Michael Messina

Quantum control of I2 in the gas phase and in condensed phase solid Kr matrix

We present experimental results and theoretical simulations for an example of quantum control in both gas and condensed phase environments. Specifically, we show that the natural spreading of vibrational wavepackets in anharmonic potentials can be counteracted when the wavepackets are prepared with properly tailored ultrafast light pulses, both for gas phase I2 and for I2 embedded in a cold Kr matrix. We use laser induced fluorescence to probe the evolution of the shaped wavepacket. In the gas phase, at 313 K, we show that molecular rotations play an important role in determining the localization of the prepared superposition. In the simulations, the role of rotations is taken into account using both exact quantum dynamics and nearly classical theory. For the condensed phase, since the dimensionality of the system precludes exact quantum simulations, nearly classical theory is used to model the process and to interpret the data. Both numerical simulations and experimental results indicate that a properly ...

Time‐dependent Hartree wave packet dynamical techniques for computation of electronically excited state optical spectra of many‐body quantum systems

An approximate solution technique for computing spectra of many‐body molecular systems is proposed. We focus for concreteness on 0 K electronic absorption and emission spectra. From a time‐domain perspective, it is necessary to propagate a well‐defined initial Schrodinger wave packet on a specified potential energy surface in order to extract such spectra. In order to perform this task for systems with many degrees of freedom, we investigate the utility of a time‐dependent Hartree factorization, in which the wave packet for the complete system is variationally factorized into a product of wave packets of smaller dimensionality. This method is shown to be both flexible and reliable for prototypical model systems associated with the physical problem of impurity spectra in host crystals. Successful application is made to a recently measured emission spectrum of I2 embedded in an argon matrix.

Quantum control of multidimensional systems: Implementation within the time‐dependent Hartree approximation

The exact formulation of quantum control is now well known and sufficiently general to describe multidimensional quantum systems. The implementation of this formalism relies on the solution of the time‐dependent Schrodinger equation (TDSE) of the system under study, and thus far has been limited for computational reasons to simple quantum systems of very small dimensionality. To study quantum control in larger systems, such as polyatomic molecules and condensed phases, we explore an implementation of the control formalism in which the TDSE is solved approximately using the time‐dependent Hartree (TDH) approximation. We demonstrate formally that the TDH approximation greatly simplifies the implementation of control in the weak response regime for multidimensional systems. We also present numerical examples to show that the TDH approximation for the weak response case is sufficiently accurate to predict the laser fields that best drive a quantum system to a desired goal at a desired time, in systems contain...

Quantum control of dissipative systems: Exact solutions

Optimal quantum control theory, which predicts the tailored light fields that best drive a system to a desired target, is applied to the quantum dissipative dynamics of systems linearly coupled to a Gaussian bath. To calculate the material response function required for optimizing the light field, the analytical solution is derived for the two-level Brownian harmonic oscillator model and the recently developed method for directly simulating the Gaussian force is implemented for anharmonic Brownian oscillators. This study confirms the feasibility of quantum control in favorable condensed phase environments and explores new quantum control features in the presence of dissipation, including memory effects and temperature dependence.

Centroid‐density quantum rate theory: Variational optimization of the dividing surface

A generalization of Feynman path integral quantum activated rate theory is presented that has classical variational transition state theory as its foundation. This approach is achieved by recasting the expression for the rate constant in a form that mimics the phase‐space integration over a dividing surface that is found in the classical theory. Centroid constrained partition functions are evaluated in terms of phase‐space imaginary time path integrals that have the coordinate and momenta centroids tied to the dividing surface. The present treatment extends the formalism developed by Voth, Chandler, and Miller [J. Chem. Phys. 91, 7749 (1989)] to arbitrary nonplanar and/or momentum dependent dividing surfaces. The resulting expression for the rate constant reduces to a strict variational upper bound to the rate constant in both the harmonic and classical limits. In the case of an activated system linearly coupled to a harmonic bath, the dividing surface may contain explicit solvent coordinate dependence so...

Centroid‐density quantum rate theory: Dynamical treatment of classical recrossing

A new method is presented for the calculation of quantum mechanical rate constants for activated processes. This method is a hybrid approach involving Feynman path integrals and classical dynamics that is an extension of previous work of Messina, Schenter, and Garrett [J. Chem. Phys. 98, 8525 (1993)]. We make an ansatz for the quantum mechanical analog to the classical flux correlation function expression for the rate constant. This expression involves an imaginary‐time, phase‐space Feynman path integral, with the dividing surface and characteristic function expressed as a function of the phase‐space centroid variables. The reactive flux correlation function is obtained from a classical‐like expression in which the characteristic function is evaluated by evolving the phase‐space centroid variables as if they were classical dynamical variables. We show that the theory gives exact analytic results in the high temperature and harmonic limits. The theory is further tested on a model anharmonic two‐dimensional...

Time‐of‐flight spectra of a particle scattering from a collinear harmonic lattice at finite temperature

A new formalism is developed for computing the time‐of‐flight spectrum of a particle scattering from a collinear harmonic lattice prepared at finite temperature. We use a time‐domain transcription to construct an S‐matrix formalism that can be easily implemented via Gaussian wave packet dynamics. Numerical results are presented for a particle scattered from a lattice containing 100 oscillators at several temperature values.

Quantum activated rate theory: Variational optimization of planar dividing surfaces

A variational procedure is presented for finding the optimal planar dividing surface within a centroid‐density based quantum rate theory for the model of a general reaction coordinate coupled to a harmonic bath. The approach described here is a limiting form of the method for choosing the best coordinate and momentum dependent dividing surfaces that was previously presented by the authors [J. Chem. Phys. 98, 8525 (1993)]. The present approach can also be considered a direct quantum mechanical generalization of the classical variational method of Berezhkovskii, Pollak, and Zitserman [J. Chem. Phys. 97, 2422 (1992)]. We also relate this method to the analytical approach of Voth [Chem. Phys. Lett. 170, 289 (1990)] that incorporates a transmission coefficient in the centroid‐density based quantum rate theory. The variational procedure is also applicable to systems coupled to a continuum of oscillators, and it is shown that this procedure can be efficiently implemented for an arbitrary number of oscillators in...

Approximate path integral methods for partition functions

We review several approximate methods for evaluating quantum mechanical partition functions with the goal of obtaining a method that is easy to implement for multidimensional systems but accurately incorporates quantum mechanical corrections to classical partition functions. A particularly promising method is one based upon an approximation to the path integral expression of the partition function. In this method, the partition‐function expression has the ease of evaluation of a classical partition function, and quantum mechanical effects are included by a weight function. Anharmonicity is included exactly in the classical Boltzmann average and local quadratic expansions around the centroid of the quantum paths yield a simple analytic form for the quantum weight function. We discuss the relationship between this expression and previous approximate methods and present numerical comparisons for model one‐dimensional potentials and for accurate three‐dimensional vibrational force fields for H2O and SO2.

A semi-classical implementation of quantum control using Gaussian wave packet dynamics

Abstract Quantum control has previously been implemented using the exact time dependent Schrodinger equation (TDSE). Such calculations are limited by computational difficulty to systems with only a few degrees of freedom. In order to implement quantum control in many-atom systems, with sufficient accuracy and computational speed, we explore here a semi-classical implementation in the weak response regime whereby the TDSE is solved approximately using Gaussian wave packet (GWP) dynamics. We demonstrate by example that, for suitable systems and targets, the GWP representation of the evolving quantum system can be used to accurately calculate globally optimal light fields.