Showing papers in "Journal of Physics B in 2004"

Bosonizing one-dimensional cold atomic gases

Abstract: We present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The results are obtained using Haldane's harmonic-fluid approach (also known as 'bosonization'), and are valid for both bosons and fermions, in weakly and strongly interacting regimes. The harmonic-fluid approach and the method of computing the correlation functions using conformal transformations are explained in great detail. As an application relevant to one-dimensional systems of cold atomic gases, we consider the model of bosons interacting with a zero-range potential. The Luttinger-liquid parameters are obtained from the exact solution by solving the Bethe-ansatz equations in finite-size systems. The range of applicability of the approach is discussed, and the prefactor of the one-body density matrix of bosons is fixed by finding an appropriate parametrization of the weak-coupling result. The formula thus obtained is shown to be accurate, when compared with recent diffusion Monte Carlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.

Solving the three-body Coulomb breakup problem using exterior complex scaling

Abstract: Electron-impact ionization of the hydrogen atom is the prototypical three-body Coulomb breakup problem in quantum mechanics. The combination of subtle correlation effects and the difficult boundary conditions required to describe two electrons in the continuum have made this one of the outstanding challenges of atomic physics. A complete solution of this problem in the form of a 'reduction to computation' of all aspects of the physics is given by the application of exterior complex scaling, a modern variant of the mathematical tool of analytic continuation of the electronic coordinates into the complex plane that was used historically to establish the formal analytic properties of the scattering matrix. This review first discusses the essential difficulties of the three-body Coulomb breakup problem in quantum mechanics. It then describes the formal basis of exterior complex scaling of electronic coordinates as well as the details of its numerical implementation using a variety of methods including finite difference, finite elements, discrete variable representations and B-splines. Given these numerical implementations of exterior complex scaling, the scattering wavefunction can be generated with arbitrary accuracy on any finite volume in the space of electronic coordinates, but there remains the fundamental problem of extracting the breakup amplitudes from it. Methods are described for evaluating these amplitudes. The question of the volume-dependent overall phase that appears in the formal theory of ionization is resolved. A summary is presented of accurate results that have been obtained for the case of electron-impact ionization of hydrogen as well as a discussion of applications to the double photoionization of helium.

Symplectic invariants, entropic measures and correlations of Gaussian states

Abstract: We present a derivation of the Von Neumann entropy and mutual information of arbitrary two-mode Gaussian states, based on the explicit determination of the symplectic eigenvalues of a generic covariance matrix. The key role of the symplectic invariants in such a determination is pointed out. We show that the Von Neumann entropy depends on two symplectic invariants, while the purity (or the linear entropy) is determined by only one invariant, so that the two quantities provide two different hierarchies of mixed Gaussian states. A comparison between mutual information and entanglement of formation for symmetric states is considered, taking note of the crucial role of the symplectic eigenvalues in qualifying and quantifying the correlations present in a generic state.

Reading diffraction images in strong field ionization of diatomic molecules

Abstract: We present a theoretical analysis of how intense, few-cycle infrared laser pulses can be used to image the structure of small molecules with nearly 1 fs temporal and sub-A spatial resolution. We identify and analyse several physical mechanisms responsible for the distortions of the diffraction image and describe a recipe for recovering an un-distorted image from angle and energy-resolved electron spectra. We also identify holographic patterns in the photoelectron spectra and discuss the requirements to enhancing the hologram resolution for imaging the scattering potential.

Resonant structures in the low-energy electron continuum for single ionization of atoms in the tunnelling regime

Abstract: We present high-resolution fully differential experimental data on single ionization of He, Ne and Ar by ultra-short (25 fs, 6 fs) 795 nm laser pulses at intensities 0.15–2.0 × 1015 W cm−2. We show that the ATI-like pattern can survive deep in the tunnelling regime and that the atomic structure plays an important role in the formation of the low-energy photoelectron spectra even at high intensities. The absence of ponderomotive shifts, the splitting of the peaks and their degeneration for few-cycle pulses indicate that the observed structures originate from a resonant process.

B-spline Breit?Pauli R-matrix calculations for electron collisions with argon atoms

Abstract: We have applied the Breit–Pauli B-spline R-matrix method described earlier (J. Phys. B: At. Mol. Opt. Phys. 37 (2004) 2173) to the treatment of e–Ar collisions. An individually optimized, term-dependent set of non-orthogonal valence orbitals is used to account for the strong term dependence in the one-electron orbitals. Concentrating on the near-threshold regime for excitation of the 3p54s manifold, we obtain excellent agreement with benchmark experimental data for the production of metastable atoms and for excitation of the VUV-emitting J = 1 levels. A detailed partial-wave resolved resonance analysis shows that many of the structures listed by Buckman and Clark (Rev. Mod. Phys. 66 (1994) 539) are composed of overlapping resonances. These, together with their principal components and decay channels, are identified and, in some cases, alternative classifications are suggested.

Testing the multi-configuration time-dependent Hartree-Fock method

Abstract: We test the multi-configuration time-dependent Hartree–Fock method as a new approach towards the numerical calculation of dynamical processes in multi-electron systems using the harmonic quantum dot and one-dimensional helium in strong laser pulses as models. We find rapid convergence for quantities such as ground-state population, correlation coefficient and single ionization towards the exact results. The method converges, where the time-dependent Hartree–Fock method fails qualitatively.

Physics with electrostatic rings and traps

Abstract: The recent development of electrostatic devices which allow us to store keV ion beams has launched several new kinds of investigations. We review the basic ideas behind the development of the electrostatic ion storage ring and the electrostatic ion beam trap techniques. The various experiments performed with atomic and molecular ion beams, ranging from the measurement of lifetimes of metastable atomic states up to biological applications and single component plasma studies are discussed.

Atomic Structure Dependence of Nonsequential Double Ionization of He, Ne and Ar in Strong Laser Pulses

Abstract: The ion momentum spectra for nonsequential double ionization of rare gases (He, Ne and Ar) in 23 fs 795 nm laser pulses were measured in the intensity range 0.075–1.25 PW cm−2. In the studies published, confusing differences in the shape of momentum distributions among different targets are consistently explained within a recollision scenario: excitation during recollision plus subsequent field ionization, not implemented in most theoretical approaches, evidently plays a decisive role for He and Ar nonsequential double ionization whereas it plays only a minor role for Ne.

Electron-impact excitation of neon: a pseudo-state convergence study

Abstract: A number of convergent close-coupling and R-matrix with pseudo-state (RMPS) calculations for H-like, He-like, Li-like and Be-like ions have demonstrated that coupling to the target continuum can have large effects on the electron-impact excitation cross sections of neutral and low-charge species. However, no one has yet attempted such advanced calculations on a system as complex as neutral neon. We report on a series of RMPS calculations of electron-impact excitation of Ne using recently developed parallel Breit-Pauli R-matrix programs. Our largest calculation included 235 spectroscopic and pseudo-state levels in the close-coupling expansion of the target. Although the results clearly reveal the importance of coupling to the target continuum in this atom, the pseudo-state expansion is not yet sufficiently complete to provide reliable cross sections for energies above the ionization limit. However, this is the largest intermediate-coupling calculation that can be performed with present computer resources. Thus, we have also carried out a series of RMPS calculations in LS coupling with different pseudo-state expansions. Comparisons of these results have allowed us to determine the approximate size of the pseudo-state expansion required to achieve convergence in future intermediate-coupling calculations for neon.

Vibrational structure in inner shell photoionization of molecules

Abstract: The sudden removal of an inner shell electron from a molecule by photoionization generally leads to the production of vibrationally excited cationic states. Recent experimental results on this phenomenon, most of them obtained on third generation synchrotron radiation sources, are reviewed. Most of the examples that will be discussed involve small molecules with second row constituent atoms, such as C, N and O. In detail, the inner shell photoelectron spectra of CH4, CO, N2, O2, CO2, ethane, furan and benzene will be discussed. Emphasis will be placed on the coupling of the vibrational with the electronic structure in the case of degenerate or nearly degenerate electronic final states.

Adiabatic association of ultracold molecules via magnetic-field tunable interactions

Abstract: We consider in detail the situation of applying a time-dependent external magnetic field to a 87Rb atomic Bose–Einstein condensate held in a harmonic trap, in order to adiabatically sweep the interatomic interactions across a Feshbach resonance to produce diatomic molecules. To this end, we introduce a minimal two-body Hamiltonian depending on just five measurable parameters of a Feshbach resonance, which accurately determines all low-energy binary scattering observables, in particular, the molecular conversion efficiency of just two atoms. Based on this description of the microscopic collision phenomena, we use the many-body theory of Kohler and Burnett (2002 Phys. Rev. A 65 033601) to study the efficiency of the association of molecules in a 87Rb Bose–Einstein condensate during a linear passage of the magnetic-field strength across the 100 mT Feshbach resonance. We explore different, experimentally accessible, parameter regimes, and compare the predictions of Landau–Zener, configuration interaction, and two-level mean-field calculations with those of the microscopic many-body approach. Our comparative studies reveal a remarkable insensitivity of the molecular conversion efficiency with respect to both the details of the microscopic binary collision physics and the coherent nature of the Bose–Einstein condensed gas, provided that the magnetic-field strength is varied linearly. We provide the reasons for this universality of the molecular production achieved by linear ramps of the magnetic-field strength, and identify the Landau–Zener coefficient determined by Mies et al (2000 Phys. Rev. A 61 022721) as the main parameter that controls the efficiency.

Two-pulse alignment of molecules

Abstract: Field-free alignment of gas-phase molecules can be achieved by creating rotational wavepackets with a short laser pulse. We demonstrate that the degree of alignment can be improved by illuminating the molecules with a second laser pulse at a specific time during the evolution of the original rotational wavepacket.

Chemical reactions in the limit of zero kinetic energy: virtual states and Ramsauer minima in F + H2 → HF + H

Abstract: The behaviour of reactive scattering at ultracold temperatures is explored by calculating the real and imaginary parts of the scattering length for the reaction of F with a molecule composed of a pair of pseudo-hydrogen atoms of arbitrary mass. The origin of a low energy feature in the cross section for the reaction of F with H2 and its absence for the reaction with D2 is investigated. Close-coupling calculations of the scattering matrix show that the F–H2 feature arises from the presence of a virtual state associated with the van der Waals well in the entrance channel and that the virtual state is responsible for the enhanced zero temperature rate coefficient of the F–H2 reaction. For a mass of about 1.12 hydrogen masses the virtual state turns into a zero energy resonance and the corresponding zero temperature rate coefficient is 1 × 10−9 cm3 s−1 despite an energy barrier of 300 K. Evidence in support of the virtual state is also provided by the detection of a deep Ramsauer–Townsend minimum in the elastic component of the total cross section for F–H2 which the present calculations predict to occur at low energies.

Dynamics of positive- and negative-mass solitons in optical lattices and inverted traps

Abstract: We study the dynamics of one-dimensional solitons in attractive and repulsive Bose–Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. First, we demonstrate analytically that, in the repulsive BEC, where the soliton is of the gap type, its effective mass is negative. This gives rise to a prediction for the experiment: such a soliton cannot be held by the usual parabolic trap, but it can be captured (performing slow harmonic oscillations, with a period that is estimated to be ~0.01 s in realistic experimental conditions) by an anti-trapping inverted parabolic potential. We also study the motion of the soliton in a long system, concluding that, in the cases of both the positive and negative mass, it moves freely, provided that its amplitude is below a certain critical value; above it, the soliton's velocity decreases due to interaction with the OL. At a later stage, the damped motion becomes chaotic. We also investigate the evolution of a two-soliton pulse in the attractive model. The pulse generates a persistent breather, if its amplitude is not too large; otherwise, fusion into a single fundamental soliton takes place. Collisions between two solitons captured in the parabolic trap or anti-trap are considered too. Depending on their amplitudes and phase difference, the solitons either perform stable oscillations, colliding indefinitely many times, or merge into a single soliton. Effects reported in this work for BECs can also be formulated for optical solitons in nonlinear photonic crystals. In particular, the capture of the negative-mass soliton in the anti-trap implies that a bright optical soliton in a self-defocusing medium with a periodic structure of the refractive index may be stable in an anti-waveguide.

Implementation of exterior complex scaling in B-splines to solve atomic and molecular collision problems

Abstract: B-spline methods are now well established as widely applicable tools for the evaluation of atomic and molecular continuum states. The mathematical technique of exterior complex scaling has been shown, in a variety of other implementations, to be a powerful method with which to solve atomic and molecular scattering problems, because it allows the correct imposition of continuum boundary conditions without their explicit analytic application. In this paper, an implementation of exterior complex scaling in B-splines is described that can bring the well-developed technology of B-splines to bear on new problems, including multiple ionization and breakup problems, in a straightforward way. The approach is demonstrated for examples involving the continuum motion of nuclei in diatomic molecules as well as electronic continua. For problems involving electrons, a method based on Poisson's equation is presented for computing two-electron integrals over B-splines under exterior complex scaling.

Low-energy electron collisions with water: elastic and rotationally inelastic scattering

Abstract: Differential, integral and momentum transfer cross sections for the vibrationally elastic and rotationally inelastic scattering of electrons from water at low collision energies (E < 7 eV) are reported. The R-matrix method is used to compute the body-fixed T-matrices while the scattering calculations are performed within the fixed-nuclei approximation corrected with the standard Born-closure formula. Our calculations are compared with the very recent experimental results of Cho et al (2003 Radiat. Phys. Chem. 68 115). The differential and momentum transfer cross sections are in good agreement with the experimental results. The relative contribution of the rotationally inelastic processes is investigated in some detail. In particular, the importance of the pure elastic process at very low energy is emphasized.

Electron impact excitation of the argon 3p54s configuration: differential cross-sections and cross-section ratios

Abstract: New electron-impact differential cross-section (DCS) and DCS ratio measurements for the excitation of the four levels making up the 3p54s configuration of argon are reported at incident electron energies of 14, 15, 17.5, 20, 30, 50 and 100 eV. These cross-sections were obtained using a conventional high resolution electron spectrometer. Elastic electron scattering from argon was used as a calibration standard. Electron–helium DCSs were used to determine the instrumental transmission of the spectrometer. Further checks of the relative shape of these DCS measurements were made using the method of gas mixtures (Ne mixed with Ar). We also present results from new calculations of these DCSs using the R-matrix method, the unitarized first-order many-body theory, the semi-relativistic distorted-wave Born approximation, and the relativistic distorted-wave method. Comparison with available experimental DCSs and DCS ratios is also presented.

Measurements of elastic electron scattering by water vapour extended to backward angles

Abstract: Absolute differential cross sections for elastic electron scattering by water vapour have been measured at nine incident electron energies between 4 to 50 eV and over scattering angles between 10° and 180°, using a crossed-beam electron spectrometer. A magnetic angle-changing device based on the design of Read and co-workers has been used to extend the measurements to backward angles (125° to 180°). The elastic integral and momentum transfer cross sections are derived from these elastic differential cross sections. Previous experimental results at backward angles, available only up to 156°, are consistently higher than the present results. We also compare, where possible, with results from recent theoretical calculations.

S-wave resonances in e + -He scattering below the Ps (n = 2) excitation threshold

Abstract: Two S-wave resonances in the positron–helium system are calculated using the stabilization method. A model potential for helium is used to represent the He+ ion core and the outer electron. Hylleraas-type wavefunctions are used to represent the correlation effects between the outer electron, the positron and the He+ core. Resonance energies and widths for two resonances lying below the Ps (n = 2) threshold are reported.

Electron?H+3 collisions at intermediate energies

Abstract: A new procedure is presented for the ab initio study of electron-molecule collision at energies straddling the target ionization threshold. The R-matrix with pseudostates method, which allows for the inclusion of discretized continuum states in a close-coupling expansion, is adapted to molecular targets using even-tempered basis sets. Calculations for electron collisions with the H-3(+) molecular ion provide converged polarizabilities, electronic excitation and ionization cross sections.

Dissociative ionization at high laser intensities: importance of resonances and relaxation for fragmentation

Abstract: We investigated dissociative single and double ionization of the metal carbonyls Ni(CO)4, Fe(CO)5 and Cr(CO)6 in the gas phase by means of laser pulses of different durations (30–110 fs) and wavelengths (0.8 and 1.35 µm) at intensities of 2 × 1012–2 × 1014 W cm−2. The mass spectra show striking differences: for example, Fe(CO)5 strongly fragments at 0.8 µm but little at 1.35 µm, whereas for Ni(CO)4 fragmentation is higher at 1.35 µm than at 0.8 µm; chromium carbonyl shows little fragmentation at both wavelengths. In other cases, fragmentation first decreases and then increases again with intensity. These and other phenomena, also published ones, can readily be understood from long-known principles, namely resonances in the parent ions, sometimes also in the neutral molecules, in particular if relaxations are also taken into account. We emphasize that fragmentation and ionization are two separate processes. We also point out that in the process of dissociative ionization in intense laser radiation, one should generally consider intermediate states, even if there is no one-photon resonance.

Two-dimensional loosely and tightly bound solitons in optical lattices and inverted traps

Abstract: We study the dynamics of nonlinear localized excitations ('solitons') in two-dimensional (2D) Bose?Einstein condensates (BECs) with repulsive interactions, loaded into an optical lattice (OL), which is combined with an external parabolic potential First, we demonstrate analytically that a broad ('loosely bound', LB) soliton state, based on a 2D Bloch function near the edge of the Brillouin zone (BZ), has a negative effective mass (while the mass of a localized state is positive near the BZ centre) The negative-mass soliton cannot be held by the usual trap, but it is safely confined by an inverted parabolic potential (anti-trap) Direct simulations demonstrate that the LB solitons (including those with intrinsic vorticity) are stable and can freely move on top of the OL The frequency of the elliptic motion of the LB-soliton's centre in the anti-trapping potential is very close to the analytical prediction which treats the solition as a quasi-particle In addition, the LB soliton of the vortex type features real rotation around its centre We also find an abrupt transition, which occurs with the increase of the number of atoms, from the negative-mass LB states to tightly bound (TB) solitons An estimate demonstrates that for the zero-vorticity states, the transition occurs when the number of atoms attains a critical number Ncr ~ 103, while for the vortex the transition takes place at Ncr ~ 5 ? 103 atoms The positive-mass LB states constructed near the BZ centre (including vortices) can also move freely The effects predicted for BECs also apply to optical spatial solitons in bulk photonic crystals

The photoionization and fragmentation of C60 in the energy range 26–130 eV

Abstract: We report on experimental results for the ionization and fragmentation of C60 after excitation with synchrotron radiation in the energy range 26–130 eV. The cross-section energy dependence of the produced Cq+60 ions (q = 1, 2, 3) and charged fragments is analysed. The Cq+60-ion yields (q = 2, 3) are explained within the framework of T D Thomas' model for multiple ionization.

Numerical treatment of diatomic two-electron molecules using a B-spline based CI method

Abstract: A B-spline based configuration–interaction method for diatomic two-electron molecules has been developed and implemented. The molecular symmetry of the problem is fully accounted for by using the prolate-spheroidal coordinate system. The performance of the method is demonstrated in a number of test applications. This includes the calculation of the energies of the ground and excited states of H2 (even autoionizing doubly-excited states) as well as transition dipole moments. Furthermore, a partial photoionization cross-section for HeH+ was calculated. In all these cases a favourable comparison to the literature values is found. This indicates the broad applicability of the present approach.

High resolution kinetic energy release spectra and angular distributions from double ionization of nitrogen and oxygen by short laser pulses

Abstract: We have used momentum imaging techniques to measure in high resolution the kinetic energy release spectra and angular distributions of coincident O + and N + ion pairs produced by short laser pulses (8–35 fs) on targets of N2 and O2 at peak intensities between 1 and 12 × 10 14 Wc m −2 . We record the full momentum vectors of both members of each pair and achieve a kinetic energy release resolution of less than 0.3 eV. We find that the process proceeds through well-defined electronic states of the excited molecular dications. Using linear and circularly polarized light, we identify two mechanisms for the production of these states, rescattering and sequential ionization. By using 8 fs pulses, we observe that the internuclear distance can be frozen during the pulse. For low intensities and 8 fs pulses, emission from N2 is strongly directed along the polarization vector, while that for O2 is not, a result we interpret as being due to the different symmetries of the outer orbitals of these molecules. For high intensities and longer pulses, the distributions increasingly fold towards the polarization vector, ultimately peaking at zero degrees for both molecules. For oxygen, a local peaking for molecules aligned at right angles to the polarization vector is seen. A discussion and interpretation of the results are presented. (Some figures in this article are in colour only in the electronic version)

Partial cross sections for positive and negative ion formation following electron impact on uracil

Abstract: We report absolute partial cross sections for the formation of selected positive and negative ions resulting from electron interactions with uracil. Absolute calibration of the measured partial cross sections for the formation of the three most intense positive ions, the parent C4H4N2O+2 ion and the C3H3NO+ and OCN+ fragment ions, was achieved by normalization of the total single uracil ionization cross section (obtained as the sum of all measured partial single ionization cross sections) to a calculated cross section based on the semi-classical Deutsch–Mark formalism at 100 eV. Subsequently, we used the OCN+ cross section in conjunction with the known sensitivity ratio for positive and negative ion detection in our apparatus (obtained from the well-known cross sections for SF+4 and SF−4 formation from SF6) to determine the dissociative attachment cross section for OCN− formation from uracil. This cross section was found to be roughly an order of magnitude smaller, about 5 × 10−22 m2 at 6.5 eV, compared to our previously reported preliminary value. We attribute this discrepancy to the difficult determination of the uracil target density in the earlier work. Using a reliably calculated cross section for normalization purposes avoids this complication.

Three-dimensional simulation of jet formation in collapsing condensates

Abstract: We numerically study the behaviour of collapsing and exploding condensates using the parameters of the experiments by Donley et al (2001 Nature 412 295). Our studies are based on a full three-dimensional numerical solution of the Gross–Pitaevskii equation (GPE) including three-body loss. We determine the three-body loss rate from the number of remnant condensate atoms and collapse times, and obtain only one possible value which fits with the experimental results. We then study the formation of jet atoms by interrupting the collapse, and find very good agreement with the experiment. Furthermore, we investigate the sensitivity of the jets to the initial conditions. According to our analysis, the dynamics of the burst atoms is not described by the GPE with three-body loss incorporated.

Lifetime of a K-shell vacancy in atomic carbon created by 1s → 2p photoexcitation of C+

Abstract: Lifetimes for K-shell vacancy states in atomic carbon have been determined by measurement of the natural linewidth of the 1s → 2p photoexcited states of C + ions. The K-shell vacancy states produced by photoionization of atomic carbon are identical to those produced by 1s → 2p photoexcitation of a C + ion: 1s2s 2 2p 22 D, 2 P, and 2 S autoionizing states occur in both cases. These vacancy states stabilize by emission of an electron to produce C 2+ ions. Measurements are reported for the lifetime of the 1s2s 2 2p 22 D, 2 P and 2 S autoionizing states of C + :6 .3± 0.9 fs, 11.2 ± 1.1 fs and 5.9 ± 1.3 fs respectively. Knowledge of such lifetimes is important for comparative studies of the lifetimes of Kshell vacancies in carbon-containing molecules, benchmarking theory, and interpreting satellite x-ray spectra from astrophysical sources such as x-ray binaries. Absolute cross sections were measured for both ground-state and metastable-state ions providing a stringent test of state-of-the-art theoretical calculations. Carbon is ubiquitous in nature and is the building block of life. This atom in its various stages of ionization has relatively few electrons, and is thus amenable to theoretical study. Lifetimes