Control of concerted back-to-back double ionization dynamics in helium.

Double ionization (DI) is a fundamental process that despite its apparent simplicity provides rich opportunities for probing and controlling the electronic motion. Even for the simplest multielectron atom, helium, new DI mechanisms are still being found. To first order in the field strength, a strong external field doubly ionizes the electrons in helium such that they are ejected into the same direction (front-to-back motion).

Communication: Systematic elimination of Stokes divergences emanating from complex phase space caustics.

Stokes phenomenon refers to the fact that an asymptotic expansion of complex functions can differ in different regions of the complex plane, and that beyond the so-called Stokes lines the expansion has an unphysical divergence. An important special case is when the Stokes lines emanate from phase space caustics of a complex trajectory manifold. In this case, symmetry determines that to second order there is a double coverage of the space, one portion of which is unphysical.

Multivalued classical mechanics arising from singularity loops in complex time.

Complex-valued classical trajectories in complex time encounter singular times at which the momentum diverges. A closed time contour around such a singular time may result in final values for q and p that differ from their initial values. In this work, we develop a calculus for determining the exponent and prefactor of the asymptotic time dependence of p from the singularities of the potential as the singularity time is approached.

Quantum Dynamics in Phase Space using Projected von Neumann Bases.

We describe the mathematical underpinnings of the biorthogonal von Neumann method for quantum mechanical simulations (PvB). In particular, we present a detailed discussion of the important issue of nonorthogonal projection onto subspaces of biorthogonal bases, and how this differs from orthogonal projection. We present various representations of the Schrödinger equation in the reduced basis and discuss their relative merits.

Communication: overcoming the root search problem in complex quantum trajectory calculations.

Three new developments are presented regarding the semiclassical coherent state propagator. First, we present a conceptually different derivation of Huber and Heller's method for identifying complex root trajectories and their equations of motion [D. Huber and E.

The von Neumann basis in non-Cartesian coordinates: application to floppy triatomic molecules.

We extend the periodic von Neumann basis to non-Cartesian coordinates. The bound states of two isomerizing triatomic molecules, LiCN/LiNC and HCN/HNC, are calculated using the vibrational Hamiltonian in Jacobi coordinates. The phase space localization of the basis functions leads to a flexible and accurate representation of the Hamiltonian.

Excited-state wavepacket and potential reconstruction by coherent anti-Stokes Raman scattering.

Among the major challenges in the chemical sciences is controlling chemical reactions and deciphering their mechanisms. Since much of chemistry occurs in excited electronic states, in the last three decades scientists have employed a wide variety of experimental techniques and theoretical methods to recover excited-state potential energy surfaces and the wavepackets that evolve on them. These methods have been partially successful but generally do not provide a complete reconstruction of either the excited state wavepacket or potential.

Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation.

We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schrödinger equation, and the population exchange arises naturally from amplitude-transfer terms.

Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation.

We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D.

Phase-space approach to solving the time-independent Schrödinger equation.

We propose a method for solving the time-independent Schrödinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice [F. Dimler et al.

Communication: Phase space wavelets for solving Coulomb problems.

Recently we introduced a phase space approach for solving the time-independent Schrödinger equation using a periodic von Neumann basis with bi-orthogonal exchange (pvb) [A. Shimshovitz and D. J.

Communication: phase space approach to laser-driven electronic wavepacket propagation.

We propose a phase space method to propagate a quantum wavepacket driven by a strong external field. The method employs the periodic von Neumann basis with biorthogonal exchange recently introduced for the calculation of the energy eigenstates of time-independent quantum systems [A. Shimshovitz and D.

Multi-dimensional wavepacket and potential reconstruction by resonant coherent anti-Stokes Raman scattering: application to H2O and HOD.

We have recently proposed a methodology for reconstructing excited-state (ExS) molecular wavepackets, and the corresponding potential energy surface, from three-pulse resonant coherent anti-Stokes Raman scattering and knowledge of the ground-state potential [Avisar and Tannor, Phys. Rev. Lett.

Complete reconstruction of the wave function of a reacting molecule by four-wave mixing spectroscopy.

Probing the real time dynamics of a reacting molecule remains one of the central challenges in chemistry. Here we show how the time-dependent wave function of an excited-state reacting molecule can be completely reconstructed from resonant coherent anti-Stokes Raman spectroscopy. The method assumes knowledge of the ground potential but not of any excited potential.

Are there traps in quantum control landscapes?

There has been great interest in recent years in quantum control landscapes. Given an objective J that depends on a control field ε the dynamical landscape is defined by the properties of the Hessian δ²J/δε² at the critical points δJ/δε=0. We show that contrary to recent claims in the literature the dynamical control landscape can exhibit trapping behavior due to the existence of special critical points and illustrate this finding with an example of a 3-level Λ system.

Adaptive coherent control using the von Neumann basis.

Recently we introduced the von Neumann representation as a joint time-frequency description for femtosecond laser pulses. Here we show that the von Neumann basis can be implemented into an evolutionary algorithm for adaptive optimization in coherent control. We perform simulations that demonstrate the efficiency compared to other parametrizations in the frequency domain.

Trajectory based non-markovian dissipative tunneling.

The influence of a dissipative environment on scattering of a particle by a barrier is investigated by using the recently introduced bohmian mechanics with complex action [J. Chem. Phys.

Wavepacket and potential reconstruction by four-wave mixing spectroscopy: preliminary application to polyatomic molecules.

We have recently shown how the excited-state wavepacket of a polyatomic molecule can be completely reconstructed from resonant coherent anti-Stokes Raman spectroscopy [Avisar and Tannor, Phys. Rev. Lett.

Molecular quantum control landscapes in von Neumann time-frequency phase space.

Recently we introduced the von Neumann representation as a joint time-frequency description for femtosecond laser pulses and suggested its use as a basis for pulse shaping experiments. Here we use the von Neumann basis to represent multidimensional molecular control landscapes, providing insight into the molecular dynamics. We present three kinds of time-frequency phase space scanning procedures based on the von Neumann formalism: variation of intensity, time-frequency phase space position, and/or the relative phase of single subpulses.

Complex trajectory method in time-dependent WKB.

We present a significant improvement to a complex time-dependent WKB (CWKB) formulation developed by Boiron and Lombardi [J. Chem. Phys.

The von Neumann picture: a new representation for ultrashort laser pulses.

In recent years, the use of joint time-frequency representations to characterize and interpret shaped femtosecond laser pulses has proven to be very useful. However, the number of points in a joint time-frequency representation is daunting as compared with those in either the frequency or time representation. In this article we introduce the use of the von Neumann representation, in which a femtosecond pulse is represented on a discrete lattice of evenly spaced time-frequency points using a non-orthogonal Gaussian basis.

Interference in Bohmian mechanics with complex action.

In recent years, intensive effort has gone into developing numerical tools for exact quantum mechanical calculations that are based on Bohmian mechanics. As part of this effort we have recently developed as alternative formulation of Bohmian mechanics in which the quantum action S is taken to be complex [Y. Goldfarb et al.

Unified derivation of Bohmian methods and the incorporation of interference effects.

We present a unified derivation of Bohmian methods that serves as a common starting point for the derivative propagation method (DPM), Bohmian mechanics with complex action (BOMCA), and the zero-velocity complex action method (ZEVCA). The unified derivation begins with the ansatz psi = eiS/Planck's where the action (S) is taken to be complex, and the quantum force is obtained by writing a hierarchy of equations of motion for the phase partial derivatives. We demonstrate how different choices of the trajectory velocity field yield different formulations such as DPM, BOMCA, and ZEVCA.

Bohmian mechanics with complex action: a new trajectory-based formulation of quantum mechanics.

In recent years there has been a resurgence of interest in Bohmian mechanics as a numerical tool because of its local dynamics, which suggest the possibility of significant computational advantages for the simulation of large quantum systems. However, closer inspection of the Bohmian formulation reveals that the nonlocality of quantum mechanics has not disappeared-it has simply been swept under the rug into the quantum force. In this paper we present a new formulation of Bohmian mechanics in which the quantum action, S, is taken to be complex.

Calculating multidimensional discrete variable representations from cubature formulas.

Finding multidimensional nondirect product discrete variable representations (DVRs) of Hamiltonian operators is one of the long standing challenges in computational quantum mechanics. The concept of a "DVR set" was introduced as a general framework for treating this problem by R. G.