Robert E. Zillich

Extrapolated high-order propagators for path integral Monte Carlo simulations

We present a new class of high-order imaginary time propagators for path integral Monte Carlo simulations that require no higher order derivatives of the potential nor explicit quadratures of Gaussian trajectories. Higher orders are achieved by an extrapolation of the primitive second-order propagator involving subtractions. By requiring all terms of the extrapolated propagator to have the same Gaussian trajectory, the subtraction only affects the potential part of the path integral. The resulting violation of positivity has surprisingly little effects on the accuracy of the algorithms at practical time steps. Thus in principle, arbitrarily high order algorithms can be devised for path integral Monte Carlo simulations. We verified the fourth, sixth, and eighth order convergences of these algorithms by solving for the ground state energy and pair distribution function of liquid (4)He, which is representative of a dense, and strongly interacting, quantum many-body system.

Roton-rotation coupling of acetylene in 4He.

Rotational absorption spectra of acetylene in superfluid 4He calculated using a path-integral correlation function approach are seen to result in an anomalously large distortion constant in addition to a reduced rotational constant, with values in excellent agreement with recent experiments. Semianalytic treatment of the dynamics with a combined correlated basis function-diffusion Monte Carlo method reveals that this anomalous behavior is due to strong coupling of the higher rotational states of the molecule with the roton and maxon excitations of 4He, and the associated divergence of the 4He density of states in this region.

Dynamics of 4He droplets

Optimized variational calculations have been carried out for clusters of 4He between N=20 and N=1000 atoms. For small cluster sizes with less or equal to 112 particles, where comparisons with existing diffusion Monte Carlo results are possible, we find good agreement for the ground state energies and densities. Using a somewhat simpler approximation, we also calculate the bound state energies of 3He atoms attached to these clusters. We then calculate excitations and the dynamic structure function. The complex and nonlocal self-energy introduced for that purpose gives access to the calculation of both elastic and inelastic scattering processes for 4He and 3He atoms impinging on the clusters.

Electronically excited rubidium atom in helium clusters and films. II. Second excited state and absorption spectrum

Following our work on the study of helium droplets and film doped with one electronically excited rubidium atom Rb(∗) ((2)P) [M. Leino, A. Viel, and R. E. Zillich, J. Chem. Phys. 129, 184308 (2008)], we focus in this paper on the second excited state. We present theoretical studies of such droplets and films using quantum Monte Carlo approaches. Diffusion and path integral Monte Carlo algorithms combined with a diatomics-in-molecule scheme to model the nonpair additive potential energy surface are used to investigate the energetics and the structure of Rb(∗)He(n) clusters. Helium films as a model for the limit of large clusters are also considered. As in our work on the first electronic excited state, our present calculations find stable Rb(∗)He(n) clusters. The structures obtained are however different with a He-Rb(∗)-He exciplex core to which more helium atoms are weakly attached, preferentially on one end of the core exciplex. The electronic absorption spectrum is also presented for increasing cluster sizes as well as for the film.

Theoretical study of Rb2 in He(N): potential energy surface and Monte Carlo simulations.

An analytical potential energy surface for a rigid Rb₂ in the ³Σ(u)⁺ state interacting with one helium atom based on accurate ab initio computations is proposed. This 2-dimensional potential is used, together with the pair approximation approach, to investigate Rb₂ attached to small helium clusters He(N) with N = 1-6, 12, and 20 by means of quantum Monte Carlo studies. The limit of large clusters is approximated by a flat helium surface. The relative orientation of the dialkali axis and the helium surface is found to be parallel. Dynamical investigations of the pendular and of the in-plane rotation of the rigid Rb₂ molecule on the surface are presented.

Laser-Induced Rotation of Iodine Molecules in Helium Nanodroplets: Revivals and Breaking Free

Rotation of molecules embedded in helium nanodroplets is explored by a combination of fs laser-induced alignment experiments and angulon quasiparticle theory. We demonstrate that at low fluence of the fs alignment pulse, the molecule and its solvation shell can be set into coherent collective rotation lasting long enough to form revivals. With increasing fluence, however, the revivals disappear-instead, rotational dynamics as rapid as for an isolated molecule is observed during the first few picoseconds. Classical calculations trace this phenomenon to transient decoupling of the molecule from its helium shell. Our results open novel opportunities for studying nonequilibrium solute-solvent dynamics and quantum thermalization.

Communication: Dopant-induced solvation of alkalis in liquid helium nanodroplets

Alkali metal atoms and small alkali clusters are classic heliophobes and when in contact with liquid helium they reside in a dimple on the surface. Here we show that alkalis can be induced to submerge into liquid helium when a highly polarizable co-solute, C60, is added to a helium nanodroplet. Evidence is presented that shows that all sodium clusters, and probably single Na atoms, enter the helium droplet in the presence of C60. Even clusters of cesium, an extreme heliophobe, dissolve in liquid helium when C60 is added. The sole exception is atomic Cs, which remains at the surface.

Rotational spectra of methane and deuterated methane in helium

We present calculations of the rotational excitations of CH(4) and CD(4) in helium using correlated basis function theory for excited states of spherical top molecules, together with ground state helium density distributions computed by diffusion Monte Carlo simulations. We derive the rotational self-energy for symmetric top molecules, generalizing the previous analysis for linear molecules. The analysis of the self-energy shows that in helium the symmetry of a rigid spherical rotor is lost. In particular, rotational levels with J=2 split into states of E and of F(2) symmetry. This splitting can be analyzed in terms of an effective tetrahedral distortion that is induced by coupling of the molecular rotation to density fluctuations of the helium. Additional splitting occurs within each symmetry group as a result of rotational coupling to the high density of states between the roton and maxon excitations of (4)He, which also results in broad bands in the corresponding rotational absorption spectra. Connecting these pure rotational dynamics of methane to experimental rovibrational spectra, our results imply that the R(1) line of CH(4) is significantly broadened, while the P(2) is not broadened by rotational relaxation, which is consistent with experiment. Comparison of our results for CH(4) and CD(4) shows that the reduction in the moment of inertia in (4)He scales approximately quadratically with the gas phase moment of inertia, as has also been observed experimentally.

CONCENTRATION DEPENDENCE OF THE EFFECTIVE MASS OF 3HE ATOMS IN 3HE-4HE MIXTURES

Recent measurements by Yorozu et al. (S. Yorozu, H. Fukuyama, and H. Ishimoto, Phys. Rev. B 48, 9660 (1993)) as well as by Simons and Mueller (R. Simons and R. M. Mueller, Czhechoslowak Journal of Physics Suppl. 46, 201 (1976)) have determined the effective mass of He-3 atoms in a He-3/He-4 mixture with great accuracy. We here report theoretical calculations for the dependence of that effective mass on the He-3 concentration. Using correlated basis functions perturbation theory to infinite order to compute effective interactions in the appropriate channels, we obtain good agreement between theory and experiment.

Lineshape of rotational spectrum of CO in He4 droplets

In a recent experiment the rovibrational spectrum of CO isotopomers in superfluid helium-4 droplets was measured, and a Lorentzian lineshape with a large line width of 0.024 K (half width at half maximum) was observed [von Haeften et al., Phys. Rev. B 73, 054502 (2006)]. In the accompanying theoretical analysis it was concluded that the broadening mechanism may be homogeneous and due to coupling to collective droplet excitations (phonons). Here we generalize the lineshape analysis to account for the statistical distribution of droplet sizes present in nozzle expansion experiments. These calculations suggest an alternative explanation for the spectral broadening, namely, that the coupling to phonons can give rise to an inhomogeneous broadening as a result of averaging isolated rotation-phonon resonances over a broad cluster size distribution. This is seen to result in Lorentzian lineshapes, with a width and peak position that depend weakly on the size distribution, showing oscillatory behavior for the narrower size distributions. These oscillations decrease with droplet size and for large enough droplets ( approximately 10(4)) the line widths saturate at a value equal to the homogeneous line width calculated for the bulk limit.