A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors. It is based on the combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. The latter allows us to calculate graphically the irreducible tensorial products of the second quantization operators and their commutators, and to formulate additional rules for operations with diagrams. The additional rules allow us to find graphically the normal form of the complicated tensorial products of the operators. All matrix elements (diagonal and non-diagonal with respect to configurations) differ only by the values of the projections of the quasispin momenta of separate shells and are expressed in terms of completely reduced matrix elements (in all three spaces) of the second quantization operators. As a result, it allows us to use standard quantities uniformly for both diagona and off-diagonal matrix elements.
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…
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 …
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 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…
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…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given. These methods are compared in various aspects, and the advantages or shortcomings of each particular method are discussed. Efficient method to find the abovementioned quantities in LS coupling is presented, based on the use of symmetry properties of operators and matrix elements in three spaces (orbital, spin and quasispin), second quantization in coupled tensor…
An improved algorithm to evaluate the nonrelativistic three-electron Hylleraas-Configuration Interaction (Hy-CI) kinetic energy integrals over Slater orbitals and the Hamiltonian in Hylleraas coordinates is shown. The resulting analytical expressions are general for all quantum numbers of the orbitals. From there, the restriction of employing orbitals with quantum numbers $l \le 2$ of the above algorithm presented in paper I of this series has been removed. With the new algorithm it is possible, in the direct integration method described in this series, to carry out Hy-CI atomic structure calc…
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…
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…
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 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 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…
Phase retrieval from angular streaking of XUV atomic ionization
Research School of Physics, The Australian National University（澳大利亚国立大学物理研究生院）；General, Theoretical and Computer Physics, Saratov State University（萨马拉国立大学一般、理论与计算物理）；Center for Relativistic Laser Science, Institute for Basic Science (IBS)（基础科学研究院相对论激光科学中心）；Stanford PULSE Institute, SLAC National Accelerator Laboratory（斯坦福PULSE研究所，SLAC国家加速器实验室）
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 performed scattering experiments using a rubidium (Rb) atomic beam on paraffin films and measured the angular and velocity distributions of scattered atoms. The paraffin films were prepared in various ways and characterized by atomic force microscopy and X-ray diffraction. The films exhibited various roughnesses and crystal structures. The paraffin films preserved the spin polarization of the scattered atoms. The measured angular distributions of all prepared films were consistent with Knudsen's cosine law. The velocity distributions were well fitted by Maxwell's distribution, characterized…
In the present paper, we consider nonresonant corrections to $ 2s-ns/nd $ transition frequencies in hydrogen for the experiments based on two-photon spectroscopy. A detailed study of angular correlations of quantum interference effects within the framework of rigorous quantum electrodynamics is given. Closed expressions for the resonant two-photon scattering cross sections on an atomic level with dependence on all atomic quantum numbers including fine and hyperfine structure are derived. These expressions are applied for the description of experiments based on two-photon spectroscopy with fixi…
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…
We deduce the quantization of the atomic orbit for the hydrogen's atom model proposed by Bohr without using his hypothesis of angular momentum quantization. We show that his hypothesis can be deduced from and is a consequence of the Planck's energy quantization.
We establish the existence of spin-statistic selection rules (SSSR) for multi-equal-photon transitions in atomic systems. These selection rules are similar to those for systems of many equivalent electrons in atomic theory. The latter ones are the direct consequence of Pauli exclusion principle. In this sense the SSSR play the role of the exclusion principle for photons: they forbid some particular states for the photon systems. We established several SSSR for few-photon systems. 1) First rule (SSSR-1): two-equivalent photons involved in any atomic transition can have only even values of the t…
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 analyze the formation of the low-energy structure (LES) in above-threshold ionization spectra first observed by Quan et al.\ \cite{quan09} and Blaga et al.\ \cite{blaga09} using both quasi-classical and quantum approaches. We show this structure to be largely classical in origin resulting from a two-dimensional focusing in the energy-angular momentum plane of the strong-field dynamics in the presence of the atomic potential. The peak at low energy is strongly correlated with high angular momenta of the photoelectrons. Quantum simulations confirm this scenario. Resulting parameter dependence…
This library (collection of subroutines) is presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. These quantities include the coefficients of fractional parentage, the reduced coefficients of fractional parentage as well as reduced and completely reduced matrix elements for several operators. So the library is assigned for any computational scheme. 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 quas…
On the basis of a quantum microscopic approach we study the dynamics of the afterglow of a dilute Gaussian atomic ensemble excited by pulsed radiation. Taking into account the vector nature of the electromagnetic field we analyze in detail the angular and polarization distribution of single-photon superradiance of such an ensemble. The dependence of the angular distribution of superradiance on the length of the pulse and its carrier frequency as well as on the size and the shape of the atomic clouds is studied. We show that there is substantial dependence of the superradiant emission on the po…
Laboratory optical atomic clocks achieve remarkable accuracy (now counted to 18 digits or more), opening possibilities to explore fundamental physics and enable new measurements. However, their size and use of bulk components prevent them from being more widely adopted in applications that require precision timing. By leveraging silicon-chip photonics for integration and to reduce component size and complexity, we demonstrate a compact optical-clock architecture. Here a semiconductor laser is stabilized to an optical transition in a microfabricated rubidium vapor cell, and a pair of interlocke…
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 present a magnetometer based on optically pumped Cs atoms that measures the magnitude and direction of a 1 $μ$T magnetic field. Multiple circularly polarized laser beams were used to probe the free spin precession of the Cs atoms. The design was optimized for long-time stability and achieves a scalar resolution better than 300 fT for integration times ranging from 80 ms to 1000 s. The best scalar resolution of less than 80 fT was reached with integration times of 1.6 to 6 s. We were able to measure the magnetic field direction with a resolution better than 10 $μ$rad for integration times fr…
Tunnelling, one of the key features of quantum mechanics, ignited an ongoing debate about the value, meaning and interpretation of 'tunnelling time'. Until recently the debate was purely theoretical, with the process considered to be instantaneous for all practical purposes. This changed with the development of ultrafast lasers and in particular, the 'attoclock' technique that is used to probe the attosecond dynamics of electrons. Although the initial attoclock measurements hinted at instantaneous tunnelling, later experiments contradicted those findings, claiming to have measured finite tunne…
Numerical attoclock is a theoretical model of attosecond angular streaking driven by a very short, nearly a single oscillation, circularly polarized laser pulse. The reading of such an attoclock is readily obtained from a numerical solution of the time-dependent Schrödinger equation as well as a semi-classical trajectory simulation. By making comparison of the two approaches, we highlight the essential physics behind the attoclock measurements. In addition, we analyze the predictions of the Keldysh-Rutherford model of the attoclock [Phys. Rev. Lett. 121, 123201 (2018)]. In molecular hydrogen, …
Polariton formalism is applied for studying the propagation of a probe field of light in a cloud of cold atoms influenced by two control laser beams of larger intensity. The laser beams couple resonantly three hyperfine atomic ground states to a common excited state thus forming a tripod configuration of the atomic energy levels involved. The first control beam can have an optical vortex with the intensity of the beam going to zero at the vortex core. The second control beam without a vortex ensures the loseless (adiabatic) propagation of the probe beam at a vortex core of the first control la…
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 develop a novel technique for modeling of atomic and molecular ionization in superposition of XUV and IR fields with characteristics typical for attosecond streaking and RABBITT experiments. The method is based on solving the time-dependent Schrödinger equation in the coordinate frame expanding along with the photoelectron wave packet. The efficiency of the method is demonstrated by calculating angular anisotropy of photoemission time delay of the H$_2^+$ ion in a field configuration of recent RABBITT experiments.
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…
Atom density profile arising in the atomic beam after passing through the one or two microfabricated structures (MS) is considered. Two limiting cases the beam with large and small angular divergence are considered. An equivalence of the considerations based on the Fresnel-Kirchhoff theory of diffraction and on the atomic recoil-effect is established. Higher order gratings' profiles produced in the collinear beam owing to the atomic Talbot effect are calculated. For an atomic beam with large angular divergence, two regimes of atoms' scattering off the MS, classical and quantum, are analyzed. F…
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…
Results of the most sophisticated measurements in coincidence of the angular resolved K-shell photo- and Auger-electrons, and of two atomic ions produced by dissociation of N2 molecule, are analyzed. Detection of photoelectrons at certain angles allows separating the Auger decay processes of the 1σg and 1σu core hole states. The Auger electron angular distributions for each of these hole states are measured as a function of the kinetic energy release of two atomic ions and are compared with the corresponding theoretical angular distributions. From that comparison one can disentangle the contri…
Atomic properties such as field shift constants, magnetic dipole and electric quadrupole hyperfine structure constants, Landé $g_J$ factors, and electric quadrupole moments that are described by electronic operators with different ranks and radial behaviors are studied and the role of electron correlation effects in their determination are investigated. We have adopted the Dirac-Hartree-Fock method, the second- and third-order relativistic many-body perturbation theories, and an all-order relativistic many-body method in the coupled-cluster theory framework considering only the linearized term…
In this paper we propose a dark-state-based trapping strategy to break the optical diffraction limit for microscopy. We utilize a spatially dependent coupling field and a probe laser field with temporal and spatial modulation to interact with three-level atoms. The temporal modulation allows us to reduce the full width at half maximum (FWHM) of point spread function, and the spatial modulation help us obtain better spatial resolution than Gaussian beam. In addition, we also propose a proof-of-principle experiment protocol and discuss its feasibility.
A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version of the Anco program now provides these coefficients for both, scalar as well as non-scalar one-particle operators as they arise frequently in the study of transition probabilities, photoionization and electron capture processes, the alignment transfer through excited atomic states, collision strengths, and in many other investigations. The program is based o…
Orbital-angular-momentum partition in hydrogen photoionization by a monochromatic vortex beam
Peking University（北京大学）；Wuhan Institute of Technology（武汉工程大学）；Huazhong University of Science and Technology（华中科技大学）；Guangdong Technion - Israel Institute of Technology（广东以色列理工学院）；Technion – Israel Institute of Technology（以色列理工学院）
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…
The quantum processes involved in the interaction of matter with, separately, an electron vortex(EV) and an optical vortex (OV) are described, with matter modelled in terms of a neutral two particle atomic system, allowing for both the internal (electronic-type) motion and the gross (center of mass-type) motion of matter to be taken into account. The coupling of the atomic system to the EV is dominated by Coulomb forces, while that of the OV is taken in the $\mathbf{p}\cdot\mathbf{A}$ canonical form which couples $\mathbf{A}$, the transverse vector potential of the optical vortex, to the linea…
Trapped atomic ions are a proven and powerful tool for the fundamental research of quantum physics. They have emerged in recent years as one of the most promising candidates for several practical technologies including quantum computers, quantum simulators, atomic clocks, mass spectrometers and quantum sensors. Advanced fabrication techniques, taken from established and nascent disciplines, are being deployed to create novel, reliable devices with a view to large scale integration and commercial compatibility. This review will cover the fundamentals of ion trapping before proceeding with a dis…
The coherent control of electron beams and ultrafast electron wave packets dynamics have attracted significant attention in electron microscopy as well as in atomic physics. In order to unify the conceptual pictures developed in both fields, we demonstrate the generation and manipulation of tailored electron orbital angular momentum (OAM) superposition states either by employing customized holographic diffraction masks in a transmission electron microscope or by atomic multiphoton ionization utilizing pulse-shaper generated carrier-envelope phase stable bichromatic ultrashort laser pulses. Bot…
The exact values of the presently determined components 26of the angular Fock coefficients at the two-particle coalescences were obtained and systematized. The Green Function approach was successfully applied to simplify the most complicated calculations. The boundary conditions for the Fock coefficient components in the hyperspherical angular coordinates, which follows from the Kato cusp conditions for the two-electron wave function in the natural interparticle coordinates, were derived. The validity of the obtained boundary conditions was verified on examples of all the presently determined …
We analyze atomic photoexcitation into the discrete states by twisted photons, or photons carrying extra orbital angular momentum along their direction of propagation. From the angular momentum and parity considerations, we are able to relate twisted-photon photoexcitation amplitudes to their plane-wave analogues, independently of the details of the atomic wave functions. We analyzed the photo-absorption cross sections of mixed-multipolarity $E2-M1$ transitions in ionized atoms and found fundamental differences coming from the photon topology. Our theoretical analysis demonstrates that it is p…
A new iterative version of population projection analysis is formulated and applied to determine relativistic effective atomic configurations of superheavy elements Cn and Fl and their lighter homologues (Hg and Pb) in the molecules of their fluorides and oxides. The dependence of the computed populations on the initial reference atomic spinors is completely avoided. The difference in population of atomic spinors with the same orbital angular momentum and different total angular momenta is demonstrated to be essential for understanding the peculiarities of chemical bonding in superheavy elemen…
