Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap

Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137, 064301 (2012), we theoretically illustrate the possibility of using the motional states of a $Cd^+$ ion trapped in a slightly anharmonic potential to simulate the single-particle time-dependent Schr\"odinger equation. The simulated wave packet is discretized on a spatial grid and the grid points are mapped on the ion motional states which define the qubit network. The localization probability at each grid point is obtained from the population in the corresponding motional state. The quantum gate is the elementary evolution operator corresponding to the time-dependent Schr\"odinger equation of the simulated system. The corresponding matrix can be estimated by any numerical algorithm. The radio-frequency field able to drive this unitary transformation among the qubit states of the ion is obtained by multi-target optimal control theory. The ion is assumed to be cooled in the ground motional state and the preliminary step consists in initializing the qubits with the amplitudes of the initial simulated wave packet. The time evolution of the localization probability at the grids points is then obtained by successive applications of the gate and reading out the motional state population. The gate field is always identical for a given simulated potential, only the field preparing the initial wave packet has to be optimized for different simulations. We check the stability of the simulation against decoherence due to fluctuating electric fields in the trap electrodes by applying dissipative Lindblad dynamics.Comment: 31 pages, 8 figures. Revised version. New title, new figure and new reference

Ab initio calculation of H + He+^+ charge transfer cross sections for plasma physics

The charge transfer in low energy (0.25 to 150 eV/amu) H($nl$) + He$^+(1s)$ collisions is investigated using a quasi-molecular approach for the $n=2,3$ as well as the first two $n=4$ singlet states. The diabatic potential energy curves of the HeH$^+$ molecular ion are obtained from the adiabatic potential energy curves and the non-adiabatic radial coupling matrix elements using a two-by-two diabatization method, and a time-dependent wave-packet approach is used to calculate the state-to-state cross sections. We find a strong dependence of the charge transfer cross section in the principal and orbital quantum numbers $n$ and $l$ of the initial or final state. We estimate the effect of the non-adiabatic rotational couplings, which is found to be important even at energies below 1 eV/amu. However, the effect is small on the total cross sections at energies below 10 eV/amu. We observe that to calculate charge transfer cross sections in a $n$ manifold, it is only necessary to include states with $n^{\prime}\leq n$, and we discuss the limitations of our approach as the number of states increases.Comment: 14 pages, 10 figure

Cold collisions of C2−_{2}^{-} anions with Li and Rb atoms in hybrid traps

We present a theoretical investigation of reactive and non-reactive collisions of Li and Rb atoms with C$_{2}^{-}$ molecular anions at low temperatures in the context of sympathetic cooling in hybrid trap experiments. Based on recently reported accurate potential energy surfaces for the singlet and triplet states of the Li-C$_{2}^{-}$ and Rb-C$_{2}^{-}$ systems, we show that the associative electronic detachment reaction is slow if the colliding partners are in their ground state, but fast if they are excited. The results are expected to be representative of the alkali-metal series. We also investigate rotationally inelastic collisions in order to explore the cooling of the translational and rotational degrees of freedom of C$_2^-$ in hybrid ion-atom traps. The effect of micromotion is taken into account by considering Tsallis distributions of collision energies. We show that the translational cooling occurs much more rapidly than rotational cooling and that the presence of excited atoms leads to losses of anions on a timescale comparable to that of rotational cooling.Comment: ICPEAC 2019 conferenc

Evidence for two-electron processes in the mutual neutralization of O- with O+ and N+ at Subthermal Collision Energies

We have measured total absolute cross sections for the Mutual Neutralization (MN) of O- with O+/N+. A fine resolution (of about 50 meV) in the kinetic energy spectra of the product neutral atoms allows unique identification of the atomic states participating in the mutual neutralization process. Cross sections and branching ratios have also been calculated down to 1 meV center-of-mass collision energy for these two systems with a multi-channel Landau-Zener model and an asymptotic method for the ionic-covalent coupling matrix elements. The importance of two-electron processes in one-electron transfer is demonstrated by the dominant contribution of a core-excited configuration of the nitrogen atom in N+ + O- collisions. This effect is partially accounted for by introducing configuration mixing in the evaluation of coupling matrix elements.Comment: 5 pages, 4 figure

Ab initio calculation of the 66 low lying electronic states of HeH+^+: adiabatic and diabatic representations

We present an ab initio study of the HeH$^+$ molecule. Using the quantum chemistry package MOLPRO and a large adapted basis set, we have calculated the adiabatic potential energy curves of the first 20 $^1 \Sigma^+$, 19 $^3\Sigma^+$, 12 $^1\Pi$, 9 $^3\Pi$, 4 $^1\Delta$ and 2 $^3\Delta$ electronic states of the ion in CASSCF and CI approaches. The results are compared with previous works. The radial and rotational non-adiabatic coupling matrix elements as well as the dipole moments are also calculated. The asymptotic behaviour of the potential energy curves and of the various couplings between the states is also studied. Using the radial couplings, the diabatic representation is defined and we present an example of our diabatization procedure on the $^1\Sigma^+$ states.Comment: v2. Minor text changes. 28 pages, 18 figures. accepted in J. Phys.

Combined CI+MBPT calculations of energy levels and transition amplitudes in Be, Mg, Ca, and Sr

Configuration interaction (CI) calculations in atoms with two valence electrons, carried out in the V(N-2) Hartree-Fock potential of the core, are corrected for core-valence interactions using many-body perturbation theory (MBPT). Two variants of the mixed CI+MBPT theory are described and applied to obtain energy levels and transition amplitudes for Be, Mg, Ca, and Sr