David Grimes

Electric potential invariants and ions-in-molecules effective potentials for molecular Rydberg states

The dependence of multipole moments and polarizabilities on external fields appears in many applications including biomolecular molecular mechanics, optical non-linearity, nanomaterial calculations, and the perturbation of spectroscopic signatures in atomic clocks. Over a wide range of distances, distributed multipole and polarizability potentials can be applied to obtain the variation of atom-centered atoms-in-molecules electric properties like bonding-quenched polarizability. For cylindrically symmetric charge distributions, we examine single-center and atom-centered effective polarization potentials in a non-relativistic approximation for Rydberg states. For ions, the multipole expansion is strongly origin-dependent, but we note that origin-independent invariants can be defined. The several families of invariants correspond to optimized representations differing by origin and number of terms. Among them, a representation at the center of dipole polarizability optimizes the accuracy of the potential with terms through 1/r4. We formulate the single-center expansion in terms of polarization-modified effective multipole moments, defining a form related to the source-multipole expansion of Brink and Satchler. Atom-centered potentials are an origin independent alternative but are limited both by the properties allowed at each center and by the neglected effects like bond polarizability and charge flow. To enable comparisons between single-center effective potentials in Cartesian or spherical form and two-center effective potentials with differing levels of mutual induction between atomic centers, we give analytical expressions for the bond-length and origin-dependence of multipole and polarizability terms projected in the multipole and polarizability expansion of Buckingham. The atom-centered potentials can then be used with experimental data and ab initio calculations to estimate atoms-in-molecules properties. Some results are given for BaF+ and HF showing the utility and limitations of the approach. More detailed results on X 1Σ+ CaF+ are published separately.

Direct single-shot observation of millimeter-wave superradiance in Rydberg-Rydberg transitions

We have directly detected millimeter wave (mm-wave) free space superradiant emission from Rydberg states (

Coherent laser-millimeter-wave interactions en route to coherent population transfer

n \sim 30

CPMMW SPECTROSCOPY OF RYDBERG STATES OF NITRIC OXIDE

) of barium atoms in a single shot. We trigger the cooperative effects with a weak initial pulse and detect with single-shot sensitivity and 20 ps time resolution, which allows measurement and shot-by-shot analysis of the distribution of decay rates, time delays, and time-dependent frequency shifts. Cooperative line shifts and decay rates are observed that exceed values that would correspond to the Doppler width of 250 kHz by a factor of 20 and the spontaneous emission rate of 50 Hz by a factor of

EFFECTIVE ION-IN-MOLECULE POTENTIALS FOR NON-PENETRATING RYDBERG STATES OF POLAR MOLECULES

10^5

LASER-MILLIMETER-WAVE TWO-PHOTON RABI OSCILLATIONS EN ROUTE TO COHERENT POPULATION TRANSFER

. The initial superradiant output pulse is followed by evolution of the radiation-coupled many-body system toward complex long-lasting emission modes. A comparison to a mean-field theory is presented which reproduces the quantitative time-domain results, but fails to account for either the frequency-domain observations or the long-lived features.

ATOMIC PROPERTIES FROM ELECTRONIC STRUCTURE: X 1Σ+ CaF+

We demonstrate coherent two-photon population transfer to Rydberg states of barium atoms using a combination of a pulsed dye laser and a chirped-pulse millimeter-wave spectrometer. Numerical calculations, using a density matrix formalism, reproduce our experimental results and explain the factors responsible for the observed fractional population transferred, optimal experimental conditions, and possibilities for future improvements. The long coherence times associated with the millimeter-wave radiation aid in creating coherence between the ground state and Rydberg states, but higher-coherence laser sources are required to achieve stimulated Raman adiabatic passage and for applications to molecules.

Single-shot high-resolution heterodyne detection of millimeter wave superradiance in Rydberg-Rydberg transitions

The spectroscopy of Rydberg states of NO has a long history [1], stimulating both experimental and theoretical advances in our understanding of Rydberg structure and dynamics. The closed-shell ion-core (Σ) and small NO dipole moment result in regular patterns of Rydberg series in the Hund’s case (d) limit, which are well-described by long-range electrostatic models (e.g., [2]). We will present preliminary data on the core-nonpenetrating Rydberg states of NO (orbital angular momentum, ` ≥ 3) collected by chirped-pulse millimeter-wave (CPmmW) spectroscopy. Our technique directly detects electronic free induction decay (FID) between Rydberg states with ∆n* ≈ 1 in the region of n* ∼ 40-50, providing a large quantity (12 GHz bandwidth in a single shot) of high quality (resolution ∼ 350 kHz) spectra. Transitions between high-`, core-nonpenetrating Rydberg states act as reporters on the subtle details of the ion-core electric structure.

IT IS ALL ABOUT PHASE AND IT IS NOT STAR TREK

Effective potentials? What about Quantum Defect Theory fitting? • Interpretation of Rydberg spectroscopic data for polar molecules makes use of effective potentials that include both ionic bonding and polarizability in order to represent electric properties of the ion core. Quantum defect theory (QDT) models the spectrum but effective potentials yield physical properties. • Convergence properties of multipole + polarization potentials depend on the origin of the expansion. (origin at centers of (charge, dipole, mass, polarizability), but there are families of origin-invariant reductions. • Multipole series are asymptotic. They are most accurate when the terms omitted are minimized by a good choice of origin. • Atom-centered potentials remove the origin-dependence but are not generally more accurate than single-center expansions. The literature form is not selfconsistent. The two forms make different predictions of core properties. • BaF+ is shown as an example. Stephen L. Coy, David D. Grimes, Yan Zhou, Robert W. Field(1) and Bryan M. Wong(2)