Molecular dynamics study of the sonic horizon of microscopic Laval nozzles.

A Laval nozzle can accelerate expanding gas above supersonic velocities, while cooling the gas in the process. This work investigates this process for microscopic Laval nozzles by means of nonequilibrium molecular dynamics simulations of stationary flow, using grand-canonical Monte Carlo particle reservoirs. We study the steady-state expansion of a simple fluid, a monoatomic gas interacting via a Lennard-Jones potential, through an idealized nozzle with atomically smooth walls. We obtain the thermodynamic state variables pressure, density, and temperature but also the Knudsen number, speed of sound, velocity, and the corresponding Mach number of the expanding gas for nozzles of different sizes. We find that the temperature is well defined in the sense that the each velocity components of the particles obey the Maxwell-Boltzmann distribution, but it is anisotropic, especially for small nozzles. The velocity autocorrelation function reveals a tendency towards condensation of the cooled supersonic gas, although the nozzles are too small for the formation of clusters. Overall we find that microscopic nozzles act qualitatively like macroscopic nozzles in that the particles are accelerated to supersonic speeds while their thermal motion relative to the stationary flow is cooled. We find that, like macroscopic Laval nozzles, microscopic nozzles also exhibit a sonic horizon, which is well defined on a microscopic scale. The sonic horizon is positioned only slightly further downstream compared to isentropic expansion through macroscopic nozzles, where it is situated in the most narrow part. We analyze the sonic horizon by studying space-time density correlations, i.e., how thermal fluctuations at two positions of the gas density are correlated in time and find that after the sonic horizon there are indeed no upstream correlations on a microscopic scale.

Nonadiabatic Laser-Induced Alignment Dynamics of Molecules on a Surface.

We demonstrate that a sodium dimer, Na_{2}(1^{3}Σ_{u}^{+}), residing on the surface of a helium nanodroplet, can be set into rotation by a nonresonant 1.0 ps infrared laser pulse. The time-dependent degree of alignment measured, exhibits a periodic, gradually decreasing structure that deviates qualitatively from that expected for gas-phase dimers. Comparison to alignment dynamics calculated from the time-dependent rotational Schrödinger equation shows that the deviation is due to the alignment dependent interaction between the dimer and the droplet surface. This interaction confines the dimer to the tangential plane of the droplet surface at the point where it resides and is the reason that the observed alignment dynamics is also well described by a 2D quantum rotor model.

Rotational Coherence Spectroscopy of Molecules in Helium Nanodroplets: Reconciling the Time and the Frequency Domains.

Alignment of OCS, CS_{2}, and I_{2} molecules embedded in helium nanodroplets is measured as a function of time following rotational excitation by a nonresonant, comparatively weak ps laser pulse. The distinct peaks in the power spectra, obtained by Fourier analysis, are used to determine the rotational, B, and centrifugal distortion, D, constants. For OCS, B and D match the values known from IR spectroscopy. For CS_{2} and I_{2}, they are the first experimental results reported. The alignment dynamics calculated from the gas-phase rotational Schrödinger equation, using the experimental in-droplet B and D values, agree in detail with the measurement for all three molecules. The rotational spectroscopy technique for molecules in helium droplets introduced here should apply to a range of molecules and complexes.

Rotational dissociation of impulsively aligned van der Waals complexes.

The nonadiabatic alignment dynamics of weakly bound molecule-atom complexes, induced by a moderately intense 300 fs nonresonant laser pulse, is calculated by direct numerical solution of the time-dependent Schrödinger equation. Our method propagates the wave function according to the coupled channel equations for the complex, which can be done in a very efficient and stable manner out to large times. We present results for two van der Waal complexes, CS2-He and HCCH-He, as respective examples of linear molecules with large and small moments of inertia. Our main result is that at intensities typical of nonadiabatic alignment experiments, these complexes rapidly dissociate. In the case of the CS2-He complex, the ensuing rotational dynamics resembles that of isolated molecules, whereas for the HCCH-He complex, the detachment of the He atom severely perturbs and essentially quenches the subsequent rotational motion. At intensities of the laser pulse ≲2.0 × 1012 W/cm2, it is shown that the molecule-He complex can rotate and align without breaking apart. We discuss the implications of our findings for recent experiments on iodine molecules solvated in helium nanodroplets.

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.

Solvation of Mg in helium-4: Are there meta-stable Mg dimers?

Experiments with 4He nanodroplets doped with Mg atoms were interpreted as the observation of the formation of weakly bound magnesium complexes. We present results for single Mg and Mg dimer solvation using the hypernetted chain/Euler-Lagrange (HNC-EL) method as well as path integral Monte Carlo simulations. We find that the phonon-mediated, indirect Mg-Mg interaction adds an oscillatory component to the direct Mg-Mg interaction. We undertake a step-by-step examination of the ingredients of the calculation of the phonon-induced interaction, comparing the results of semi-analytic HNC-EL calculations for bulk and single impurity results with experiments as well as Monte Carlo data. We do not find evidence for a sufficiently strong secondary minimum in the effective Mg-Mg interaction to support a metastable state.

Homogeneous Bose gas of dipolar molecules in the mean field approximation.

We present a mean field analysis of the effects of molecular rotation on the excitation spectrum and stability of ultracold dipolar gases. For an unpolarized homogeneous gas interacting with a pure dipole-dipole interaction, we find that for the rotational state L = 1 the dipole-dipole interaction causes a splitting of the translation-rotation energy levels into a single M = 0 and a doubly degenerate M = ±1 excitation. For all other rotational states, the dipole-dipole interaction does not lead to coupling of translations and rotations and therefore has no effect on the rotational degeneracy of the excitations. The addition of arbitrarily small electric fields is found to introduce instabilities similar to those known to arise in the fully polarized dipolar gas. As in the case of a fully polarized gas, addition of a large enough short range repulsive potential is seen to stabilize the system, with the critical value of the repulsive interaction required for stabilization being larger when rotations are included.

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.

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.

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.

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.

Electronically excited rubidium atom in a helium cluster or film.

We present theoretical studies of helium droplets and films doped with one electronically excited rubidium atom Rb( *) ((2)P). Diffusion and path integral Monte Carlo approaches are used to investigate the energetics and the structure of clusters containing up to 14 helium atoms. The surface of large clusters is approximated by a helium film. The nonpair additive potential energy surface is modeled using a diatomic in molecule scheme. Calculations show that the stable structure of Rb( *)He(n) consists of a seven helium atom ring centered at the rubidium, surrounded by a tirelike second solvation shell. A very different structure is obtained when performing a "vertical Monte Carlo transition." In this approach, a path integral Monte Carlo equilibration starts from the stable configuration of a rubidium atom in the electronic ground state adsorbed to the helium surface after switching to the electronically excited surface. In this case, Rb( *)He(n) relaxes to a weakly bound metastable state in which Rb( *) sits in a shallow dimple. The interpretation of the results is consistent with the recent experimental observations [G. Aubock et al., Phys. Rev. Lett. 101, 035301 (2008)].

Lineshape of rotational spectrum of CO in (4)He 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.

Solvation structure and rotational dynamics of LiH in 4He clusters.

We present results of path integral Monte Carlo simulations of LiH solvated in superfluid 4He clusters of size up to N = 100. Despite the light mass of LiH and the strongly anisotropic LiH-He potential with a large repulsion at the hydrogen end, LiH is solvated inside the cluster for sufficiently large N. Using path integral correlation function analysis, we have determined the dipole (J = 1) rotational excitations of the cluster and a corresponding effective rotational constant Beff of the solvated LiH. We predict that Beff is greatly reduced with respect to the gas-phase rotational constant B, to a value of only about 6% of B. This exceptionally large reduction of the rotational constant is due to the highly anisotropic 4He solvation structure around LiH. It does not follow the previously established trend of a relatively small B reduction for light molecules, showing the strongest reduction of all molecules in 4He to date. Comparison of the calculated rotational spectra of LiH in helium obeying Bose and Boltzmann statistics, respectively, demonstrates that the Bose statistics of helium is an essential requirement for obtaining well-defined molecule rotational spectra in helium-4.