contribution. The oscillation structure of angular differential cross sections was observed. The present experimental results are compared with other experiments at low energy and the predictions of the molecular Columbic barrier model.

Relativistic electron energy conversion in one photon in crystals

Interaction of relativistic electrons with crystal axis is traditionally described in terms of channeling model—i.e. as a motion in some homogeneous averaged axial potential. However, real crystals are made of atoms, positioned periodically. Interaction of electrons with periodical potential must be accompanied with transitions of discrete portions of momentum Δ p∥ = 2π nℏ /d, n = 1, 2, 3,ṡ, defined by the potential period d. Transmission of sufficient portion of longitudinal momentum to the lattice may be accompanied by the emission of photon with correspondingly high energy. In case of relativistic electrons with energies E1 ∼ GeV or more, nearly all the electron's energy may be converted into just one photon.

Electron Injection for Direct Acceleration by A Gaussian Laser Field Under the Influence of Azimuth Magnetic Field

Electron injection for direct acceleration by a circularly polarized Gaussian laser field under the influence of azimuth magnetic field is studied. The electron energy gain, \(\gamma\) versus electron's injection angle \(\delta\) at different values laser intensity parameters and laser spot size shows the energy enhancement on increasing the parameters. For a small change in angle of injection then there appears a significant change in electron energy gain also for the variation of energy gain and magnetic field energy gain increases when value of \(\delta\) $ is 8.5, 8.0, 13.5 and 13, respectively. It is observed that \(\delta\) should be small and optimized for appropriate momentum to maximize the electron energy gain due to a relativistic longitudinal momentum and the variation of the scattering angle of the electron \(\theta\) with respect to electron's injection angle \(\delta\) in the presence of magnetic field shows a relatively lower scattering is observed with optimized values of injection angle in the presence of magnetic field.

DIFFUSION COEFFICIENTS IN MOMENTUM FOR A RELATIVISTIC ELECTRON BEAM IN AN UNDULATOR

We consider a motion of a relativistic electron beam in a spatially periodic magnetic field of an undulator taking into account the influence of the spontaneous radiation fields on this motion. The diffusion coefficients in longitudinal momentum of electrons are found. It is shown that in initially monoenergetic electron beam a mean square spread due to influence of the incoherent fields on electron motion may have a predominant effect compared with the spread caused by the quantum fluctuations.

All-Optical Scheme for Generation of Isolated Attosecond Electron Pulses.

We theoretically propose an all-optical scheme for generation of isolated electron pulses with subfemtosecond durations for ultrafast electron microscopy and diffraction. The scheme is based on simultaneous longitudinal and transverse momentum modulation of freely propagating electrons at two distinct frequencies via ponderomotive interaction with tailored light fields of three phase-controlled laser pulses in vacuum. After a drift distance, an attosecond electron pulse train is formed with the individual pulses displaced in the transverse direction. Spatial filtering of the electron beam by an aperture leads to isolation of an individual attosecond pulse with a duration of <100 as. Subfemtosecond isolated electron pulses will enable direct space-time imaging of attosecond electronic dynamics in atoms, molecules, and solids with atomic spatial resolution, allowing us to directly observe phenomena such as electron tunneling or electron-electron interaction in strong laser fields of few-cycle laser pulses.

Exploring the origin of small−x saturation in the collinear approach

A modification of the collinear evolution equations as an appropriate approach to improve the behavior of parton distribution functions in the region of small longitudinal momentum fractions, and to find more theoretical arguments to clarify the possible appearence of saturation regime is suggested. It is argued that parton diffusion in the rapidity space at large parton densities along the space-time evolution could result in the emergence of a natural saturation scale on which freezing actually occurs.

Circularly polarized Raman scattering in silicon

AbstractThe two‐dimensional layered materials such as graphene and transition metal dichalcogenides reveal the unique structure of the electron‐hole spectrum that generates discrete degrees of freedom related to the electron spin and the valley pseudospin. Optical phonons with the angular momentum may induce the transitions between the quantum levels in this system. Therefore, the investigation of these phonons is of particular importance now. One of the most popular methods for the determination of the angular momentum of optical phonons is circularly polarized Raman spectroscopy, common features of which were not entirely discovered so far due to a restricted set of studied materials. Here, we use this method to examine optical phonons in Si as an example of a high‐symmetry model crystal. The decomposition of scattered light into the circularly polarized components with the subsequent angle‐resolved analysis is employed. This allows us to find that Raman scattering by longitudinal optical phonons occurs with conservation of the photon helicity in accordance to the angular momentum conservation law, since the longitudinal optical phonon angular momentum is zero. In contrast, transverse optical phonon reverses photon helicity, meaning that its angular momentum is 2ħ. It is shown that Raman scattering of circularly polarized light is described well taking into account the angular momentum conservation law in addition to the main conclusions of the classical theory developed for the case of linearly polarized light.

Study of kaon structure using the light-cone quark model

We investigate the various distributions explaining multi-dimensional structure of kaon at the level of its constituents ($u$ and $\bar{s}$) using the light-cone quark model. The overlap form of wavefunctions associated with the light-cone quark model is adopted for the calculations. The generalized parton distributions(GPDs)of $u$ and $\bar{s}$ quarks are presented for the case when the momentum transfer in the longitudinal direction is non-zero. The dependence of kaon GPDs is studied in terms of variation of quark longitudinal momentum fraction, momentum transfer in longitudinal direction and total momentum transfer to the final state of hadron. The transverse impact-parameter dependent GPDs are also studied by taking the Fourier transformation of general GPDs. Further, the quantum phase-space distributions; Wigner distributions are studied for the case of unpolarized, longitudinally-polarized and transversely-polarized parton in an unpolarized kaon. The Wigner distributions are analysed in the transverse impact-parameter plane, the transverse momentum plane and the mixed plane. Further, to get a complete picture of kaon in terms of its valence quarks, the variation of longitudinal momentum fraction carried by quark and antiquark in the generalized transverse momentum-dependent parton distributions (GTMDs) is studied for different values of transverse quark and antiquark momentum $({\bf k}_\perp)$ as well as for different values of momentum transferred to the kaon in transverse direction $({\bf \Delta}_\perp)$. This has been done for zero as well as non-zero skewedness representing respectively the absence and presence of momentum transfer to the final state of kaon in longitudinal direction. Furthermore, the possible spin-orbit correlation for $u$ and $\bar{s}$ in kaon is elaborated in context of Wigner distributions and GTMDs.