We present the angular distribution of electrons knocked out from an atom in a fast charge particle collision at small momentum transfer. It is determined not only by dipole but also by quadrupole transitions, the contribution of which can be considerably enhanced as compared to the case of photoionization. There the non-dipole parameters are suppressed as compared to the dipole ones by the parameter ωR/c << 1, where is the photon energy, R is the ionized shell radius and c is the speed of light. This suppression in fast electron-atom collisions can be considerably reduced: the corresponding expansion parameter ωR/ ν<< 1 is much bigger than in photoionization, since the speed of the incoming electron is much smaller than c. In formation of the angular distribution it is decisively important that the ionizing field in collision process is longitudinal, while in photoionization - it is transversal.
We illustrate the general formulas by concrete results for outer s-, p-, and some nd-subshells of multi-electron noble gas atoms Ar, Kr and Xe, at several transferred momentum values: q=0.0, 0.1, 1.1, 2.1. Even for very small transferred momentum q, i.e. in the so-called optical limit, the deviations from the photoionization case are prominent.
`Additional' ionization of light atoms and ions during nuclear $β^{-}$ decay is investigated. The procedure which can be used to determine the corresponding transition probabilities and the velocity/energy spectrum of secondary electrons is developed. Emission of very fast secondary electrons ($δ-$electrons) from $β^{-}$-decaying atoms is also briefly discussed.
Ionization of the final ${}^{3}$He$^{+}$ ion during the nuclear $β^{-}$-decay of the tritium atom is discussed. The velocity spectrum of the emitted secondary electrons is derived in the explicit form. Our method allows to determine the relative and absolute probabilities of formation of the final states in few-electron atoms which include `free' secondary electrons moving with different velocities. \noindent PACS number(s): 23.40.-s, 12.20.Ds and 14.60.Cd
Light beams carrying orbital angular momentum, such as Laguerre-Gaussian beams, give rise to the violation of the standard dipolar selection rules during the interaction with matter yielding, in general, an exchange of angular momentum larger than hbar per absorbed photon. By means of ab initio 3D numerical simulations, we investigate in detail the interaction of a hydrogen atom with intense Gaussian and Laguerre-Gaussian light pulses. We analyze the dependence of the angular momentum exchange with the polarization, the orbital angular momentum, and the carrier-envelope phase of light, as well…
Partitioning of helium atom's correlation energy into radial and angular contributions, although of fundamental interest, has eluded critical scrutiny. Conventionally, radial and angular correlation energies of helium atom are defined for its ground state as deviations, from Hartree--Fock and exact values, of the energy obtained using a purely radial wavefunction devoid of any explicit dependence on the interelectronic distance. Here, we show this rationale to associate the contribution from radial-angular coupling entirely to the angular part underestimating the radial one, thereby also incor…
We demonstrate that the angular distribution of electrons knocked out from an atom by a fast charge particle is determined not only by dipole but also by quadrupole transitions, the contribution of which can be considerably enhanced as compared to the case of photoionization. To obtain these matrix elements one has to study the angular distribution of electrons emitted by the atom in its collision with a fast charged particle. The distribution has to be measured relative to the momentum q transferred from the projectile to the target atom. The situation is similar, but not identical to the pho…
Recent experiments involving the interaction of optical vortices with atoms in quadrupole transitions have been shown to be accompanied by the exchange of orbital angular momentum (OAM) between the electronic states of the atom and the optical vortex field. Earlier work by both theory and experiment had ruled out the transfer of a vortex OAM to the electronic degrees of freedom in an electric dipole atomic transition and it has been confirmed that the lowest multipolar order involving an OAM transfer to the electronic motion is indeed the electric quadrupole. Hitherto, the quadrupole transitio…
We measure the angular dependence of the resonant dipole-dipole interaction between two individual Rydberg atoms with controlled relative positions. By applying a combination of static electric and magnetic fields on the atoms, we demonstrate the possibility to isolate a single interaction channel at a Förster resonance, that shows a well-defined angular dependence. We first identify spectroscopically the Förster resonance of choice and we then perform a direct measurement of the interaction strength between the two atoms as a function of the angle between the internuclear axis and the quantiz…
We propose a scheme to distinguish the orbital angular momentum state of the Laguerre-Gaussian (LG) beam based on the electromagnetically induced transparency modulated by a microwave field in atomic ensembles. We show that the transverse phase variation of a probe beam with the LG mode can be mapped into the spatial intensity distribution due to the change of atomic coherence caused by the microwave. The proposal may provide a useful tool for studying higher-dimensional quantum information based on atomic ensembles.
We analyze the collective light scattering by cold atoms in free space of a pump laser beam possessing orbital angular momentum. We derive a set of coupled equations for the atomic motion in which the vacuum-mode field is adiabatically eliminated. The resulting equations describe collective recoil as due to either transfer of linear momentum or orbital angular momentum. For a transverse annular atomic distribution the initial equilibrium with uniform atomic phases and no scattered field, is unstable. The atoms are set in rotation and bunched in phase at different harmonics depending on the pum…
We obtain an expression for the matrix element for a twisted (Laguerre-Gaussian profile) photon scattering from a hydrogen atom. We consider photons incoming with an orbital angular momentum (OAM) of $\ell \hbar$, carried by a factor of $e^{i \ell ϕ}$ not present in a plane-wave or pure Gaussian profile beam. The nature of the transfer of $+2\ell$ units of OAM from the photon to the azimuthal atomic quantum number of the atom is investigated. We obtain simple formulae for these OAM flip transitions for elastic forward scattering of twisted photons when the photon wavelength $λ$ is large compar…
The problem of angular correlation in the double photoionization (DPI) of rare gas atoms is considered in some depth. We refer particularly to the efficiency operator for the detection of an electron by a detector having cylindrical symmetry. The different factors in the efficiency operator are discussed in detail keeping in mind the fundamental epistemological question of the role of the detection process in such experiments.
Exchange of orbital angular momentum between Laguerre-Gaussian beam of light and center-of-mass motion of an atom or molecule is well known. We show that orbital angular momentum of light can also be transferred to the internal electronic or rotational motion of an atom or a molecule provided the internal and center-of-mass motions are coupled. However, this transfer does not happen directly to the internal motion, but via center-of-mass motion. If atoms or molecules are cooled down to recoil limit then an exchange of angular momentum between the quantized center-of-mass motion and the interna…
In this paper we have tried to establish a theory for angular correlation between the photo- and Auger electrons in the two-step double photoionization of a rare gas atom. The basic finding of this paper is that a general theoretical expression for the angular correlation function is established in the problem of double photoionization of atoms in the presence of linearly polarized monochromatic light. We consider the case of a xenon atom and the incident light is of (94.5 eV) with arbitrary linear polarization. The theoretical results are compared with the experiments done by K(\ddot{a} )mmer…
Photoelectron angular distributions of the two-photon ionization of neutral atoms are theoretically investigated. Numerical calculations of two-photon ionization cross sections and asymmetry parameters are carried out within the independent-particle approximation and relativistic second-order perturbation theory. The dependence of the asymmetry parameters on the polarization and energy of the incident light as well as on the angular momentum properties of the ionized electron are investigated. While dynamic variations of the angular distributions at photon energies near intermediate level reso…
The problem of angular correlation in the double photoionization (DPI) of rare gas atoms is considered in some depth. We refer particularly to the efficiency operator for the detection of an electron by a detector having the shape of a right circular cylinder. The different factors in the efficiency operator are discussed in detail keeping in mind the fundamental epistemological question of the role of the observer (or his equipment) in such experiments.
Many atomic processes result in the emission of photons. Analysis of the properties of emitted photons, such as energy and angular distribution as well as polarization, is regarded as a powerful tool for gaining more insight into the physics of corresponding processes. Another characteristic of light is the projection of its angular momentum upon propagation direction. This property has attracted a special attention over the last decades due to studies of twisted (or vortex) light beams. Measurements being sensitive to this projection may provide valuable information about the role of angular …
We investigate the angular distribution of electrons that are emitted in the ionization of hydrogen-like ions by twisted photons. Analysis is performed based on the first-order perturbation theory and the non-relativistic Schrödinger equation. Special attention is paid to the dependence of the electron emission pattern on the impact parameter b of the ion with respect to the centre of the twisted wave front. In order to explore such a dependence, detailed calculations were carried out for the photoionization of the 1s ground and 2 py excited states of neutral hydrogen atoms. Based on these cal…
The Rabi frequency (coupling strength) of an electric-dipole transition is an important experimental parameter in laser-cooling and other atomic physics experiments. Though the relationship between Rabi frequency and atomic wavefunctions and/or atomic lifetimes is discussed in many references, there is a need for a concise, self-contained, accessible introduction to such calculations suitable for use by the typical student of laser cooling (experimental or theoretical). In this paper, I outline calculations of the Rabi frequencies for atoms with sub-structure due to orbital, spin and nuclear a…
We suggest a technique based on the transfer of topological charge from applied laser radiation to directional and coherent optical fields generated in ladder-type excited atomic media to identify the major processes responsible for their appearance. As an illustration, in Rb vapours we analyse transverse intensity and phase profiles of the forward-directed collimated blue and near-IR light using self-interference and astigmatic transformation techniques when either or both of two resonant laser beams carry orbital angular momentum. Our observations unambiguously demonstrate that emission at 1…
We consider the process of double photoionization (DPI) in a rare gas atom as a two-step process, namely (i) photoionization in an inner shell followed by (ii) the emission of an Auger electron from an outer shell. An angular correlation function for the two emitted electrons is defined by analogy with the theory of angular correlation in nuclear physics. An expression is obtained for this angular correlation function by a statistical method which makes use of the density and efficiency operators. The latter takes care of the attenuation of the probability of detection of an electrons due to t…
The Fock expansion, which describes the properties of two-electron atoms near the nucleus, is studied. The angular Fock coefficients $ψ_{k,p}(α,θ)$ with the maximum possible value of subscript $p$ are calculated on examples of the coefficients with $5\leq k \leq 10$. The presented technique makes it possible to calculate such angular coefficients for any arbitrarily large $k$. The mentioned coefficients being leading in the logarithmic power series representing the Fock expansion may be indispensable for the development of simple methods for calculating the helium-like electronic structure. Th…
We investigate the influence of two resonant laser beams on the mechanical properties of degenerate atomic gases. The control and probe beams of light are considered to have Orbital Angular Momenta (OAM) and act on the three-level atoms in the Electromagnetically Induced Transparency (EIT) configuration. The theory is based on the explicit analysis of the quantum dynamics of cold atoms coupled with two laser beams. Using the adiabatic approximation, we obtain an effective equation of motion for the atoms driven to the dark state. The equation contains a vector potential type interaction as wel…
We present the results of calculations of outer shell non-dipole angular anisotropy parameters for semi-filled shell atoms in the Hartree-Fock (HF) one-electron approximation and with account of inter-electron correlations in the frame of the Spin Polarized Random Phase Approximation with Exchange (SP RPAE). We demonstrate for the first time that this characteristic of photoionization process is essentially sensitive to the fact whether the photoelectron has the same or opposite spin orientation to that of the semi-filled shell.
We report the experimental observation of alignment to orientation conversion in the 7D_3/2 and 9D_3/2 states of Cs in the presence of an external dc electric field, and without the influence of magnetic fields or atomic collisions. Initial alignment of angular momentum states was created by two-step excitation with linearly polarized laser radiation. The appearance of transverse orientation of angular momentum was confirmed by the observation of circularly polarized light. We present experimentally measured signals and compare them with the results of a detailed theoretical model based on the…
A universal dimer is subject to secondary collisions with atoms when formed in a cloud of ultracold atoms via three-body recombination. We show that in a collisionally opaque medium, the value of the scattering length that results in the maximum number of secondary collisions may not correspond to the Efimov resonance at the atom-dimer threshold and thus can not be automatically associated with it. This result explains a number of controversies in recent experimental results on universal three-body states and supports the emerging evidence for the significant finite range corrections to the fi…
We present angular distributions of photoelectrons of atomic model systems excited by intense linearly polarized laser pulses in the VUV- and XUV-regime. We solve the multi-dimensional time-dependent Schrödinger equation for one particle on large spatial grids and investigate the direction dependence of the ionized electrons for isotropic s-states as well as p-states. Although the ponderomotive potential is small compared to the binding energy of the initially bound electron and the photon energy of the exciting laser field, richly structured photoelectron angular distributions are found which…
We study the generation of angular momentum carrying states for a single cold particle by breaking the symmetry of a spatial adiabatic passage process in a two-dimensional system consisting of three harmonic potential wells. By following a superposition of two eigenstates of the system, a single cold particle is completely transferred to the degenerate first excited states of the final trap, which are resonantly coupled via tunneling to the ground states of the initial and middle traps. Depending on the total time of the process, angular momentum is generated in the final trap, with values tha…
We devise an efficient algorithm for the symbolic calculation of irreducible angular momentum and spin (LS) eigenspaces within the $n$-fold antisymmetrized tensor product $\wedge^n V_u$, where $n$ is the number of electrons and $u = \mathrm{s}, \mathrm{p}, \mathrm{d},\dots$ denotes the atomic subshell. This is an essential step for dimension reduction in configuration-interaction (CI) methods applied to atomic many-electron quantum systems. The algorithm relies on the observation that each $L_z$ eigenstate with maximal eigenvalue is also an $\boldsymbol{L}^2$ eigenstate (equivalently for $S_z$…
We simulate angular resolved RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) measurements on valence shells of noble gas atoms (Ne, Ar, Kr, and Xe). Our non-perturbative numerical simulation is based on solution of the time-dependent Schrödinger equation for a target atom driven by an ionizing XUV and dressing IR fields. From these simulations we extract the angular dependent magnitude and phase of the RABBITT oscillations and deduce the corresponding angular anisotropy β parameter and Wigner time delay $τ_W$ for the single XUV photon absorption which i…
The single ionization of noble gas atoms by the combined action of XUV attopulses and an infrared laser field is theoretically investigated by means of a non-perturbative model that under certain approximations gives closed-form expressions for the angular distributions of photoelectrons. Interestingly, our model allow us to interpret the angular distributions as two-center interferences where the separation between the centers is governed by the infrared laser field. Angular distributions are compared to the available experimental data showing a good agreement. Finally, we deduce the conditio…
In this paper a library for spin--angular integration in LS-coupling for many-electron atoms is presented. The software is an implementation of a methodology based on the second quantization in coupled tensorial form, the angular momentum theory in 3 spaces (orbital, spin and quasispin), and the graphical technique of angular momentum. This implementation extends applications of the relevant methodology to open f- shells and leads to faster execution of angular integration codes. The possibility of using some library routines for solving various angular momentum problems in atomic physics is a…
Core-polarization interactions are investigated in low-energy electron elastic scattering from the atoms In,Sn,Eu,Au and At through the calculation of their electron affinities. The complex angular momentum method wherein is embedded the vital electron-electron correlations is used. The core-polarization effects are studied through the well investigated rational function approximation of the Thomas-Fermi potential,which can be analytically continued into the complex plane. The EAs are extracted from the large resonance peaks in the calculated low-energy electron atom scattering total cross sec…
We show that bosonic atoms loaded into orbital angular momentum $l=1$ states of a lattice in a diamond-chain geometry provides a flexible and simple platform for exploring a range of topological effects. This system exhibits robust edge states, and the relative phases arising naturally in the tunnelling amplitudes lead to the appearance of Aharanov-Bohm caging in the lattice. We discuss how these properties can be realised and observed in ongoing experiments.
We study the total cross section and angular distribution in Rayleigh scattering by hydrogen atom in the ground state, within the framework of Dirac relativistic equation and second-order perturbation theory. The relativistic states used for the calculations are obtained by making use of the finite basis set method and expressed in terms of B-splines and B-polynomials. We pay particular attention to the effects that arise from higher (non-dipole) terms in the expansion of the electron-photon interaction. It is shown that the angular distribution of scattered photons, while it is symmetric with…
The tunneling ionization of a hydrogen atom excited in the presence of a static electric field is investigated for the case where, before being extracted, the electron has an orbital angular momentum L perpendicular to the field E. The escaping electron has a nonzero mean transverse velocity <vT> in the direction of E cross <L>. This asymmetry is similar to the Collins effect in the fragmentation into hadrons of a transversely polarized quark. In addition, the linear Stark effect make <L> and <vT> oscillate in time. The degree of asymmetry is calculated at leading order in E for an initial sta…
Within the framework of a model representing the potential of a graphene sheet U(z) as an electro-neutral layer formed by smeared carbon atoms, the effect of this potential on spectral characteristics of atoms adsorbed on a graphene sheet has been studied. Since the distance between the adsorbed atom nucleus and sheet surface significantly exceeds the radii of inner atomic shells the potential U(z) makes influence on the continuum wave functions only. Their behavior in the upper semi-space (z>0) and in the lower one (z<0) where the adsorbed atom is located is defined by a jump of the logarithm…
We show that the combination of two achiral components - atomic or molecular target plus a circularly polarized photon - can yield chirally structured photoelectron angular distributions. For photoionization of CO, the angular distribution of carbon K-shell photoelectrons is chiral when the molecular axis is neither perpendicular nor (anti-)parallel to the light propagation axis. In photo-double-ionization of He, the distribution of one electron is chiral, if the other electron is oriented like the molecular axis in the former case and if the electrons are distinguishable by their energy. In b…
It is shown that the atom-molecule collision problem in the presence of an external electric field can be solved using the total angular momentum representation in the body-fixed coordinated frame, leading to a computationally efficient method for ab initio modeling of low-temperature scattering phenomena. Our calculations demonstrate rapid convergence of the cross sections for vibrational and Stark relaxation in He-CaD collisions with the number of total angular momentum states in the basis set, leading to a 5-100 fold increase in computational efficiency over the previously used methods base…
We present measurements, using two complementary methods, of the breakdown of atomic angular momentum selection rules in He-broadened Rb vapor. Atomic dark states are rendered weakly absorbing due to fine-structure mixing during Rb-He collisions. The effect substantially increases the photon demand for optical pumping of dense vapors.
We theoretically investigate the quantum properties of nS, nP, and nD Rydberg atoms in a magnetic Ioffe-Pritchard trap. In particular, it is demonstrated that the two-body character of Rydberg atoms significantly alters the trapping properties opposed to point-like particles with identical magnetic moment. Approximate analytical expressions describing the resulting Rydberg trapping potentials are derived and their validity is confirmed for experimentally relevant field strengths by comparisons to numerical solutions of the underlying Schroedinger equation. In addition to the electronic propert…
The dipole-dipole interaction between two Rydberg atoms depends on the relative orientation of the atoms and on the change in the magnetic quantum number. We simulate the effect of this anisotropy on the energy transport in an amorphous many atom system subject to a homogeneous applied electric field. We consider two experimentally feasible geometries and find that the effects should be measurable in current generation imaging experiments. In both geometries atoms of $p$ character are localized to a small region of space which is immersed in a larger region that is filled with atoms of $s$ cha…
The improvement of the multi-mode capability of quantum memory can further improve the utilization efficiency of the quantum memory and reduce the requirement of quantum communication for storage units. In this letter, we experimentally investigate the multi-mode light multiplexing storage of orbital angular momentum (OAM) mode based on rubidium vapor, and demultiplexing by a photonic OAM mode splitter which combines a Sagnac loop with two dove prisms. Our results show a mode extinction ratio higher than 80$\%$ at 1 $μ$s of storage time. Meanwhile, two OAM modes have been multiplexing stored a…
This is a sequel to an earlier article on the theory of angular correlation for double photoionization. Here we consider the two-step double photoionization of a rare gas atom under the influence of a polarized photon beam described by appropriate Stokes parameters. Cylindrical mirror analysers (CMA) are used to detect the outgoing electrons. Theoretical values of the correlation functions are obtained for linearly polarized light. Two different situations is handled. Once, the value of the correlation function is obtained keeping the photo-electron in a fixed direction. The other case the dir…
We investigate the coherent control of the photo\-electron angular distribution in bichromatic atomic ionization. Neon is selected as target since it is one of the most popular systems in current gas-phase experiments with free-electron lasers (FELSs). In particular, we tackle practical questions, such as the role of the fine-structure splitting, the pulse length, and the intensity. Time-dependent and stationary perturbation theory are employed, and we also solve the time-dependent Schrödinger equation in a single-active electron model. We consider neon ionized by a FEL pulse whose fundamental…
We discuss a possibility to observe fast secondary electrons ($δ-$electrons) during nuclear $β^{-}$-decay in few-electron atoms and ions. Formulas for the corresponding probabilities and explicit expression for the energy spectrum of $δ-$electrons are derived in the closed analytical forms.
We demonstrate the rapid readout of terahertz (THz) orbital angular momentum (OAM) beams using an atomic-vapour based imaging technique. OAM modes with both azimuthal and radial indices are created using phase-only transmission plates. The beams undergo terahertz to optical conversion in an atomic vapour, before being imaged in the far field using an optical CCD camera. In addition to the spatial intensity profile, we also observe the self-interferogram of the beams by imaging through a tilted lens, allowing the sign and magnitude of the azimuthal index to be read out directly. Using this tech…
We present here the results of calculations of photoelectrons' angular anisotropy and spin-polarization parameters for a number of semi-filled shell atoms. We consider ionization of outer or in some cases next to the outer electrons in a number of elements from I, V, and VI groups of the Periodic Table. All calculations are performed with account of multi-electron correlations in the frame of the Spin Polarized version of the Random Phase Approximation with Exchange - SP RPAE. We consider the dipole angular distribution and spin polarization of photoelectrons from semi-filled subshells and fro…
We study the single-particle properties of a system formed by ultracold atoms loaded into the manifold of $l=1$ Orbital Angular Momentum (OAM) states of an optical lattice with a diamond chain geometry. Through a series of successive basis rotations, we show that the OAM degree of freedom induces phases in some tunneling amplitudes of the tight-binding model that are equivalent to a net $π$ flux through the plaquettes and give rise to a topologically non-trivial band structure and protected edge states. In addition, we demonstrate that quantum interferences between the different tunneling proc…
The new regime of resonant nuclear photoexcitation rendered possible by x-ray free electron laser beams interacting with solid state targets is investigated theoretically. Our results unexpectedly show that secondary processes coupling nuclei to the atomic shell in the created cold high-density plasma can dominate direct photoexcitation. As an example we discuss the case of $^{93m}$Mo isomer depletion for which nuclear excitation by electron capture as secondary process is shown to be orders of magnitude more efficient than the direct laser-nucleus interaction. General arguments revisiting the…
