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arXiv2013

Electron shakeoff following the ?+ decay of trapped 35Ar+ ions

The electron shakeoff of $^{35}$Cl atoms resulting from the $β$$^+$ decay of $^{35}$Ar$^+$ ions has been investigated using a Paul trap coupled to a recoil-ion spectrometer. The charge-state distribution of the recoiling daughter nuclei is compared to theoretical calculations accounting for shakeoff and Auger processes. The calculations are in excellent agreement with the experimental results and enable to identify the ionization reaction routes leading to the formation of all charge states.

nucl-ex↗

arXiv2014

Higher Ionization Energies of Atoms in Density Functional Theory

Density functional theory (DFT) is an exact alternative formulation of quantum mechanics, in which it is possible to calculate the total energy, the spin and the charge density of many-electron systems in the ground state. In practice, it is necessary to use uncontrolled approximations that can mainly be verified against experimental data. Atoms and ions are simple systems, where the approximations of DFT can be easily tested. We have calculated within DFT the total energies, spin and higher ionization energies of all the ions of elements with 1 $\leq$ Z $\leq$ 29. We find the calculations in close agreement with experiment, with an error of typically less than ca. 1% for 1 $\leq$ Z $\leq$ 29. Surprisingly, the error depends on the electronic configuration of the ion in both local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof general gradient approximation (PBE-GGA) and independent of both self-interaction correction (SIC) and relativistic corrections. Larger errors are found for systems in which the spin-spin correlation is significant, which indicates the possible benefit from an orbital-dependent formulation of the correlation energy functional.

physics.atom-ph↗

arXiv2013

Non-existence of Taylor expansion in time due to cusps

In the usual treatment of electronic structure, all matter has cusps in the electronic density at nuclei. Cusps can produce non-analytic behavior in time, even in response to perturbations that are time-analytic. We analyze these non-analyticities in a simple case from many perspectives. We describe a method, the s-expansion, that can be used in several such cases, and illustrate it with a variety of examples. These include both the sudden appearance of electric fields and disappearance of nuclei, in both one and three dimensions. When successful, the s-expansion yields the dominant short-time behavior, no matter how strong the external electric field, but agrees with linear response theory in the weak limit. We discuss the relevance of these results to time-dependent density functional theory.

physics.atom-ph↗

arXiv2013

Ion impact induced Interatomic Coulombic Decay in neon and argon dimers

We investigate the contribution of Interatomic Coulombic Decay induced by ion impact in neon and argon dimers (Ne$_2$ and Ar$_2$) to the production of low energy electrons. Our experiments cover a broad range of perturbation strengths and reaction channels. We use 11.37 MeV/u S$^{14+}$, 0.125 MeV/u He$^{1+}$, 0.1625 MeV/u He$^{1+}$ and 0.150 MeV/u He$^{2+}$ as projectiles and study ionization, single and double electron transfer to the projectile as well as projectile electron loss processes. The application of a COLTRIMS reaction microscope enables us to retrieve the three-dimensional momentum vectors of the ion pairs of the fragmenting dimer into Ne$^{q+}$/Ne$^{1+}$ and Ar$^{q+}$/Ar$^{1+}$ (q = 1, 2, 3) in coincidence with at least one emitted electron.

physics.atm-clus↗

arXiv2013

Intensity landscape and the possibility of magic trapping of alkali Rydberg atoms in infrared optical lattices

Motivated by compelling advances in manipulating cold Rydberg (Ry) atoms in optical traps, we consider the effect of large extent of Ry electron wave function on trapping potentials. We find that when the Ry orbit lies outside inflection points in laser intensity landscape, the atom can stably reside in laser intensity maxima. Effectively, the free-electron AC polarizability of Ry electron is modulated by intensity landscape and can accept both positive and negative values. We apply these insights to determining magic wavelengths for Ry-ground-state transitions for alkali atoms trapped in infrared optical lattices. We find magic wavelengths to be around 10 $μ\mathrm{m}$, with exact values that depend on Ry state quantum numbers.

physics.atom-ph↗

arXiv2013

Dynamic formation of Rydberg aggregates at off-resonant excitation

The dynamics of a cloud of ultra-cold two-level atoms is studied at off-resonant laser driving to a Rydberg state. We find that resonant excitation channels lead to strongly peaked spatial correlations associated with the buildup of asymmetric excitation structures. These aggregates can extend over the entire ensemble volume, but are in general not localized relative to the system boundaries. The characteristic distances between neighboring excitations depend on the laser detuning and on the interaction potential. These properties lead to characteristic features in the spatial excitation density, the Mandel $Q$ parameter, and the total number of excitations. As an application an implementation of the three-atom CSWAP or Fredkin gate with Rydberg atoms is discussed. The gate not only exploits the Rydberg blockade, but also utilizes the special features of an asymmetric geometric arrangement of the three atoms. We show that continuous-wave off-resonant laser driving is sufficient to create the required spatial arrangement of atoms out of a homogeneous cloud.

physics.atom-ph↗

arXiv2013

Coherent manipulation of cold Rydberg atoms near the surface of an atom chip

Coherent superpositions of the 49s and 48s Rydberg states of cold Rb atoms were studied near the surface of an atom chip. The superpositions were created and manipulated using microwaves resonant with the two-photon 49s-48s transition. Coherent behavior was observed using Rabi flopping, Ramsey sequences, spin-echo and spin-locking. These results are discussed in the context of Rydberg atoms as electric field noise sensors. We consider the coherence of systems quadratically coupled to noise fields with 1/f^k power spectral densities (k \approx 1).

physics.atom-ph↗

arXiv2013

Production of very-high-$n$ strontium Rydberg atoms

The production of very-high-$n$, $n\sim300$-500, strontium Rydberg atoms is explored using a crossed laser-atom beam geometry. $n$$^{1}$S$_{0}$ and $n$$^{1}$D$_{2}$ states are created by two-photon excitation via the 5s5p $^{1}$P$_{1}$ intermediate state using radiation with wavelengths of $\sim$~461 and $\sim$ 413 nm. Rydberg atom densities as high as $\sim 3 \times 10^{5}$ cm$^{-3}$ have been achieved, sufficient that Rydberg-Rydberg interactions can become important. The isotope shifts in the Rydberg series limits are determined by tuning the 461 nm light to preferentially excite the different strontium isotopes. Photoexcitation in the presence of an applied electric field is examined. The initially quadratic Stark shift of the $n$$^{1}$P$_{1}$ and $n$$^{1}$D$_{2}$ states becomes near-linear at higher fields and the possible use of $n{}^{1}$D$_{2}$ states to create strongly-polarized, quasi-one-dimensional electronic states in strontium is discussed. The data are analyzed with the aid of a two-active-electron (TAE) approximation. The two-electron Hamiltonian, within which the Sr$^{2+}$ core is represented by a semi-empirical potential, is numerically diagonalized allowing calculation of the energies of high-$n$ Rydberg states and their photoexcitation probabilities.

physics.atom-ph↗

arXiv2013

Wigner phase space distribution as a wave function

We demonstrate that the Wigner function of a pure quantum state is a wave function in a specially tuned Dirac bra-ket formalism and argue that the Wigner function is in fact a probability amplitude for the quantum particle to be at a certain point of the classical phase space. Additionally, we establish that in the classical limit, the Wigner function transforms into a classical Koopman-von Neumann wave function rather than into a classical probability distribution. Since probability amplitude need not be positive, our findings provide an alternative outlook on the Wigner function's negativity.

quant-ph↗

arXiv2013

Development of a relativistic coupled-cluster method for one electron detachment theory: Application to Mn IX, Fe X, Co XI and Ni XII ions

We have developed one electron detachment theory from a closed-shell atomic configuration in the relativistic Fock-space coupled-cluster ansatz. Using this method, we determine sensitivity coefficients to the variation of the fine structure constant in the first three important low-lying transitions of the astrophysically interesting highly charged Mn IX, Fe X, Co XI and Ni XII ions. The potential of this method has been assessed by evaluating the detachment energies of the removed electrons and determining lifetimes of the atomic states in the above ions. To account the sensitivity of the higher order relativistic effects, we have used the four component wave functions of the Dirac-Coulomb-Breit Hamiltonian with the leading order quantum electrodynamics (QED) corrections. A systematic study has been carried out to highlight the importance of the Breit and QED interactions in the considered properties of the above ions.

physics.atom-ph↗

arXiv2013

Time-dependent renormalized natural orbital theory applied to the two-electron spin-singlet case: ground state, linear response, and autoionization

Favorably scaling numerical time-dependent many-electron techniques such as time-dependent density functional theory (TDDFT) with adiabatic exchange-correlation potentials typically fail in capturing highly correlated electron dynamics. We propose a method based on natural orbitals, i.e., the eigenfunctions of the one-body reduced density matrix, that is almost as inexpensive numerically as adiabatic TDDFT, but which is capable of describing correlated phenomena such as doubly excited states, autoionization, Fano profiles in the photoelectron spectra, and strong-field ionization in general. Equations of motion (EOM) for natural orbitals and their occupation numbers have been derived earlier. We show that by using renormalized natural orbitals (RNO) both can be combined into one equation governed by a hermitian effective Hamiltonian. We specialize on the two-electron spin-singlet system, known as being a "worst case" testing ground for TDDFT, and employ the widely used, numerically exactly solvable, one-dimensional helium model atom (in a laser field) to benchmark our approach. The solution of the full, nonlinear EOM for the RNO is plagued by instabilities, and resorting to linear response is not an option for the ultimate goal to study nonperturbative dynamics in intense laser fields. We therefore make two rather bold approximations: we employ the initial-state-"frozen" effective RNO Hamiltonian for the time-propagation and truncate the number of RNO to only two per spin. Surprisingly, it turns out that even with these strong approximations we obtain a highly accurate ground state, reproduce doubly-excited states, and autoionization.

physics.atom-ph↗

arXiv2013

Analytical model of overlapping Feshbach resonances

Feshbach resonances in ultracold collisions often result from an interplay between many collision channels. Simple two-channel models can be introduced to capture the basic features, but cannot fully reproduce the situation when several resonances from different closed channels contribute to the scattering process. Using the formalism of multichannel quantum defect theory we develop an analytical model of overlapping Feshbach resonances. We find a general formula for the variation of the scattering length with magnetic field in the vicinity of an arbitrary number of resonances, characterized by simple parameters. Our formula is in excellent agreement with numerical coupled channels calculations for several cases of overlapping resonances in the collisions of two $^7$Li atoms or two Cs atoms.

physics.atom-ph↗

arXiv2013

Sturmian theory of three-body recombination: application to the formation of H$_2$ in primordial gas

A Sturmian theory of three-body recombination is presented which provides a unified treatment of bound states, quasi-bound states, and continuum states. The Sturmian representation provides a numerical quadrature of the two-body continuum which may be used to generate a complete set of states within any desired three-body recombination pathway. Consequently, the dynamical calculation may be conveniently formulated using the simplest energy transfer mechanism, even for reactive systems which allow substantial rearrangement. The Sturmian theory generalizes the quantum kinetic theory of Snider and Lowry [J. Chem. Phys. 61, 2330 (1974)] to include metastable states which are formed as independent species. Steady-state rate constants are expressed in terms of a pathway-independent part plus a non-equilibrium correction which depends on tunneling lifetimes and pressure. Numerical results are presented for H$_2$ recombination due to collisions with H and He using quantum mechanical coupled states and infinite order sudden approximations. These results may be used to remove some of the uncertainties that have limited astrophysical simulations of primordial star formation.

physics.atom-ph↗

arXiv2013

Quantum interference-enhanced deep sub-Doppler cooling of 39 K atoms in gray molasses

We report enhanced sub-Doppler cooling of the bosonic atoms of $^{39}$K facilitated by formation of dark states tuned for the Raman resonance in the $Λ-$configuration near the D1 transition. Temperature of about 12 $μ$K is achieved in the two stage D2-D1 molasses and spans a very large parameter region where quantum interference persists robustly. We also present results on enhanced radiation heating with sub-natural linewidth (0.07$Γ$) and signature Fano like profile of a coherently driven 3-level atomic system. The Optical Bloch Equations relevant for the three-level atom in bichromatic light field is solved with the method of continued fractions to show that cooling occurs only for a small velocity class of atoms, emphasizing the need for pre-cooling in D2 molasses stage.

physics.atom-ph↗

arXiv2013

Double Bragg diffraction: A tool for atom optics

The use of retro-reflection in light-pulse atom interferometry under microgravity conditions naturally leads to a double-diffraction scheme. The two pairs of counterpropagating beams induce simultaneously transitions with opposite momentum transfer that, when acting on atoms initially at rest, give rise to symmetric interferometer configurations where the total momentum transfer is automatically doubled and where a number of noise sources and systematic effects cancel out. Here we extend earlier implementations for Raman transitions to the case of Bragg diffraction. In contrast with the single-diffraction case, the existence of additional off-resonant transitions between resonantly connected states precludes the use of the adiabatic elimination technique. Nevertheless, we have been able to obtain analytic results even beyond the deep Bragg regime by employing the so-called "method of averaging," which can be applied to more general situations of this kind. Our results have been validated by comparison to numerical solutions of the basic equations describing the double-diffraction process.

physics.atom-ph↗

arXiv2013

Collectively-enhanced optomechanical coupling in periodic arrays of scatterers

We investigate the optomechanical properties of a periodic array of identical scatterers placed inside an optical cavity and extend the results of [A. Xuereb, C. Genes, and A. Dantan, Phys. Rev. Lett. 109, 223601 (2012)]. We show that operating at the points where the array is transmissive results in linear optomechanical coupling strengths between the cavity field and collective motional modes of the array that may be several orders of magnitude larger than is possible with an equivalent reflective ensemble. We describe and interpret these effects in detail and investigate the nature of the scaling laws of the coupling strengths for the different transmissive points in various regimes.

quant-ph↗

arXiv2013

Dispersive optical nonlinearities in an EIT-Rydberg medium

We investigate dispersive optical nonlinearities that arise from Rydberg excitation blockade in cold Rydberg gases. We consider a two-photon transition scheme and study the non-linear response to a weak optical probe in presence of a strong control beam. For very low probe fields, the dominant nonlinearities are of the third order and they can be exactly evaluated in a steady state regime. In a more general case, the change in average atomic populations and coherences due to Rydberg interactions can be characterized by properly defined scaling parameters, which are generally complex numbers but in certain situations take the usual meaning of the number of atoms in a blockade sphere. They can be used in a simple "universal scaling" formula to determine the dispersive optical nonlinearity of the medium. We also develop a novel technique to account for the Rydberg interaction effects, by simplifying the treatment of nonlocal interaction terms, the so-called collisional integrals. We find algebraic relations that only involve two-body correlations, which can be solved numerically. All average populations and coherences are then obtained straightforwardly.

quant-ph↗

arXiv2013

Correlation trends in the ground state static electric dipole polarizabilities of closed-shell atoms and ions

We employ the closed-shell perturbed relativistic coupled-cluster (RCC) theory developed by us earlier [Phys. Rev. A {\bf 77}, 062516 (2008)] to evaluate the ground state static electric dipole polarizabilities (αs) of several atomic systems. In this work, we have incorporated a class of higher order many-body effects in our calculations that had not been taken into account in the above paper. We highlight their importance in improving the accuracy of $α$. We also calculate the ground state αs of the inert gas atoms and several iso-electronic singly and doubly charged ions in order to make a comparative study of the trends of the correlation effects. Furthermore, we have developed a method to construct intermediate diagrams that are required for the computation of the unperturbed singles and doubles coupled-cluster amplitudes. Our RCC results are compared with those of many-body perturbation theory at different orders to demonstrate the importance of higher order correlation effects for the accurate determination of (αs) of the systems that we have considered.

physics.atom-ph↗