An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $- α\cos (θ)/r^2$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the radial equation can become attractive for low angular momenta. In this paper, we develop a general framework for an ion-dipole reactive scattering, focusing on the regime of large $α$. We introduce modified spherical harmonics as solutions of the angular part of the Schrödinger equation and derive several useful approximations in the limit of large $α$. We present a formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for the elastic and reactive collision rates. The solutions of the radial equation are given by Bessel functions, and we analyse their behaviour in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.
Analytic expressions describe universal elastic and reactive rates of quasi-two-dimensional and quasi-one-dimensional collisions of highly reactive ultracold molecules interacting by a van der Waals potential. Exact and approximate calculations for the example species of KRb show that stability and evaporative cooling can be realized for spin-polarized fermions at moderate dipole and trapping strength, whereas bosons or unlike fermions require significantly higher dipole or trapping strengths.
We study polar alkali dimer scattering in a quasi-1D geometry for both reactive and non-reactive species. Elastic and reactive rates are computed as a function of the amplitude of a static electric field within a purely long-range model with suitable boundary conditions at shorter range. We describe the diatomic molecules as rigid rotors and results are compared to the fixed-dipole approximation. We show in particular that for molecules with a sufficiently strong induced dipole moment oriented perpendicular to the trap axis, the long-range repulsive interaction leads to the suppression of shor…
We investigate collisions of polar molecules in quasi-2D traps in the presence of an external electric field perpendicular to the collision plane. We use the quantum-defect model characterized by two dimensionless parameters: $y$ and $s$. The first of them is related to the probability of the reaction at short distances, whereas the latter one defines the wave function phase at short distances. For $y$ close to unity we obtain universal collision rates determined by the quantum reflection process from the long-range part of the interaction potential that depends only on the van der Waals coeff…
Recent experimental developments in the loading of ultracold KRb molecules into quasi-two-dimensional traps, combined with the ability to tune the ratio between elastic and loss (inelastic/reactive) collisions through application of an external electric field, are opening the door to achieving efficient evaporative cooling of reactive polar molecules. In this paper, we use Monte Carlo simulations and semianalytic models to study theoretically the experimental parameter regimes in which evaporative cooling is feasible under current trapping conditions. We investigate the effect of the anisotrop…
We study polar molecule scattering in quasi-one-dimensional geometries. Elastic and reactive collision rates are computed as a function of collision energy and electric dipole moment for different confinement strengths. The numerical results are interpreted in terms of first order scattering and of adiabatic models. Universal dipolar scattering is also discussed. Our results are relevant to experiments where control of the collision dynamics through one dimensional confinement and an applied electric field is envisioned.
We present a combined experimental and theoretical study of cold reactive collisions between laser-cooled Ca+ ions and Rb atoms in an ion-atom hybrid trap. We observe rich chemical dynamics which are interpreted in terms of non-adiabatic and radiative charge exchange as well as radiative molecule formation using high-level electronic structure calculations. We study the role of light-assisted processes and show that the efficiency of the dominant chemical pathways is considerably enhanced in excited reaction channels. Our results illustrate the importance of radiative and non-radiative process…
We report on a study of cold reactive collisions between sympathetically-cooled molecular ions and laser-cooled atoms in an ion-atom hybrid trap. Chemical reactions were studied at average collision energies <Ecoll>/k > 20 mK, about two orders of magnitude lower than has been achieved in previous experiments with molecular ions. Choosing N2+ +Rb as a prototypical system, we find that the reaction rate is independent of the collision energy, but strongly dependent on the internal state of Rb. Highly efficient charge exchange about four times faster than the Langevin rate was observed with Rb in…
Cold chemical reactions between laser-cooled Ca^+ ions and Rb atoms were studied in an ion-atom hybrid trap. Reaction rate constants were determined in the range of collision energies <E_{coll}>/k_B = 20 mK-20 K. The lowest energies were achieved in experiments using single localized Ca^+ ions. Product branching ratios were studied using resonant-excitation mass spectrometry. The dynamics of the reactive processes in this system (non-radiative and radiative charge transfer as well as radiative association leading to the formation of CaRb^+ molecular ions) have been analyzed using high-level qu…
We present a study of vibrational quenching and chemical processes of molecular ions immersed in an ultracold atomic gas by means of the quasi-classical trajectory (QCT) method. In particular, BaRb$^+(v)$ + Rb collisions are studied at cold temperatures revealing a highly efficient energy transfer between the translational degrees of freedom and internal degrees of the molecular ion. Thus leading to a large vibrational quenching cross section which follows the Langevin capture model prediction. These results play a key role on the understanding of relaxation phenomena of cold molecular ions in…
We study a hybrid quantum system composed of an ion and an electric dipole. We show how a trapped ion can be used to measure the small electric field generated by a classical dipole. We discuss the application of this scheme to measure the electric dipole moment of cold polar molecules, whose internal state can be controlled with ultrafast laser pulses, by trapping them in the vicinity of a trapped ion.
We analyze reactive collisions of a single Ba$^+$ ion in contact with an ultracold gas of Rb atoms at low three-body collision energies of 2.2(9) mK$\times k_{\mathrm{B}}$. Mapping out the Ba$^+$ loss rate dependence on the Rb atom density we can discern two-body reactive collisions from three-body ones and for the first time determine both rate coefficients which are $k_2=3.1(6)(6)\times 10^{-13}\textrm{cm}^{3}\textrm{s}^{-1}$ and $k_3=1.04(4)(45)\times 10^{-24}\textrm{cm}^{6}\textrm{s}^{-1}$, respectively (statistical and systematic errors in parenthesis). Thus, the measured ternary recombin…
We report an optical dipole trap for calcium. The trap is created by focusing a 488 nm argon-ion laser beam into a calcium magneto-optical trap. The argon-ion laser photo-ionizes atoms in the trap because of a near-resonance with the 4s4f 1F3 level. By measuring the dipole trap decay rate as a function of argon-ion laser intensity, we determine the 1F3 photo-ionization cross section at our wavelength to be approximately 230 Mb.
The static dipole polarizabibility for the $1sσ$ electron state of the $\mathrm{H}_{2}^{+}$ hydrogen molecular ion is calculated within Born-Oppenheimer approximation. The variational expansion with randomly chosen exponents has been used for numerical studies. The results obtained for the dipole polarizability are accurate to the nine digits.
Progress in ultracold experiments with polar molecules requires a clear understanding of their interactions and reactivity at ultra-low collisional energies. Two important theoretical steps in this process are the characterization of interaction potentials between molecules and the modeling of reactive scattering mechanism. Here, we report on the {\it abinitio} calculation of isotropic and anisotropic van der Waals interaction potentials for polar KRb and RbCs colliding with each other or with ultracold atoms. Based on these potentials and two short-range scattering parameters we then develop …
The recently reported precise experimental determination of the dipole polarizability of the H_2^+ molecular ion ground state [P.L. Jacobson, R.A. Komara, W.G. Sturrus, and S.R. Lundeen, Phys. Rev. A 62, 012509 (2000)] reveals a discrepancy between theory and experiment of about 0.0007a_0^3, which has been attributed to relativistic and QED effects. In present work we analyze an influence of the relativistic effects on the scalar dipole polarizability of an isolated H_2^+ molecular ion. Our conclusion is that it accounts for only 1/5 of the measured discrepancy.
We develop a general quantum theory for reactive collisions involving power-law potentials (-1/r^n) valid from the ultracold up to the high-temperature limit. Our quantum defect framework extends the conventional capture models to include the non-universal case when the short-range reaction probability P^{re} < 1. We present explicit analytical formulas as well as numerical studies for the van der Waals (n = 6) and polarization (n = 4) potentials, and relate our work to recent merged beam experiments on Penning ionization for collision energies below 0.1 meV [Henson et al, Science 338, 234(201…
The one-electron quantum-electrodynamic corrections to the magnetic-dipole transition amplitude between the fine-structure levels (1s^2 2s^2 2p) ^2P_3/2 - ^2P_1/2 in boronlike ions are calculated to all orders in (αZ). The results obtained serve for improving the theoretical accuracy of the lifetime of the (1s^2 2s^2 2p) ^2P_3/2 level in boronlike argon.
The interaction between the electric dipole moment of a trapped molecular ion and the configuration of the confined Coulomb crystal couples the orientation of the molecule to its motion. We consider the practical feasibility of harnessing this interaction to initialize, process, and read out quantum information encoded in molecular ion qubits without optically illuminating the molecules. We present two schemes wherein a molecular ion can be entangled with a co-trapped atomic ion qubit, providing, among other things, a means for molecular state preparation and measurement. We also show that vir…
We study a simple model consisting of an atomic ion and a polar molecule trapped in a single setup, taking into consideration their electrostatic interaction. We determine analytically their collective modes of excitation as a function of their masses, trapping frequencies, distance, and the molecule's electric dipole moment. We then discuss the application of these collective excitations to cool molecules, to entangle molecules and ions, and to realize two-qubit gates between them. We finally present a numerical analysis of the possibility of applying these tools to study magnetically ordered…
The energy splitings for $J = 1$, $F=3/2$, $|M_F|=3/2$ hyperfine levels of the $^3Δ_1$ electronic state of $^{180}$Hf$^{19}$F$^+$ ion are calculated as functions of the external variable electric and magnetic fields within two approaches. In the first one transition to the rotating frame is performed, whereas in the second approach the quantization of rotating electromagnetic field is performed. Calculations are required for understanding possible systematic errors in the experiment to search for electron electric dipole moment (eEDM) on $^{180}$Hf$^{19}$F$^+$ ion.
The electron beam ion trap (EBIT) at the National Institute of Standards and Technology was used to produce highly-charged ions of hafnium, tantalum and gold with an open 3d shell. The extreme-ultraviolet (EUV) spectra from these ions were recorded with a flat-field grazing-incidence spectrometer in the wavelength range of 4.5 nm to 25 nm. A total of 133 new spectral lines, primarily due to magnetic-dipole transitions within the ground-state $3d^n$ configurations of the Co-like to K-like ions, were identified by comparing energy-dependent experimental spectra with a detailed collisional-radiat…
We consider the practical feasibility of using the direct, electric dipole-dipole interaction between co-trapped molecular ions for robust quantum logic without the need for static polarizing fields. The use of oscillating dipole moments, as opposed to static electric dipoles, dynamically decouples the dipoles from laboratory fields, including the electric fields of the trap itself. Further, this implementation does not require quantum control of motion, potentially removing a major roadblock to ion trap quantum computing scalability. Since the polarizing field is electromagnetic radiation, ev…
Using perturbed relativistic coupled-cluster (PRCC) theory we compute the ground state electric dipole polarizability, $α$, of doubly ionized alkaline earth metal ions $\rm{Mg}^{2+}$, $\rm{Ca}^{2+}$, $\rm{Sr}^{2+}$, $\rm{Ba}^{2+}$ and $\rm{Ra}^{2+}$. In the present work we use the Dirac-Coulomb-Breit atomic Hamiltonian and we also include the Uehling potential, which is the leading order term in the vacuum polarization corrections. We examine the correction to the orbital energies arising from the Uehling potential in the self-consistent field calculations as well as perturbatively. Our result…
The electric dipole moments of various neutral elementary particles, such as neutron, neutrinos, certain hypothetical dark matter particles and others, are predicted to exist by the standard model of high energy physics and various extensions of it. However, the predicted values are beyond the present experimental capabilities. We propose to simulate and emulate the electric dipole moment of neutral relativistic particles and the ensuing effects in the presence of electrostatic field by emulation of an extended Dirac equation in ion traps.
The sensitivity much better than $10^{-24} e$ cm may be expected in the searches for electric dipole moments (EDM) of $β$-active nuclei at ion storage rings. It would be a serious progress in studies of the CP-violation problem.
An electron beam ion trap (EBIT) is used to measure extreme ultraviolet spectra between 10 nm and 25 nm from highly-charged ions of tungsten with an open 3d shell (W XLVIII through W LVI). We found that almost all strong lines are due to the forbidden magnetic-dipole (M1) transitions within $3d^n$ ground configurations. A total of 37 spectral lines are identified for the first time using detailed collisional-radiative (CR) modeling of the EBIT spectra. A new level-merging scheme for compactification of rate equations is described. The CR simulations for Maxwellian plasmas show that several lin…
In this paper we present a technique for the precise measurement of electric dipole allowed transitions in trapped ions. By applying a probe and a cooling laser in quick succession, the full transition can be probed without causing distortion from heating the ion. In addition, two probes can be utilized to measure a dispersion-like signal, which is well suited to stabilizing the laser to the transition. We have fully characterized the parameters for the measurement and find that it is possible to measure the transition frequency to better than 100kHz with an interrogation time of 30s. The long…
Two efficient and isotope-selective resonant two-photon ionization techniques for loading barium ions into radio-frequency (RF)-traps are demonstrated. The scheme of using a strong dipole-allowed transition at λ=553 nm as a first step towards ionization is compared to the established technique of using a weak intercombination line (λ=413 nm). An increase of two orders of magnitude in the ionization efficiency is found favoring the transition at 553 nm. This technique can be implemented using commercial all-solid-state laser systems and is expected to be advantageous compared to other narrowban…
We present a fast and Quasideterministic protocol for the production of single ions and electrons from a cloud of laser cooled atoms. The approach is based on a two-step process where first a single Rydberg atom is photo-excited from a dipole-blockade configuration and subsequently ionized by an electric field pulse. We theoretically describe these excitation-ionization cycles via dynamical quantum maps and observe a rich behavior of the ionization dynamics as a function of laser Rabi frequency, pulse duration and particle number. Our results show that a fast sequential heralded production of …
The dynamic dipole polarizabilities for the Li atom and the Be+ ion in the 2s and 2p states are calculated using the variational method with a Hylleraas basis. The present polarizabilities represent the definitive values in the non-relativistic limit. Corrections due to relativistic effects are also estimated. Analytic representations of the polarizabilities for frequency ranges encompassing the n=3 excitations are presented. The recommended polarizabilities for ^7Li and ^9Be+ were 164.11 \pm 0.03 a.u. and 24.489 \pm 0.004 a.u..
We present the first systematic calculation of the electric dipole forbidden transitions in the homonuclear molecular ion H$_2^+$. We get that the transition rate from the ground "ortho" $(v\!=\!0,N\!=\!1,J\!=\!1/2)$ state to the ground "para" $(v\!=\!0,N\!=\!0,J\!=\!1/2)$ state is $4.9\!\times\!10^{-14}$ s$^{-1}$ that corresponds to the lifetime of $6.4\!\times\!10^5$ yr. The Einstein coefficient $A_{nn'}$ for the $(v\!=\!1,N\!=\!1,J\!=\!1/2)\!\to\!(v\!=\!0,N\!=\!0,J\!=\!1/2)$ transition is equal to $0.12\!\times\!10^{-9}$ s$^{-1}$, which is of "comparable" order with the values for quadrupol…
Studies of charge-charge (ion-ion, ion-electron, and electron-electron) coupling properties for ion impurities in an electron gas and for a two component plasma are carried out on the basis of a regularized electron-ion potential without short-range Coulomb divergence. This work is motivated in part by questions arising from recent spectroscopic measurements revealing discrepancies with present theoretical descriptions. Many of the current radiative property models for plasmas include only single electron-emitter collisions and neglect some or all charge-charge interactions. A molecular dynami…
A procedure is described for the precise nonrelativistic evaluation of the dipole polarizabilities of H_2^+ and D_2^+ that avoids any approximation based on the size of the electron mass relative to the nucleus mass. The procedure is constructed so that sum rules may be used to assess the accuracy of the calculation. The resulting polarizabilities are consistent with experiment within the error bars of the measurements and are far more precise than values obtained by other theoretical methods.
In a proof-of-principle experiment, we demonstrate that metastable nitric oxide molecules, NO(a$^4Π_i$), generated inside a pulsed, supersonic beam, can be detected by reactive gas-phase collisions with electronically excited Li atoms in the $2^2$P$_{3/2}$ state. Since the internal energy of NO(a$^4Π_i$, $v \leq 4$) is lower than the ionization potential of Li in the $2^2$S$_{1/2}$ electronic ground state, we observe that the product ion yield arising from autoionizing NO(a$^4Π_i$)+Li($2^2$S$_{1/2}$) collisions is a factor of 21 lower than the ion yield from NO(a$^4Π_i$)+Li($2^2$P$_{3/2}$) col…
The non-relativistic three-body Schrödinger equation of the heteronuclear molecular ion HD$^+$ is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states $v=0-3$ are calculated for total orbital momenta from 0 to 47. Energies are given with an accuracy from about 12 digits for the lowest vibrational level to at least 9 digits for the third vibrational excited level. With a simple calculation using the corresponding wave functions, accurate dipole transition probabilities per time unit between those l…
Bilodeau and Haugan [1], using Infrared laser photodetachment spectroscopy, measured the binding energies (BEs) of the ground state (4Fe9/2) and the excited state (4Fe7/2) of the Os^- ion to be 1.07780(12) eV and 0.553(3) eV, respectively. These values are consistent with those calculated using Relativistic Configuration Interaction (RCI) calculations [2]. Here we have calculated the BEs for the ground state and the two excited states of the Os^- ion using our recent complex angular momentum (CAM) methodology [3] and obtained the BEs of 1.910, 1.230 and 0.224 eV, respectively (see Figure). We …
The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric dipole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single…
Dipole-phonon quantum logic (DPQL) leverages the interaction between polar molecular ions and the motional modes of a trapped-ion Coulomb crystal to provide a potentially scalable route to quantum information science. Here, we study a class of candidate molecular ions for DPQL, the cationic alkaline-earth monoxides and monosulfides, which possess suitable structure for DPQL and can be produced in existing atomic ion experiments with little additional complexity. We present calculations of DPQL operations for one of these molecules, CaO$^+$, and discuss progress towards experimental realization…
In order to realize the full potential of ion trap quantum computers, an improved understanding is required of the motional heating that trapped ions experience. Experimental studies of the temperature-, frequency-, and ion--electrode distance-dependence of the electric field noise responsible for motional heating, as well as the noise before and after ion bombardment cleaning of trap electrodes, suggest that fluctuations of adsorbate dipoles are a likely source of so-called `anomalous heating,' or motional heating of the trapped ions at a rate much higher than the Johnson noise limit. Previou…
We define and measure the ratio (R) of the vector ac-Stark effect (or light shift) in the 6S_1/2 and 5D_3/2 states of a single trapped barium ion to 0.2% accuracy at two different off-resonant wavelengths. We earlier found R = -11.494(13) at 514.531nm and now report the value at 1111.68nm, R = +0.4176(8). These observations together yield a value of the <5D||er||4F> matrix element, previously unknown in the literature. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a new test of atomic theory and improve the understanding of atomic structure…
We demonstrate a new method for the direct measurement of atomic dipole transition matrix elements based on techniques developed for quantum information purposes. The scheme consists of measuring dispersive and absorptive off-resonant light-ion interactions and is applicable to many atomic species. We determine the dipole matrix element pertaining to the Ca II H line, i.e. the 4$^2$S$_{1/2} \leftrightarrow $ 4$^2$P$_{1/2}$ transition of $^{40}$Ca$^+$, for which we find the value 2.8928(43) ea$_0$. Moreover, the method allows us to deduce the lifetime of the 4$^2$P$_{1/2}$ state to be 6.904(26)…
In this work the inhomogeneous (zero-phonon line) and homogeneous line widths, and one projection of the permanent electric dipole moment change for the Ce 4f-5d transition in Y_2SiO_5 were measured in order to investigate the possibility for using Ce as a sensor to detect the hyperfine state of a spatially close-lying Pr or Eu ion. The experiments were carried out on Ce doped or Ce-Pr co-doped single Y_2SiO_5 crystals. The homogeneous line width was measured to be about 3 MHz, which is essentially limited by the excited state lifetime. Based on the line width measurements, the oscillator stre…
Ion-atom interactions are a comparatively recent field of research that has drawn considerable attention due to its applications in areas including quantum chemistry and quantum simulations. In first experiments, atomic ions and neutral atoms have been successfully overlapped by devising hybrid apparatuses combining established trapping methods, Paul traps for ions and optical or magneto-optical traps for neutral atoms, respectively. Since then, the field has seen considerable progress, but the inherent presence of radiofrequency (rf) fields in such hybrid traps was found to have a limiting im…
Internal states of polar molecules can be controlled by microwave-frequency electric dipole transitions. If the applied microwave electric field has a spatial gradient, these transitions also affect the motion of these dipolar particles. This capability can be used to engineer phonon-mediated quantum gates between e.g. trapped polar molecular ion qubits without laser illumination and without the need for cooling near the motional ground state. The result is a high-speed quantum processing toolbox for dipoles in thermal motion that combines the precision microwave control of solid-state qubits …
We report on single Barium ions confined in a near-infrared optical dipole trap for up to three seconds in absence of any radio-frequency fields. Additionally, the lifetime in a visible optical dipole trap is increased by two orders of magnitude as compared to the state-of-the-art using an efficient repumping method. We characterize the state-dependent potentials and measure an upper bound for the heating rate in the near-infrared trap. These findings are beneficial for entering the regime of ultracold interaction in atom-ion ensembles exploiting bichromatic optical dipole traps. Long lifetime…
