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Quantum Dissipative Dynamics and Decoherence of Dimers on Helium Droplets

Martin Schlesinger

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

In this thesis, quantum dynamical simulations are performed in order to describe the vibrational motion of diatomic molecules in a highly quantum environment, so-called helium droplets. We aim to reproduce and explain experimental findings which were obtained from dimers on helium droplets. Nanometer-sized helium droplets contain several thousands of 4-He atoms. They serve as a host for embedded atoms or molecules and provide an ultracold “refrigerator” for them. Spectroscopy of molecules in or on these droplets reveals information on both the molecule and the helium environment. The droplets are known to be in the superfluid He II phase. Superfluidity in nanoscale systems is a steadily growing field of research. Spectra obtained from full quantum simulations for the unperturbed dimer show deviations from measurements with dimers on helium droplets. These deviations result from the influence of the helium environment on the dimer dynamics. In this work, a well-established quantum optical master equation is used in order to describe the dimer dynamics effectively. The master equation allows to describe damping fully quantum mechanically. By employing that equation in the quantum dynamical simulation, one can study the role of dissipation and decoherence in dimers on helium droplets. The effective description allows to explain experiments with Rb-2 dimers on helium droplets. Here, we identify vibrational damping and associated decoherence as the main explanation for the experimental results. The relation between decoherence and dissipation in Morse-like systems at zero temperature is studied in more detail. The dissipative model is also used to investigate experiments with K-2 dimers on helium droplets. However, by comparing numerical simulations with experimental data, one finds that further mechanisms are active. Here, a good agreement is obtained through accounting for rapid desorption of dimers. We find that decoherence occurs in the electronic manifold of the molecule. Finally, we are able to examine whether superfluidity of the host does play a role in these experiments.

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In this thesis, quantum dynamical simulations are performed in order to describe the vibrational motion of diatomic molecules in a highly quantum environment, so-called helium droplets. We aim to reproduce and explain experimental findings which were obtained from dimers on helium droplets. Nanometer-sized helium droplets contain several thousands of 4-He atoms. They serve as a host for embedded atoms or molecules and provide an ultracold “refrigerator” for them. Spectroscopy of molecules in or on these droplets reveals information on both the molecule and the helium environment. The droplets are known to be in the superfluid He II phase. Superfluidity in nanoscale systems is a steadily growing field of research. Spectra obtained from full quantum simulations for the unperturbed dimer show deviations from measurements with dimers on helium droplets. These deviations result from the influence of the helium environment on the dimer dynamics. In this work, a well-established quantum optical master equation is used in order to describe the dimer dynamics effectively. The master equation allows to describe damping fully quantum mechanically. By employing that equation in the quantum dynamical simulation, one can study the role of dissipation and decoherence in dimers on helium droplets. The effective description allows to explain experiments with Rb-2 dimers on helium droplets. Here, we identify vibrational damping and associated decoherence as the main explanation for the experimental results. The relation between decoherence and dissipation in Morse-like systems at zero temperature is studied in more detail. The dissipative model is also used to investigate experiments with K-2 dimers on helium droplets. However, by comparing numerical simulations with experimental data, one finds that further mechanisms are active. Here, a good agreement is obtained through accounting for rapid desorption of dimers. We find that decoherence occurs in the electronic manifold of the molecule. Finally, we are able to examine whether superfluidity of the host does play a role in these experiments.
Many microscopic properties of the only natural superfluid element helium have become available within the last 18 years through a number of novel experiments. The diffraction of matter-waves of small helium clusters has established the unusually large bond distance (5.2 nm) and extremely weak binding energy (10−7 eV) of the dimer and other exotic properties of small helium clusters. The high-resolution spectroscopy of closed-shell chromophore molecules attached to small clusters or embedded inside large superfluid droplets have revealed that as a result of superfluidity, molecules rotate virtually without friction and that only a handful of He atoms are required for microscopic superfluidity. The frictionless translational motion of atoms and molecules inside the droplets has also been observed. These and a number of other experiments demonstrate that helium droplets are the most gentle and coldest of all cryomatrices with enormous potential for a wide range of future applications.
For the past 30 years, helium nano-droplets have been of particular interest to experimentalists.Indeed, this is a cold dense finite liquid environment which is an excellent matrix forspectroscopy applications, in atomic and molecular collision physics as well as in ultra coldchemistry with ability of isolating interesting reactions intermediates like HOCO in OH + CO→ CO2 + H or to synthesize new materials as metallic nano-wires. These phenomena areconsequences of the quantum collective behaviour of helium atoms at temperature T < 1 Kwhich classify helium nano-droplets as quantum liquids. In this thesis work we propose tomodel photo-dissociation [1] of immersed diatomic as molecular iodine, doping and rotationalexcitation of these droplets by using an home-made molecular dynamics developed by Pr.Marius Lewerenz, the CLUSTER code. To take the quantum nature of helium atoms intoaccount the methodology exploits the quantum effective potential technique [2] at experimentalwork temperature 0.37 K.With the photo-dissociation, an excitation above a molecular fragmentation limit leads to twopossible scenarios depending one the amortised energy by the helium droplets. The first one isthe fast recombination so-called ’cage effect’ [3] and the second is where photo-fragmentsreside in the helium bath. But with nano-meter scale of droplets a third scenario is possible withfragments leaving the cluster surrounded by a helium solvating shell. Results are shown forhelium nano-droplets containing thousands atoms (2500 to 9000 He) and statistics on size andvelocity of I@Hen photo-fragments have been computed and are similar to experimentaloutcomes for analogous system CH3I [4].According experiments using 1 fs X-ray flashes [5], the helium nano-droplets are geoids whichis a clue indicating a rotation on itself as the Earth. Our code can set precise angular momentumin order to study the pattern of distortion from fission to multiple splitting. To evaluate thenumbers of sub-cluster a Complete Clustering algorithm based on graph theory has beenprogrammed exhibiting a linear complexity.To conclude a study of xenon doping is presented where the recombination dynamics unveils ametastable state called Atkins’ snowball [6] and different patterns of aggregation as nano-crystals and nano-wires well known by experimentalists
Below Tλ = 2.17 K, bulk 4He is a superfluid and has a non-zero Bose-Einstein condensate fraction. This work will focus primarily on how phenomena such as superfluidity, Bose condensation and superfluid vortices are manifested in microscopic, inhomogeneous helium systems. Path Integral Monte Carlo is a powerful method for calculating the equilibrium properties of quantum systems at finite temperature. We have achieved linear scaling of computer time with number of particles through the use of neighbor lists, allowing us to simulate systems of several thousand atoms. We have derived a local superfluid estimator and used it to examine the microscopic superfluid response around a molecule rotating in a helium nanodroplet. We found that the first solvation layer is well-described by a two dimensional superfluid, with thermal excitations occuring at a lower temperature than in bulk helium. The effective moment of inertia of a linear impurity in a helium droplet is calculated, and compared with experimental scattering results. In addition, we calculated the vortex formation energy for both pure droplets and droplets doped with linear impurities, and found that the linear impurities had a negligible impact on the formation energy. A possible spectroscopic signature of vortices in doped helium droplets was suggested. After deriving a local estimator, we calculated the condensate fraction throughout the free helium surface of a semi-infinite slab. These results, along with densitydensity correlation functions, were used to characterize the surface excitations and calculate the extent to which ripplons are present. In addition, the ripplon dispersion relation was calculated using imaginary-time correlation functions, and found to be lll in good agreement with experimental results. Finally, we have calculated the Dey be-Waller factor in solid helium for a range of temperatures and densities, and compared the scaling behavior with the predictions of harmonic theory. The first non-Gaussian contribution to the density distribution was calculated.
Molecules immersed in liquid helium are excellent probes of superfluidity. Their electronic, vibrational, and rotational dynamics provide valuable clues about the superfluid at the nanoscale. Here we report on the experimental study of the laser-induced rotation of helium dimers inside the superfluid 4 He bath at variable temperature. The coherent rotational dynamics of He 2 ∗ is initiated in a controlled way by ultrashort laser pulses and tracked by means of time-resolved laser-induced fluorescence. We detect the decay of rotational coherence on the nanosecond time scale and investigate the effects of temperature on the decoherence rate. The observed temperature dependence suggests a nonequilibrium evolution of the quantum bath, accompanied by the emission of the wave of second sound. The method offers ways of studying superfluidity with molecular nanoprobes under variable thermodynamic conditions.
Free superfluid helium droplets constitute a versatile medium for a diverse range of experiments in physics and chemistry that extend from studies of the fundamental laws of superfluid motion to the synthesis of novel nanomaterials. In particular, the emergence of quantum vortices in rotating helium droplets is one of the most dramatic hallmarks of superfluidity and gives detailed access to the wave function describing the quantum liquid. This review provides an introduction to quantum vorticity in helium droplets, followed by a historical account of experiments on vortex visualization in bulk superfluid helium and a more detailed discussion of recent advances in the study of the rotational motion of isolated, nano- to micrometer-scale superfluid helium droplets. Ultrafast X-ray and extreme ultraviolet scattering techniques enabled by X-ray free-electron lasers and high-order harmonic generation in particular have facilitated the in situ detection of droplet shapes and the imaging of vortex structures inside individual, isolated droplets. New applications of helium droplets ranging from studies of quantum phase separations to mechanisms of low-temperature aggregation are discussed.
The dynamics of a mixed quantum-classical system, in which the classical subsystem interacts with a dissipative bath, is investigated. This description of the dynamics will be appropriate if the details of the bath dynamics are unimportant but its presence plays an important role in the dissipation of energy to the environment. In this dynamical description, which can be simulated employing an ensemble of stochastic surface-hopping trajectories, the strength of the dissipation is controlled by a friction coefficient. We show that if decoherence, whose effects are controlled by the bath friction, is sufficiently rapid, the equation of motion can be reduced to a master equation. Thus, decoherence and the validity of master equation models may be explored as a function of bath friction. We use this framework to study the mechanism of decoherence in a simple model nonadiabatic chemical reaction.