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Register a new userSurface hopping methodology in laser-driven molecular dynamics
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A theoretical justification of the empirical surface hopping method for the laser-driven molecular dynamics is given utilizing the formalism of the exact factorization of the molecular wavefunction [Abedi et al., PRL $textbf{105}$, 123002 (2010)] in its quantum-classical limit. Employing an exactly solvable $textrm H_2^{;+}$-like model system, it is shown that the deterministic classical nuclear motion on a single time-dependent surface in this approach describes the same physics as stochastic (hopping-induced) motion on several surfaces, provided Floquet surfaces are applied. Both quantum-classical methods do describe reasonably well the exact nuclear wavepacket dynamics for extremely different dissociation scenarios. Hopping schemes using Born-Oppenheimer surfaces or instantaneous Born-Oppenheimer surfaces fail completely.
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We present closed-form analytic solutions to non-secular Bloch-Redfield master equations for quantum dynamics of a V-type system driven by weak coupling to a thermal bath. We focus on noise-induced Fano coherences among the excited states induced by incoherent driving of the V-system initially in the ground state. For suddenly turned-on incoherent driving, the time evolution of the coherences is determined by the damping parameter $zeta=frac{1}{2}(gamma_1+gamma_2)/Delta_p$, where $gamma_i$ are the radiative decay rates of the excited levels $i=1,2$, and $Delta_p=sqrt{Delta^2 + (1-p^2)gamma_1gamma_2}$ depends on the excited-state level splitting $Delta>0$ and the angle between the transition dipole moments in the energy basis. The coherences oscillate as a function of time in the underdamped limit ($zetagg1$), approach a long-lived quasi-steady state in the overdamped limit ($zetall 1$), and display an intermediate behavior at critical damping ($zeta= 1$). The sudden incoherent turn-on generates a mixture of excited eigenstates $|e_1rangle$ and $|e_2rangle$ and their in-phase coherent superposition $|phi_+rangle = frac{1}{sqrt{2bar{r}}}(sqrt{r_1} |e_1rangle + sqrt{r_2}|e_2rangle)$, which is remarkably long-lived in the overdamped limit (where $r_1$ and $r_2$ are the incoherent pumping rates). Formation of this coherent superposition {it enhances} the decay rate from the excited states to the ground state. In the strongly asymmetric V-system where the coupling strengths between the ground state and the excited states differ significantly, we identify additional asymptotic quasistationary coherences, which arise due to slow equilibration of one of the excited states. Finally, we demonstrate that noise-induced Fano coherences are maximized with respect to populations when $r_1=r_2$ and the transition dipole moments are fully aligned.
We analyze the attosecond electron dynamics in hydrogen molecular ion driven by an external intense laser field using ab-initio numerical simulations of the corresponding time-dependent Schr{{o}}dinger equation and Bohmian trajectories. To this end, we employ a one-dimensional model of the molecular ion in which the motion of the protons is frozen. The results of the Bohmian trajectory calculations do agree well with those of the ab-initio simulations and clearly visualize the electron transfer between the two protons in the field. In particular, the Bohmian trajectory calculations confirm the recently predicted attosecond transient localization of the electron at one of the protons and the related multiple bunches of the ionization current within a half cycle of the laser field. Further analysis based on the quantum trajectories shows that the electron dynamics in the molecular ion can be understood via the phase difference accumulated between the Coulomb wells at the two protons. Modeling of the dynamics using a simple two-state system leads us to an explanation for the sometimes counter-intuitive dynamics of an electron opposing the classical force of the electric field on the electron.
The transition between two distinct mechanisms for the laser-induced field-free orientation of CO molecules is observed via measurements of orientation revival times and subsequent comparison to theoretical calculations. In the first mechanism, which we find responsible for the orientation of CO up to peak intensities of 8 x 10^13 W/cm^2, the molecules are impulsively oriented through the hyperpolarizability interaction. At higher intensities, asymmetric depletion through orientation-selective ionization is the dominant orienting mechanism. In addition to the clear identification of the two regimes of orientation, we propose that careful measurements of the onset of the orientation depletion mechanism as a function of the laser intensity will provide a relatively simple route to calibrate absolute rates of non-perturbative strong-field molecular ionization.
Trajectory surface hopping (TSH) is one of the most widely used quantum-classical algorithms for nonadiabatic molecular dynamics. Despite its empirical effectiveness and popularity, a rigorous derivation of TSH as the classical limit of a combined quantum electron-nuclear dynamics is still missing. In this work we aim to elucidate the theoretical basis for the widely used hopping rules. Naturally, we concentrate thereby on the formal aspects of the TSH. Using a Gaussian wave packet limit, we derive the transition rates governing the hopping process at a simple avoided level crossing. In this derivation, which gives insight into the physics underlying the hopping process, some essential features of the standard TSH algorithm are retrieved, namely i) non-zero electronic transition rate (hopping probability) at avoided crossings; ii) rescaling of the nuclear velocities to conserve total energy; iii) electronic transition rates linear in the nonadiabatic coupling vectors. The well-known Landau-Zener model is then used for illustration.
We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical, the other where the center-of-mass motion is treated classically while rotational motion is quantized. We study the rotational dynamics and their influence on the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion, and that it departs from the Mathieu equation solution found for atomic ions. For the case of quantum rotations, we also evidence the effect of the above-mentioned coupling on the rotational states of the ion.
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