A time dependent density functional treatment of superfluid dynamics: Equilibration of the electron bubble in superfluid 4He

Unravelling the full relaxation dynamics of superexcited helium nanodroplets

The relaxation dynamics of superexcited superfluid He nanodroplets is thoroughly investigated by means of extreme-ultraviolet (XUV) femtosecond electron and ion spectroscopy complemented by time-dependent density functional theory (TDDFT). Three main paths leading to the emission of electrons and ions are identified: droplet autoionization, pump-probe photoionization, and autoionization induced by re-excitation of droplets relaxing into levels below the droplet ionization threshold. The most abundant product ions are He2+, generated by droplet autoionization and by photoionization of droplet-bound excited He atoms. He+ appear with some pump-probe delay as a result of the ejection He atoms in their lowest excited states from the droplets. The state-resolved time-dependent photoelectron spectra reveal that intermediate excited states of the droplets are populated in the course of the relaxation, terminating in the lowest-lying metastable singlet and triplet He atomic states. The slightly faster relaxation of the triplet state compared to the singlet state is in agreement with the simulation showing faster formation of a bubble around a He atom in the triplet state.

Dynamics of impurity clustering in superfluid 4He nanodroplets

Snapshot taken at 75 ps of the capture of six Ar atoms hitting a ⁴He₅₀₀₀ droplet at 100 m s⁻¹.

First Observation of Bright Solitons in Bulk Superfluid ^{4}He

The existence of bright solitons in bulk superfluid ^{4}He is demonstrated by time-resolved shadowgraph imaging experiments and density functional theory (DFT) calculations. The initial liquid compression that leads to the creation of nonlinear waves is produced by rapidly expanding plasma from laser ablation. After the leading dissipative period, these waves transform into bright solitons, which exhibit three characteristic features: dispersionless propagation, negligible interaction in a two-wave collision, and direct dependence between soliton amplitude and the propagation velocity. The experimental observations are supported by DFT calculations, which show rapid evolution of the initially compressed liquid into bright solitons. At high amplitudes, solitons become unstable and break down into dispersive shock waves.

A thermodynamic model to predict electron mobility in superfluid helium

Electron mobility in superfluid helium is modeled between 0.1 and 2.2 K by a van der Waals-type thermodynamic equation of state, which relates the free volume of solvated electrons to temperature, density, and phase dependent internal pressure. The model is first calibrated against known electron mobility reference data along the saturated vapor pressure line and then validated to reproduce the existing mobility literature values as a function of pressure and temperature with at least 10% accuracy. Four different electron mobility regimes are identified: (1) Landau critical velocity limit (T ≈ 0), (2) mobility limited by thermal phonons (T < 0.6 K), (3) thermal phonon and discrete roton scattering ("roton gas") limited mobility (0.6 K < T < 1.2 K), and (4) the viscous liquid ("roton continuum") limit (T > 1.2 K) where the ion solvation structure directly determines the mobility. In the latter regime, the Stokes equation can be used to estimate the hydrodynamic radius of the solvated electron based on its mobility and fluid viscosity. To account for the non-continuum behavior appearing below 1.2 K, the temperature and density dependent Millikan-Cunningham factor is introduced. The hydrodynamic electron bubble radii predicted by the present model appear generally larger than the solvation cavity interface barycenter values obtained from density functional theory (DFT) calculations. Based on the classical Stokes law, this difference can arise from the variation of viscosity and flow characteristics around the electron. The calculated DFT liquid density profiles show distinct oscillations at the vacuum/liquid interface, which increase the interface rigidity.

Interaction of Helium Rydberg State Molecules with Dense Helium

The interaction potentials of the He₂^* excimer, in the a³Σ_u, b³Π_g, c³Σ_g, and d³Σ_u electronic states with a ground state helium atom are presented. The symmetry of the interaction potentials closely follows the excimer Rydberg electron density with pronounced short-range minima appearing along the nodal planes of the Rydberg orbital. In such cases, a combination of the electrostatic short-range attraction combined with Pauli repulsion leads to the appearance of unusual long-range maxima in the potentials. Bosonic density functional calculations show that the ³d state excimer resides in a localized solvation bubble in dense helium at 4.5 K, with radii varying from 12.7 Å at 0.1 MPa to 10.8 Å at 2.4 MPa. The calculated ³d → ³b pressure-induced fluorescence band shifts are in good agreement with experimental results determined by application of corona discharge. The magnitude of the spectral shifts indicate that the observed He₂^* molecules emit from dense helium whereas the corresponding fluorescence signal from the discharge zone appears quenched. This implies that fluorescence spectroscopy involving this electronic transition can only be used to probe the state of the surrounding medium rather than the discharge zone itself.

Electron mobility in liquid and supercritical helium measured using corona discharges: a new semi-empirical model for cavity formation

Electron mobilities in supercritical and liquid helium were investigated as a function of the density. The mobilities were derived from I(V) curves measured in a high-pressure cryogenic cell using a corona discharge in point-plane electrode geometry for charge generation. The presented data spans a wide pressure and temperature range due to the versatility of our experimental set-up. Where data from previous investigations is available for comparison, very good agreement is found. We present a semi-empirical model to calculate electron mobilities both in the liquid and supercritical phase. This model requires the electron-helium scattering length and thermodynamic state equations as the only input and circumvents any need to consider surface tension. Our semi-empirical model reproduces experimental data very well, in particular towards lower densities where transitions from localised to delocalised electron states were observed.

Explosion of electron bubbles attached to quantized vortices in liquid He4

Electron bubbles in superfluid (4)He have been recently observed in low-temperature cavitation measurements under experimental conditions where quantized vortices are also present in the liquid, and which might be attached to the bubbles. We have calculated, within density functional theory, the structure and energetics of electron bubbles pinned to linear vortices in liquid (4)He at low temperature, and the pressure at which such structures become mechanically unstable. Our results are in semiquantitative agreement with the experiments. We discuss dynamical effects not included in the theoretical model used in the present calculations, and which could explain some discrepancies between our results and the experimental data.

Photostimulated electron detrapping and the two-state model for electron transport in nonpolar liquids

In common nonpolar liquids, such as saturated hydrocarbons, there is a dynamic equilibrium between trapped (localized) and quasifree (extended) states of the excess electron (the two-state model). Using time-resolved dc conductivity, the effect of 1064 nm laser photoexcitation of trapped electrons on the charge transport has been observed in liquid n-hexane and methylcyclohexane. The light promotes the electron from the trap into the conduction band of the liquid. From the analysis of the two-pulse, two-color photoconductivity data, the residence time of the electrons in traps has been estimated as ca. 8.3 ps for n-hexane and ca. 13 ps for methylcyclohexane (at 295 K). The rate of detrapping decreases at lower temperature with an activation energy of ca. 200 meV (280-320 K); the lifetime-mobility product for quasifree electrons scales linearly with the temperature. We suggest that the properties of trapped electrons in hydrocarbon liquids can be well accounted for using the simple spherical cavity model. The estimated localization time of the quasifree electron is 20-50 fs; both time estimates are in agreement with the "quasiballistic" model. This localization time is significantly lower than the value of 310+/-100 fs obtained using time-domain terahertz (THz) spectroscopy for the same system [E. Knoesel, M. Bonn, J. Shan, F. Wang, and T. F. Heinz, J. Chem. Phys. 121, 394 (2004)]. We suggest that the THz signal originates from the oscillations of electron bubbles rather than the free-electron plasma; vibrations of these bubbles may be responsible for the deviations from the Drude behavior observed below 0.4 THz. Various implications of these results are discussed.

Photoelectron imaging of helium droplets

The photoionization and photoelectron spectroscopy of He nanodroplets (10(4) atoms) has been studied by photoelectron imaging with photon energies from 22.5-24.5 eV. Total electron yield measurements reveal broad features, whose onset is approximately 1.5 eV below the ionization potential of atomic He. The photoelectron spectra are dominated by very low energy electrons, with <E(k)> less than 0.6 meV. These results are attributed to the formation and autoionization of highly vibrationally excited He(*)(n) Rydberg states within the cluster, followed by strong final state interactions between the photoelectron and the droplet.