Multidimensional Classical Liouville Dynamics with Quantum Initial Conditions

A simple and numerically efficient approach to Wigner transforms and classical Liouville dynamics in phase-space is presented. The Wigner transform can be obtained with a given accuracy by optimal decomposition of an initial quantum-mechanical wavefunction in terms of a minimal set of Gaussian wavepackets. The solution of the classical Liouville equation within the locally quadratic approximation of the potential energy function requires a representation of the density in terms of an ensemble of narrow Gaussian phase-space packets. The corresponding equations of motion can be efficiently solved by a modified Leap-Frog integrator. For both problems the use of Monte-Carlo based techniques allows numerical calculation in multidimensional cases where grid-based methods such as fast Fourier transforms are prohibitive. In total, the proposed strategy provides a practical and efficient tool for classical Liouville dynamics with quantum-mechanical initial states

Nonadiabatic Effects on Peptide Vibrational Dynamics Induced by Conformational Changes

Quantum dynamical simulations of vibrational spectroscopy have been carried out for glycine dipeptide (CH3-CO-NH-CH2-CO-NH-CH3). Conformational structure and dynamics are modeled in terms of the two Ramachandran dihedral angles of the molecular backbone. Potential energy surfaces and harmonic frequencies are obtained from electronic structure calculations at the density functional theory (B3LYP/6-31+G(d)) level. The ordering of the energetically most stable isomers (C7 and C5) is reversed upon inclusion of the quantum mechanical zero point vibrational energy. Vibrational spectra of various isomers show distinct differences, mainly in the region of the amide modes, thereby relating conformational structures and vibrational spectra. Conformational dynamics is modeled by propagation of quantum mechanical wave packets. Assuming a directed energy transfer to the torsional degrees of freedom, transitions between the C7 and C5 minimum energy structures occur on a sub-picosecond timescale (700 ... 800 fs). Vibrationally non-adiabatic effects are investigated for the case of the coupled, fundamentally excited amide I states. Using a two state-two mode model, the resulting wave packet dynamics is found to be strongly non-adiabatic due to the presence of a seam of the two potential energy surfaces. Initially prepared adiabatic vibrational states decay upon conformational change on a timescale of 200 ... 500 fs with population transfer of more than 50 % between the coupled amide I states. Also the vibrational energy transport between localized (excitonic) amide I vibrational states is strongly influenced by torsional dynamics of the molecular backbone where both enhanced and reduced decay rates are found. All these observations should allow the detection of conformational changes by means of time-dependent vibrational spectroscopy

Dimension reduction by balanced truncation: Application to light-induced control of open quantum systems

In linear control, balanced truncation is known as a powerful technique to reduce the state-space dimension of a system. Its basic principle is to identify a subspace of jointly easily controllable and observable states and then to restrict the dynamics to this subspace without changing the overall response of the system. This work deals with a first application of balanced truncation to the control of open quantum systems which are modeled by the Liouville-von Neumann equation within the Lindblad formalism. Generalization of the linear theory have been proposed to cope with the bilinear terms arising from the coupling between the control field and the quantum system. As an example we choose the dissipative quantum dynamics of a particle in an asymmetric double well potential driven by an external control field, monitoring population transfer between the potential wells as a control target. The accuracy of dimension reduction is investigated by comparing the populations obtained for the truncated system versus those for the original system. The dimension of the model system can be reduced very efficiently where the degree of reduction depends on temperature and relaxation rate

Fully Adaptive Propagation of the Quantum-Classical Liouville Equation

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a dynamical system are modeled quantum-mechanically while the remaining ones are treated within the classical approximation. Rothe methods established in the theory of partial differential equations are used to control both temporal and spatial discretization errors on grounds of a global tolerance criterion. The trapezoidal rule for adaptive integration of Liouville dynamics (TRAIL) [I. Horenko and M. Weiser, J. Comput. Chem. 24, 1921 (2003)] has been extended to account for non-adiabatic effects in molecular dynamics described by the quantum-classical Liouville equation. In the context of particle methods, the quality of the spatial approximation of the phase-space distributions is maximized while the numerical condition of the least-squares problem for the parameters of particles is minimized. The resulting dynamical scheme is based on a simultaneous propagation of moving particles (Gaussian and Dirac delta-like trajectories) in phase space employing a fully adaptive strategy to upgrade Dirac to Gaussian particles and, vice versa, downgrading Gaussians to Dirac-like trajectories. This allows for the combination of Monte-Carlo-based strategies for the sampling of densities and coherences in multi-dimensional problems with deterministic treatment of non-adiabatic effects. Numerical examples demonstrate the application of the method to spin-boson systems in different dimensionality. Non-adiabatic effects occuring at conical intersections are treated in the diabatic representation. By decreasing the global tolerance, the numerical solution obtained from the TRAIL scheme are shown to converge towards exact results

Intense XUV pulses from a compact HHG setup using a single harmonic

We report on a compact and spectrally intense extreme-ultraviolet (XUV) source, which is based on high-harmonic generation (HHG) driven by 395 nm pulses. In order to minimize the XUV virtual source size and to maximize the XUV flux, HHG is performed several Rayleigh lengths away from the driving laser focal plane in a high-density gas jet. As a result, a high focused XUV intensity of 5 × 1013 W cm−2 is achieved, using a beamline with a length of only two meters and a modest driving laser pulse energy of 3 mJ. The high XUV intensity is demonstrated by performing a nonlinear ionization experiment in argon, using an XUV spectrum that is dominated by a single harmonic at 22 eV. Ion charge states up to Ar3+ are observed, which requires the absorption of at least four XUV photons. The high XUV intensity and the narrow bandwidth are ideally suited for a variety of applications including photoelectron spectroscopy, the coherent control of resonant transitions and the imaging of nanoscale structures

Quantum-Classical Liouville Approach to Molecular Dynamics: Surface Hopping Gaussian Phase-Space Packets

In mixed quantum-classical molecular dynamics few but important degrees of freedom of a molecular system are modeled quantum-mechanically while the remaining degrees of freedom are treated within the classical approximation. Such models can be systematically derived as a first order approximation to the partial Wigner transform of the quantum Liouville-von Neumann equation. The resulting adiabatic quantum-classical Liouville equation (QCLE) can be decomposed into three individual propagators by means of a Trotter splitting: Phase oscillations of the coherences resulting from the time evolution of the quantum-mechanical subsystem. Exchange of densities and coherences reflecting non-adiabatic effects in quantum-classical dynamics. Classical Liouvillian transport of densities and coherences along adiabatic potential energy surfaces or arithmetic means thereof. A novel stochastic implementation of the QCLE is proposed in the present work. In order to substantially improve the traditional algorithm based on surface hopping trajectories [J. C. Tully, J. Chem. Phys. 93 (2), 1061 (1990)], we model the evolution of densities and coherences by a set of surface hopping Gaussian phase-space packets (GPPs) with variable width and with adjustable real or complex amplitudes, respectively. The dense sampling of phase-space offers two main advantages over other numerical schemes to solve the QCLE. First, it allows to perform a quantum-classical simulation employing a constant number of particles, i. e. the generation of new trajectories at each surface hop is avoided. Second, the effect of non-local operators in the exchange of densities and coherences can be treated without having to invoke the momentum jump approximation. For the example of a single avoided crossing we demonstrate that convergence towards fully quantum-mechanical dynamics is much faster for surface hopping GPPs than for trajectory-based methods. For dual avoided crossings the Gaussian-based dynamics correctly reproduces the quantum-mechanical result even when trajectory-based methods not accounting for the transport of coherences fail qualitatively

Rare-Gas Clusters in Intense Extreme-Ultraviolet Pulses from a High-Order Harmonic Source

We report evidence for two previously unidentified effects in the ionization of rare-gas clusters by intense extreme-ultraviolet pulses. First, electron spectra indicate multistep photoemission with increasing isotropy for larger clusters due to electron-atom collisions. Second, very slow (meV) electrons are interpreted as the first experimental evidence for Rydberg-like atomic state formation in the nanoplasma expansion. Only small fractions of Xe2+ ions were found, in sharp contrast to previous results recorded under comparable conditions [Murphy et al., Phys. Rev. Lett. 101, 203401 (2008)]

Tracing Electron-Ion Recombination in Nanoplasmas Produced by Extreme- Ultraviolet Irradiation of Rare-Gas Clusters

We investigate electron-ion recombination in nanoplasmas produced by the ionization of rare-gas clusters with intense femtosecond extreme-ultraviolet (XUV) pulses. The relaxation dynamics following XUV irradiation is studied using time-delayed 790-nm pulses, revealing the generation of a large number of excited atoms resulting from electron-ion recombination. In medium-sized Ar-Xe clusters, these atoms are preferentially created in the Xe core within 10 ps after the cluster ionization. The ionization of excited atoms serves as a sensitive probe for monitoring the cluster expansion dynamics up to the ns time scale