Session D26: Focus Session: Photophysics of Cold Molecules III

Spectroscopy of large hydrogen clusters in He droplets and H$_{2}$ droplets.

Clusters of molecular hydrogen (H$_{2}$) at low temperatures have been attracted much attention because of the possible superfluid phase of molecular hydrogen. Parahydrogen has been predicted to undergo Bose-Einstein condensate (BEC) and to exhibit a superfluid phase below 6 K. However, since the freezing point of H$_{2}$ (14 K) is much higher than the predicted superfluid transltion temperature, the supercooling of bulk H$_{2}$ system has not been achieved despite many attempts. Clusters are known to exhibit lower freezing and melting temperatures than their bulk system due to the size effect. In addition, the melting temperature may become significantly lower than the freezing temperature in such clusters, and coexistence of liquid and solid phases between the melting and freezing temperatures has been predicted theoretically. Thus, clusters of molecular hydrogen are very appealing system for the observation of possible superfluid phase of molecular hydrogen. Since superfluid is a macroscopic property, we have studied properties of hydrogen clusters with fairly large size ($N=100 - 10^{6}$) by using He droplet spectroscopy. Some advantages of using droplet spectroscopy for this study include (1) cluster size can be precisely controlled by its pickup process, and (2) the temperature of clusters is well defined. Laser induced fluorescence of several molecules doped in H$_{2}$ clusters showed clear evidence of non-rigidity of hydrogen clusters at 0.4 K or 4 K. We have also observed a clear difference in the LIF spectra between {\it parahydrogen} and {\it orthohydrogen} clusters. We will discuss the properties of large parahydrogen clusters from the dependence on the cluster size and concentration of orthohydrogen.   

Hydrogen clusters that remained fluid

\textit{Para}-H$_{2}$ may constitute the only other superfluid besides helium. The superfluid transition temperature is predicted to be around 2 K, well below freezing of H$_{2}$ at 13.8 K. Numerous attempts to supercool macroscopic H$_{2}$ samples proved to be unsuccessful. Our approach includes formation of H$_{2}$ clusters in a pulsed cryogenic nozzle beam expansion of a neat $p$H$_{2}$ gas as well as \textbf{\textit{X}}\textbf{{\%}} of $p$H$_{2}$ diluted in He and interrogation via Coherent Anti-Stokes Raman Scattering. At \textbf{\textit{X}}\textbf{ = 2 -- 100 {\%}} the frequency of the vibrational Q$_{1}$(0) line in clusters remains constant at about $\nu $ = 4149.7 cm$^{-1}$ very similar to 4149.6 cm$^{-1}$ as in solid $p$H$_{2}$ and lower than in liquid $p$H$_{2 }$at 18 K (4151.9 cm$^{-1})$. The rotational S$_{0}$(0) transition show some characteristic crystal field splitting having magnitude of about 6 cm$^{-1}$. The splitting pattern is different from that in the \textit{hcp} solid, suggesting different structure in solid $p$H$_{2}$ clusters. At \textbf{\textit{X}}\textbf{ $\le $ 2 {\%}}, the frequency of the Q$_{1}$(0) line increases to about 4150.5 cm$^{-1}$, which is consistent with that expected in the supercooled liquid. The S$_{0}$(0) transition in these clusters, consisting of about 5 x 10$^{4}$ molecules, appears as a single line at the same frequency as in liquid $p$H$_{2}$. The temperature of these supercooled clusters is estimated to be less than about 1 K. Possible superfluidity of the clusters is discussed.   

Three-body interactions in liquid and solid hydrogen: Evidence from vibrational spectroscopy

In the cryogenic low-density liquid and solid phases of H$_2$ and D$_2$, the H$_2$ and D$_2$ molecules retain good rotational and vibrational quantum numbers that characterize their internal degrees of freedom. High-resolution infrared and Raman spectroscopic experiments provide extremely sensitive probes of these degrees of freedom. We present here fully-first-principles calculations of the infrared and Raman spectra of liquid and solid H$_2$ and D$_2$, calculations that employ a high-quality six-dimensional coupled-cluster H$_2$-H$_2$ potential energy surface and quantum Monte Carlo treatments of the single-molecule translational degrees of freedom. The computed spectra agree very well with experimental results once we include three-body interactions among the molecules, interactions which we also compute using coupled-cluster quantum chemical methods. We predict the vibrational spectra of liquid and solid H$_2$ at several temperatures and densities to provide a framework for interpreting recent experiments designed to search for superfluid behavior in small H$_2$ droplets. We also present preliminary calculations of the spectra of mixed H$_2$/D$_2$ solids that show how positional disorder affects the spectral line shapes in these systems.   

Rotational spectrum of small, doped $^{3}$He clusters

In recent years, symmetry-adapted imaginary-time correlation functions have been extensively used to study the rotational spectrum of doped $^{4}$He clusters within the frame of the reptation quantum Monte Carlo method. The success of this approach relies on the choice of suitable correlation functions, whose spectral resolution is dominated by few, well separated eigenvalues of the Hamiltonian. Under these conditions, reliable excitation energies can be extracted by inverse Laplace transform. This method has been tailored for bosons, due to the positivity of the ground-state wave-function and to the distinctive scarcity of low-lying states. For sufficiently small systems, however, the states of the discrete spectrum can be calculated in the same manner also with Fermi statistics, using appropriate generalizations of the correlation functions. We present rotational spectra for small $^{3}$He clusters doped with molecules --such as CO2 and OCS-- whose effective moments of inertia, in $^{4}$He clusters, feature a non-trivial dependence on the system size, with a pronounced turnaround for less than 10 atoms.   

Quantum melting and superfluidity of molecular hydrogen clusters

Clusters of parahydroge comprising between 10 and 50 molecules have been extensively studied by computer simulations based on the continuous-space Worm Algorithm, which allows one to go down to temperatures as low as a few hundredths of a K. These clusters display an intriguing interplay of liquid- and solid-like behavior as a function of both temperature and cluster size. In this sense, their physics is far richer than that of helium clusters. An intriguing phenomenon predicted by our simulations is {\it quantum melting}, whereby clusters in some size range (roughly between 22 and 30 molecules) are observed to go from rigid, solid-like, to essentially structureless and liquid-like as the temperature is lowered, due to the onset of quantum exchange cycles involving all the molecules in the cluster. At low temperature these clusters turn superfluid; their local superfluid response has been analyzed, and found to be essentially uniform throughout the system in the $T\to 0$ limit, even in clusters with a pronounced shell structure. In particular, exchanges involving molecules in the inner and outer shells are shown to be underlying the superfluid response. This system can also allow one to gain insight into the relationship of the superfluid properties with Bose condensation, and aspect that has been thoroughly investigated.   

Alkaline Earth Metal Atom Complexes with HCN Trapped On/In Helium Droplets: Vibrational Excitation Induced Solvation and Desolvation

Infrared laser spectroscopy is used to probe the rotational dynamics of the binary HCN-M (M=Ca, Sr) complexes, either solvated within or bound to helium droplets. The ``surface bound'' spectral signatures reported previously for the HCN-alkali atom complexes are observed for both species, while a second band is observed for HCN-Ca that corresponds to a solvated species. IR-IR double resonance spectroscopy is used to probe the interconversion of the two distinct HCN-Ca populations. Above a threshold droplet size, vibrational excitation results in the solvation of the surface bound HCN-Sr complex.   

Imaging Photoelectron Dynamics in Doped Helium Droplets

Photoionization of He droplets doped with Xe and Kr atoms have been investigated by photoelectron imaging utilizing VUV synchrotron radiation. Photoelectron images were recorded over a wide range of He droplet sizes, photon energies, and dopant pick-up conditions. Significant ionization of dopants was observed at 21.6 eV, the absorption maximum of 2${ }^1P$electronic excited state of He droplets, suggesting an indirect ionization via excitation transfer. Photoelectron images and spectra indicate multiple pathways for photoelectrons generated by this process to escape the droplet. Special attention is paid to the excitation transfer dynamics and the electron relaxation in He droplets. It is found that excitation transfer from 2${ }^1P$state to dopants competes with relaxation to the lower 2${ }^1S$ state. The excitation is likely a localized exciton that transfers the energy to the dopant via a dipole-dipole hopping mechanism. The conduction band of He droplets as a function of droplet size is also observed. The conduction band edge reaches the bulk limit for the largest He droplets. The electron under the conduction band becomes trapped and forms an electron bubble that escapes the droplet by transcending a barrier near the liquid/vapor interface.   

Interchange-Tunneling Splitting in HCl Dimer in Helium Nanodroplets

Infrared spectra of HCl dimers have been obtained in helium nanodroplets. The splitting in the vibrationally excited state of the bonded H-Cl stretching band ($v_{2})$ in (H$^{35}$Cl - H$^{37}$Cl) dimers was obtained to be 2.7 cm$^{-1}$ as compared to 3.7 cm$^{-1}$ in free dimer. From the splitting, the strength of the interchange-tunneling interaction in liquid helium was obtained to be 0.85 cm$^{-1}$, which is about a factor of two smaller than in the free dimer. The results are compared with the previous spectroscopic study of (HF)$_{2}$ in He droplets as well as to the theoretical study of (HF)$_{2}$ and (HCl)$_{2}$ dimers in small He clusters.   

Path integral studies of methane rotations in $^4$He clusters

Path integral simulations have been carried out to study the rotations of a methane inside a single shell of $^4$He atoms at 0.3~K to address the question of whether dopant molecule rotations can be used to probe the quantum statistics and superfluidity of the shell. We examined the effects of the probe molecule on the $^4$He exchanges and their counter effects on the renormalized rotation constant of the probe systematically by varying the intrinsic moment of inertia of the methane. The observed effects show strong dependence on the intrinsic moment of inertia of the rotating probe, with a heavy probe favoring stronger templating of the $^4$He density and a corresponding suppression of exchanges in the shell, as well as a large renormalization in the probe's effective rotation constant, while a light probe shows almost no effect on the shell density or the effective rotation constant. These results can be rationalized in terms of a rotational smearing effect and suggest that there is no clearly quantifiable relationship between the superfluid fraction of the shell and the renormalized rotation constant of the probe for cases where the probe molecule has weak anisotropic interactions with the $^4$He atoms.   

Pump-probe spectroscopy of Rg-Br$_2$ linear isomers

We have recorded and analyzed the \mbox{\textit{X}$\rightarrow$\textit{B}} spectra for three Rg--Br-Br linear isomers [Rg = He, Ne, Ar] using pump-probe spectroscopy. This work is an interesting test case for the transition from quantum to quasi-classical dynamics, and how the dynamics are interconnected with changes in the potential energy surface. Helium is not only much lighter than argon, but the He-Br$_2$ potential well is much shallower than that of Ar-Br$_2$. Excitation spectra to individual Rg-Br$_2$ (\textit{B}, $\nu$') intermolecular potentials were recorded by probing the Br$_2$ (\textit{B}, $\nu$') asymptotic limit of the potential while scanning the pump laser. The continuum spectra of the three species are very different, with the He-Br$_2$ spectrum peaking at threshold while the Ar-Br$_2$ spectrum is negligible at threshold and strongly blue shifted. The linear Ne-Br$_2$ bond energy was measured to be \mbox{71 $\pm$ 3 cm$^{-1}$} by the threshold energy for the onset of the continuum. Since excitation tends to move electron density to the $\sigma^*$ orbital of the Br-Br bond near the rare gas atom, the intramolecular stretching vibration (Br-Br) and the intermolecular stretching vibration (Rg-Br) are strongly coupled. The experiments will be compared to a two dimensional model using the best available potential energy functions.   

Time-resolved photoionization of He droplets using high-harmonic

Helium droplets are widely used as nanocontainers for matrix-isolated rotational, vibrational and electronic spectroscopy. Their superfluid nature and low temperatures (0.37K) provide gentle environment for embedded atoms, molecules and complexes. However, most of the traditional spectroscopic techniques are not efficient for pure droplets, because of the very high energies of electronic transitions. One of the recent studies [1] conducted using synchrotron light demonstrated very interesting phenomena in photoionization of pure He droplets. It has been shown that below the threshold for He atom photoionization essentially zero kinetic energy electrons are emitted independent of the wavelength of the photoionizing radiation. In this contribution a new experiment will be presented utilizing a novel source of VUV radiation based on the high-harmonic generation. In this process femtosecond pulses of radiation are created, which will be used in a VUV-pump/IR-probe scheme to study dynamics of photoionization of He droplets. First results towards the time-dependent photoelectron spectra will be presented. [1] D. Peterka \textit{et al}, Phys. Rev. Lett. \textbf{91}, 043401 (2003)