We propose a fast and nondestructive spectroscopic method for single molecular ions that implements quantum logic schemes between an atomic ion and the molecular ion of interest. Our proposal relies on a hybrid coherent manipulation of the two-ion system, using optical or magnetic forces depending on the types of molecular levels to be addressed (e.g., Zeeman, rotational, vibrational or electronic degrees of freedom). The method is especially suited for the nondestructive precision spectroscopy of single molecular ions and sets a starting point for new hybrid quantum computation schemes that combine molecular and atomic ions, covering the measurement and entangling steps.

We review the solvation of atomic, molecular or cluster ions in HNDs. After briefly discussing the properties of snowballs in bulk helium we consider experimental conditions for the efficient synthesis of charged, doped HNDs. We show that the cluster ions observed in conventional mass spectrometers originate from fission of highly charged HNDs. The ionization threshold of HNDs doped with alkalis reveals the minimum cluster size required for full immersion. The abundance distributions of He ${}_N$X ${}^{\pm }$ ions frequently reveal local anomalies or magic numbers. We demonstrate that the abundance is approximately proportional to the evaporation energy. Observed and calculated magic numbers will be compiled, including data for ions solvated in molecular hydrogen. Alternative methods to forming He ${}_N$X ${}^{+}$ that do not employ HNDs will be summarized. Electronic excitation spectra of C ${}_{60}^{+}$ and polycyclic aromatic hydrocarbon ions reveal the properties of the helium adsorption layer in quantitative detail. Next we discuss theoretical efforts to describe the interaction between ions and helium. We close with summarizing the size dependence of physical quantities computed for atomic alkali and alkaline earth cations in helium, such as binding energy, superfluid fraction, structural order, radial density profiles, and the existence of first and higher solvation shells.

The time-dependent Hartree grid (TDHG) method is extended into an ab initio algorithm for obtaining exact quantum wave packet dynamics. The new algorithm employs a superposition of orthogonal zeroth order time-dependent basis functions generated from a single TDHG wave packet trajectory. The superposition coefficients are themselves time-dependent, and are responsible for mixing the basis functions in such a way as to represent exact solutions of the time-dependent Schrodinger equation. Evolution of the superposition coefficients is governed by a set of first-order linearly coupled ordinary differential equations. The couplings between coefficients are given by matrix elements of a naturally identified interaction potential taken between members of the zeroth order basis. In numerical tests involving computation of S-matrix elements for collinear inelastic atom–Morse oscillator scattering the method proves accurate, flexible and efficient, and appears to be easily extendable to more complicated systems.