Ponderomotive Potential Research Articles

Ponderomotive potential effects on strong field two-photon double ionization in neon

Abstract In the context of the recently reported experiment on photoionization in neon atom, we theoretically study the photoionization of neon atom at a comparatively intense laser field. The calculated photoelectron spectrum for a Gaussian laser pulse show an asymmetric double peak line shape at a pulse duration of 14.2 fs and peak intensity of 1x1015 W/cm2. A systematic study clearly indicates that the ponderomotive potential of the photoelectron released during photoionization of neon is instrumental in causing the visible asymmetry. 
 Interestingly, for similar laser parameters asymmetry in the the photoelectron spectrum gets significantly reduced for a Sech2
shaped laser pulse. Time resolved photoelectron spectrum reveals that even for a Sech2 shaped laser pulse the two peak photoelectron spectrum is initially asymmetric and evolves into a symmetric line shape with increase in time. The results clearly indicate that irrespective of laser pulse shape asymmetry shows a non-linear decrease as a function of time. Our study also shows the possibility of controlling the asymmetry by varying the pulse duration. The calculations establishes a correlation between the effects of direct double ionization and ponderomotive potential on the asymmetry of the photoelectron spectrum at different pulse durations.

Floquet engineering of many-body states by the ponderomotive potential

Floquet engineering of many-body states by the ponderomotive potential

Nanoplasmonic Photoelectron Rescattering in the Multiphoton-Induced Emission Regime.

In strong-field laser-matter interactions, energetic electrons can be created by photoemission and a subsequent rescattering and can attain energy as much as 10 times the ponderomotive potential (U_{p}) of the laser field. Here, we show that with the unique combination of infrared laser sources (exploiting the quadratic scaling of U_{p}) and plasmonic nanoemitters (which enhance rescattering probability by orders of magnitude) ∼10U_{p} rescattered electrons can be observed in the multiphoton-induced regime. Our experiments correspond well to a model based on the time dependent Schrödinger equation and allowed us to reveal an unexpected aspect of ultrafast electron dynamics in the multiphoton emission regime.

Ion dynamics in standing electromagnetic wave near the cyclotron resonance

The dynamics of ions under the forces exerted by a planar standing electromagnetic wave near the cyclotron resonance is studied. It is shown that ions whose cyclotron frequency is larger than the wave frequency are pushed by the ponderomotive force toward and oscillate around the wave magnetic node, while ions whose cyclotron frequency is smaller than the wave frequency are pushed to and oscillate around the wave electric node. When the difference between the cyclotron frequency and the wave frequency is large, the ion motion is governed by a time independent ponderomotive potential. When that difference is small, the ion oscillates around the wave magnetic node with varying-in-time amplitude and frequency, described approximately by solutions of the Mathieu equation. Difficulties in using such a configuration for mass separation are discussed.

Characterization of bright betatron radiation generated by direct laser acceleration of electrons in plasma of near critical density

Directed x-rays produced in the interaction of sub-picosecond laser pulses of moderate relativistic intensity with plasma of near-critical density are investigated. Synchrotron-like (betatron) radiation occurs in the process of direct laser acceleration (DLA) of electrons in a relativistic laser channel when the electrons undergo transverse betatron oscillations in self-generated quasi-static electric and magnetic fields. In an experiment at the PHELIX laser system, high-current directed beams of DLA electrons with a mean energy ten times higher than the ponderomotive potential and maximum energy up to 100 MeV were measured at 1019 W/cm2 laser intensity. The spectrum of directed x-rays in the range of 5–60 keV was evaluated using two sets of Ross filters placed at 0° and 10° to the laser pulse propagation axis. The differential x-ray absorption method allowed for absolute measurements of the angular-dependent photon fluence. We report 1013 photons/sr with energies >5 keV measured at 0° to the laser axis and a brilliance of 1021 photons s−1 mm−2 mrad−2 (0.1%BW)−1. The angular distribution of the emission has an FWHM of 14°–16°. Thanks to the ultra-high photon fluence, point-like radiation source, and ultra-short emission time, DLA-based keV backlighters are promising for various applications in high-energy-density research with kilojoule petawatt-class laser facilities.

Critical role of isopotential surfaces for magnetostatic ponderomotive forces.

By producing localized wave regions at the ends of an open-field-line magnetic confinement system, ponderomotive walls can be used to differentially confine different species in the plasma. Furthermore, if the plasma is rotating, this wall can be magnetostatic in the laboratory frame, resulting in simpler engineering and better power flow. However, recent work on such magnetostatic walls has shown qualitatively different potentials than those found in the earlier, nonrotating theory. Here, using a simple slab model of a ponderomotive wall, we resolve this discrepancy. We show that the form of the ponderomotive potential in the comoving plasma frame depends on the assumption made about the electrostatic potential in the laboratory frame. If the laboratory-frame potential is unperturbed by the magnetic oscillation, one finds a parallel-polarized wave in the comoving frame, while if each field line remains equipotential throughout the perturbation region, one finds a perpendicularly polarized wave. This in turn dramatically changes the averaged ponderomotive force experienced by a charged particle along the field line, not only its scaling, but also its direction.

Guiding centre motion for particles in a ponderomotive magnetostatic end plug

The Hamiltonian dynamics of a single particle in a rotating plasma column, interacting with an magnetic multipole is perturbatively solved for up to second order, using the method of Lie transformations. First, the exact Hamiltonian is expressed in terms of canonical action-angle variables, and then an approximate integrable Hamiltonian is introduced, using another set of actions and angles, which describe the centre of oscillation for the particle. The perturbation introduces an effective ponderomotive potential, which to leading order is positive. At the second order, the pseudopotential consists of a sum of terms of the Miller form, and can have either sign. Additionally, at second order, the ponderomotive interaction introduces a modification to the particle effective mass, when considering the motion along the column axis. It is found that particles can be axially confined by the ponderomotive potentials, but acquire radial excursions which scale as the confining potential. The radial excursions of the particle along its trajectory are investigated, and a condition for the minimal rotation frequency for which the particle remains radially confined is derived. Last, we comment on the changes to the aforementioned solution to the pseudopotentials and particle trajectory in the case of resonant motion, that is, a motion which has the same periodicity as the perturbation.

Ponderomotive effects in spin—polarized quantum plasma

Analysis of ponderomotive effects exciting from propagation of an intense laser pulse through high density quantum plasma under the influence of an axial magnetic field taking into consideration the spin–spin (up and down) exchange interaction. The effects of electron Fermi pressure, quantum Bohm potential, and electron spin have been included in the analysis. Spin polarization is a result of the concentration difference of opposite spin electrons which is produced under the influence of the applied magnetic field. Axial gradient of the ponderomotive potential of laser has been applied for the electron acceleration. An analytic solution of the electron energy gain is obtained and the influence of spin polarization is analyzed both numerically and analytically. It is observed that spin polarization, density perturbation and the magnetic field effect electron acceleration dramatically. Further, the effect of nonlinearity on the refractive index of plasma has been studied.

Magnetostatic ponderomotive potential in rotating plasma

A new end-plugging method for rotating plasmas is identified and analyzed. It uses the ponderomotive potential associated with an azimuthal magnetostatic wiggler. Studied both analytically and numerically, this process compares favorably to other end-plugging methods in open field line magnetized plasma devices.

Feasibility of a pulsed ponderomotive phase plate for electron beams

We propose a scheme for constructing a phase plate for use in an ultrafast Zernike-type phase contrast electron microscope, based on the interaction of the electron beam with a strongly focused, high-power femtosecond laser pulse and a pulsed electron beam. Analytical expressions for the phase shift using the time-averaged ponderomotive potential and a paraxial approximation for the focused laser beam are presented, as well as more rigorous quasiclassical simulations based on the quantum phase integral along classical, relativistic electron trajectories in an accurate, non-paraxial description of the laser beam. The results are shown to agree well unless the laser beam is focused to a waist size below a wavelength. For realistic (off-the-shelf) laser parameters the optimum phase shift of is shown to be achievable. When combined with RF-cavity based electron chopping and compression techniques to produce electron pulses, a femtosecond regime pulsed phase contrast microscope can be constructed. The feasibility and robustness of the scheme are further investigated using the simulations, leading to motivated choices for design parameters such as wavelength, focus size and polarization.

Time-resolved measurements of sub-optical-cycle relativistic electron beams

We propose an all-optical technique to record the time information of relativistic electron beams with sub-optical-cycle duration. The technique is based on the interaction of the electron beam with the ponderomotive potential of an optical traveling wave generated by two counter-propagating circularly polarized optical fields at different frequencies in vacuum. One of the optical pulses is a vortex laser pulse, and the other is a normal Gaussian laser pulse. The time information of the electron beam is mapped into the angular information, which can be converted into a spatial distribution after a drift section. Thus, the temporal profile and arrival time of the electron beam can be retrieved from the spatial distribution of the electron beam. The measurement has a dynamic range comparable to the period of the optical intensity grating formed by two counter-propagating laser pulses. This technique may have wide applications in many research fields that require sub-optical-cycle electron beams.

Asynchronous Inelastic Scattering of Electrons at the Ponderomotive Potential of Optical Waves.

We study free electron dynamics during inelastic interaction with the ponderomotive potential of a traveling optical wave using classical and quantum-mechanical models. We show that in the strong interaction regime, the electrons trapped in the periodic potential oscillate leading to periodic revolutions of sharp peaks of the density distributions in the real and momentum spaces. In this regime, the synchronicity between the velocity of the optical wave and the electron propagation velocity is not required. Asynchronous interaction enables acceleration or deceleration of a significant fraction of the electrons to a final spectrum with a relative spectral width of 0.5%-2.5%. This technique allows one to accelerate electrons from rest to keV energies while reaching a narrow spectrum of kinetic energies and femtosecond pulsed operation.

Properties of electron lenses produced by ponderomotive potential with Bessel and Laguerre–Gaussian beams

The properties of electron round lenses produced by the ponderomotive potential are investigated in geometrical optics. The potential proportional to the intensity distribution of a focused first-order Bessel or Laguerre–Gaussian (LG) beam is exploited to produce an electron round lens and a third-order spherical aberration (SA) corrector. Several formulas for the focal length and SA coefficients in the thin-lens approximation are derived to set the lens properties and associated light beam parameters. When the mode field of the optical beam is small, the electron trajectory calculation results show properties similar to those obtained using the formulas. Alternatively, large higher-order aberrations are introduced because of the annular distribution of the potential. The second- and higher-order Bessel and LG beams produce no focusing power and no negative third-order SA; however, they can still be used as circularly symmetric higher-order aberration correctors. Results show that the ponderomotive potential–based electron lens or phase plate forms a refractive index medium with a shape that is considerably more flexible than that achieved in the case of conventional electrostatic and magnetic electron optics. The formulas presented herein can serve as guidelines for designing preferred light fields, thus promoting the advancement of a novel technology in electron optics that exploits the electron–light interaction.

Photoelectron energy peaks shift against the radiation pressure in strong-field ionization.

The photoelectric effect describes the ejection of an electron upon absorption of one or several photons. The kinetic energy of this electron is determined by the photon energy reduced by the binding energy of the electron and, if strong laser fields are involved, by the ponderomotive potential in addition. It has therefore been widely taken for granted that for atoms and molecules, the photoelectron energy does not depend on the electron’s emission direction, but theoretical studies have questioned this since 1990. Here, we provide experimental evidence that the energies of photoelectrons emitted against the light propagation direction are shifted toward higher values, while those electrons that are emitted along the light propagation direction are shifted to lower values. We attribute the energy shift to a nondipole contribution to the ponderomotive potential that is due to the interaction of the moving electrons with the incident photons.

Magnetic-Field Effect in High-Order Above-Threshold Ionization.

We experimentally and theoretically investigate the influence of the magnetic component of an electromagnetic field on high-order above-threshold ionization of xenon atoms driven by ultrashort femtosecond laser pulses. The nondipole shift of the electron momentum distribution along the light-propagation direction for high energy electrons beyond the 2U_{p} classical cutoff is found to be vastly different from that below this cutoff, where U_{p} is the ponderomotive potential of the driving laser field. A local minimum structure in the momentum dependence of the nondipole shift above the cutoff is identified for the first time. With the help of classical and quantum-orbit analysis, we show that large-angle rescattering of the electrons strongly alters the partitioning of the photon momentum between electron and ion. The sensitivity of the observed nondipole shift to the electronic structure of the target atom is confirmed by three-dimensional time-dependent Schrödinger equation simulations for different model potentials. Our work paves the way toward understanding the physics of extreme light-matter interactions at long wavelengths and high electron kinetic energies.

Anomalous two-photon Compton scattering

X-ray free-electron lasers can generate radiation pulses with extreme peak intensities at short wavelengths. This enables the investigation of laser–matter interactions in a regime of high fields, yet at a non-relativistic ponderomotive potential, where ordinary rules of light–matter interaction may no longer apply and nonlinear processes are starting to become observable. Despite small cross-sections, first nonlinear effects in the hard x-ray regime have recently been observed in solid targets, including x-ray-optical sum-frequency generation (XSFG), x-ray second harmonic generation (XSHG) and two-photon Compton scattering (2PCS). Nonlinear interactions of bound electrons in the x-ray range are fundamentally different from those dominating at optical frequencies. Whereas in the optical regime nonlinearities are predominantly caused by anharmonicities of the atomic potential in the chemical bonds, x-ray nonlinearities far above atomic resonances are expected to be due to nonlinear oscillations of quasi-free electrons, including inner-shell atomic electrons. While the quasi-free-electron model agrees reasonably well with the experimental data for XSFG and XSHG, 2PCS measurements have led to unexpected results: the energy of the nonlinearly scattered photons from non-relativistic electrons shows a substantial unexpected red shift in addition to the Compton shift that is well beyond that predicted by a nonlinear quantum electrodynamics model for free electrons.A potential explanation for the spectral broadening is based on a previously unexplored scattering process that involves the whole atom rather than just quasi-free electrons. A first simulation that includes the atomic binding potential was successful in describing a broadening of the spectrum of the nonlinearly scattered photons to longer wavelengths for soft x-rays. However, the same model does not show any broadening at hard x-ray wavelengths, which is in agreement with other simulation approaches. To this point no calculation has been able to reproduce the experimentally observed broadening.Here we present further experimental data of 2PCS for an extended parameter range using additional diagnostics. In particular, we present measurements of the electron momentum distribution during the interaction that strongly suggest that the spectral broadening is not caused by an increased plasma temperature. We extend our measurement of the magnitude of the red shift in beryllium to in addition to the Compton shift expected for free electrons and expand the measurement of the angular distribution to include forward scattering angles. We also present first measurements of 2PCS from diamond.

Quantum Computing with Circular Rydberg Atoms

Rydberg atom arrays are a leading platform for quantum computing and simulation, combining strong interactions with highly coherent operations and flexible geometries. However, the achievable fidelities are limited by the finite lifetime of the Rydberg states, as well as technical imperfections such as atomic motion. In this work, we propose a novel approach to Rydberg atom arrays using long-lived circular Rydberg states in optical traps. Based on the extremely long lifetime of these states, exceeding seconds in cryogenic microwave cavities that suppress radiative transitions, and gate protocols that are robust to finite atomic temperature, we project that arrays of hundreds of circular Rydberg atoms with two-qubit gate errors around $10^{-5}$ can be realized using current technology. This approach combines several key elements, including a quantum nondemolition detection technique for circular Rydberg states, local manipulation using the ponderomotive potential of focused optical beams, a gate protocol using multiple circular levels to encode qubits, and robust dynamical decoupling sequences to suppress unwanted interactions and errors from atomic motion. This represents a significant improvement on the current state-of-the-art in quantum computing and simulation with neutral atoms.

Electron Round Lenses with Negative Spherical Aberration by a Tightly Focused Cylindrically Polarized Light Beam

Free electrons moving in an optical standing wave field feel the ponderomotive potential, acting as a refractive-index medium in electron optics. Emerging technologies involving this potential have been proposed and realized in electron microscopy, such as electron phase-contrast imaging using a laser standing wave in an optical enhancement cavity. However, the interaction between electrons with a cylindrically distributed optical field has not been investigated although its suitability for electron-optical imaging systems. In this study, we theoretically show that the divergence and convergence forces are provided by tightly focused cylindrically polarized light beams. The radially and azimuthally polarized beams with an annular profile are focused using a high numerical aperture optical lens. The intensity distributions at the focus function are concave and convex electron round lenses, respectively. The convex lens formed by the azimuthally polarized beam possesses negative (opposite sign) spherical aberration compared with conventional electron round lenses created by electrodes and magnetic coils. This remarkable result will contribute to the innovative design of electron-optical imaging systems and bring new capabilities into matter-wave optics.

Chip-based electrostatic beam splitting of guided kiloelectron volt electrons

We present a beam splitter for guided electrons using an electrostatic guiding potential created above the surface of two opposing planar microstructured printed circuit boards. The electric fields acting on the electrons result in a ponderomotive potential. We show that we can smoothly transition the ponderomotive potential from a single-well into a double-well, which leads to the splitting of the electron beam. Efficient beam splitting is observed over a large range of kinetic energies starting at 200 eV up to 1700 eV. We discuss future work needed to reach adiabatic beam splitting for quantum state-selective electron optics. This will pave the way for an electron interferometer on a chip and, therefore, result in until now not possible elements for electron optics and microscopy.

Knotted trajectories of neutral and charged particles in Gaussian light beams

Making use of the equivalence between paraxial wave equation and two-dimensional Schr\"odinger equation, Gaussian beams of monochromatic light, possessing knotted nodal structures are obtained in an analytical way. These beams belong to the wide class of paraxial beams called the Hypergeometric-Gaussian beams [E. Karimi, G. Zito, B. Piccirillo, L. Marrucci and E. Santamato, Opt. Lett. {\bf 32}, 3053(2007)]. Four topologies are dealt with: the unknot, the Hopf link, the Borromean rings and the trefoil. It is shown in the numerical way that neutral polarizable particles placed in such light fields, upon precise tuning of the initial conditions, can be forced to follow the identical knotted trajectories. A similar outcome is also valid for charged particles that are subject to a ponderomotive potential. This effect can serve to precisely steer particles along chosen complicated pathways exhibiting non-trivial topological character, guide them around obstacles and seems to be helpful in engineering more complex nanoparticles.