David J. Tannor

Coherent pulse sequence induced control of selectivity of reactions: Exact quantum mechanical calculations

We present a novel approach to the control of selectivity of reaction products. The central idea is that in a two‐photon or multiphoton process that is resonant with an excited electronic state, the resonant excited state potential energy surface can be used to assist chemistry on the ground state potential energy surface. By controlling the delay between a pair of ultrashort (femtosecond) laser pulses, it is possible to control the propagation time on the excited state potential energy surface. Different propagation times, in turn, can be used to generate different chemical products. There are many cases for which selectivity of product formation should be possible using this scheme. We illustrate the methodology with numerical application to a variety of model two degree of freedom systems with two inequivalent exit channels. Branching ratios obtained using a swarm of classical trajectories are in good qualitative agreement with full quantum mechanical calculations.

NON-MARKOVIAN EVOLUTION OF THE DENSITY OPERATOR IN THE PRESENCE OF STRONG LASER FIELDS

We present an accurate, efficient, and flexible method for propagating spatially distributed density matrices in anharmonic potentials interacting with solvent and strong fields. The method is based on the Nakajima–Zwanzig projection operator formalism with a correlated reference state of the bath that takes memory effects and initial/final correlations to second order in the system–bath interaction into account. A key feature of the method proposed is a special parametrization of the bath spectral density leading to a set of coupled equations for primary and N auxiliary density matrices. These coupled master equations can be solved numerically by representing the density operator in eigenrepresentation or on a coordinate space grid, using the Fourier method to calculate the action of the kinetic and potential energy operators, and a combination of split operator and Cayley implicit method to compute the time evolution. The key advantages of the method are: (1) The system potential may consist of any numb...

Phase space approach to theories of quantum dissipation

Six major theories of quantum dissipative dynamics are compared: Redfield theory, the Gaussian phase space ansatz of Yan and Mukamel, the master equations of Agarwal, Caldeira-Leggett/Oppenheim-Romero-Rochin, and Louisell/Lax, and the semigroup theory of Lindblad. The time evolving density operator from each theory is transformed into a Wigner phase space distribution, and classical-quantum correspondence is investigated via comparison with the phase space distribution of the classical Fokker-Planck (FP) equation. Although the comparison is for the specific case of Markovian dynamics of the damped harmonic oscillator with no pure dephasing, certain inferences can be drawn about general systems. The following are our major conclusions: (1) The harmonic oscillator master equation derived from Redfield theory, in the limit of a classical bath, is identical to the Agarwal master equation. (2) Following Agarwal, the Agarwal master equation can be transformed to phase space, and differs from the classical FP eq...

Laser cooling of molecular internal degrees of freedom by a series of shaped pulses

Laser cooling of the vibrational motion of a molecule is investigated. The scheme is demonstrated for cooling the vibrational motion on the ground electronic surface of HBr. The radiation drives the excess energy into the excited electronic surface serving as a heat sink. Thermodynamic analysis shows that this cooling mechanism is analogous to a synchronous heat pump where the radiation supplies the power required to extract the heat out of the system. In the demonstration the flow of energy and population from one surface to the other is analyzed and compared to the power consumption from the radiation field. The analysis of the flows shows that the phase of the radiation becomes the active control parameter which promotes the transfer of one quantity and stops the transfer of another. In the cooling process the transfer of energy is promoted simultaneously with the stopping population transfer. The cooling process is defined by the entropy reduction of the ensemble. An analysis based on the second law o...

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. This leads to a single equation for complex S, and ultimately complex x and p but there is a reward for this complexification—a significantly higher degree of localization. The quantum force in the new approach vanishes for Gaussian wave packet dynamics, and its effect on barrier tunneling processes is orders of magnitude lower than that of the classical force. In fact, the current method is shown to be a rigorous extension of generalized Gaussian wave packet dynami...

Wave packet correlation function formulation of scattering theory: The quantum analog of classical S‐matrix theory

A novel time‐dependent quantum mechanical formulation of scattering theory is developed which is well suited for the calculation of individual S‐matrix elements. Wave packets corresponding to well‐defined reactant and product channel quantum numbers are propagated in to the interaction region using Mo/ller operators, the former forward in time and the latter backwards in time. The S‐matrix element Sβα(E) is then simply related to the Fourier transform at energy E of the time‐dependent correlation function between the two wave packets in the interaction region. The symmetric treatment of reactants and products allows the entrance and exit channel dynamics to be performed highly efficiently using different coordinate systems and different interaction representations. As a result, the formulation is expected to provide an improved route to the calculation of S‐matrix elements using quantum mechanical, as well as semiclassical propagation methods. The new formulation combines elements of classical S‐matrix th...

Controlled dissociation of I2 via optical transitions between the X and B electronic states

Abstract Recent progress in both theoretical and experimental methods has led to the widespread belief that control of chemical reactions with ultrashort laser pulses is in principle achievable. In this article, the I 2 molecule, which has been the subject of a great deal of femtosecond work, is studied theoretically as a prospect for experimental control. An unconstrained optimization of the electric field is performed, with the objective of dissociation on the B state. Krotovs optimization theory is used for this unconstrained optimization, which reduces the CPU time usage by a factor of four. The field which results from the optimization yields a probability of 99% for B state dissociation. The Husimi transform of the optimal field indicates a simple underlying structure, in contrast with many previous fields obtained by optimal control theory: the optimal field closely resembles a sequence of three Gaussian pulses with the same central frequency. Analysis of the optimal field indicates it operates by a quasi-cw excitation directly into the B continuum. A constrained optimization was then performed: the electric field was restricted onto the frequency interval from 0 to 19752 cm −1 to avoid the quasi-continuous-wave excitation mechanism. The optimal solution of this problem uses a three-photon pump—dump—pump (PDP) mechanism. The optimal field was approximated by sequences of three and four Gaussian-shaped laser pulses; the optimal and the two approximating fields gave 34%, 6% and 11% for the dissociation probability, respectively. The fields from the constrained optimization have fwhm on the order of 30–50 fs and intensities in the range of 10 10 W/cm 2 and should be experimentally producible with available technology.

Laser cooling of internal degrees of freedom. II

Theoretical progress in the cooling of internal degrees of freedom of molecules using shaped laser pulses is reported. The emphasis is on general concepts and universal constraints. Several alternative definitions of cooling are considered, including reduction of the von Neumann entropy, −tr{ρlogρ} and increase of the Renyi entropy, tr{ρ2}. A distinction between intensive and extensive considerations is used to analyse the cooling process in open systems. It is shown that the Renyi entropy increase is consistent with an increase in the system phase space density and an increase in the absolute population in the ground state. The limitations on cooling processes imposed by Hamiltonian generated unitary transformations are analyzed. For a single mode system with a ground and excited electronic surfaces driven by an external field it is shown that it is impossible to increase the ground state population beyond its initial value. A numerical example based on optimal control theory demonstrates this result....

Wave Packet Correlation Function Approach to H2(ν)+H→H+H2(ν′): Semiclassical Implementation

Scattering matrix elements for the collinear H2(ν)+H→H+H2(ν′) reaction are obtained using a recently developed time-dependent approach to scattering. The correlation function between reactant channel wave packet and product channel wave packet is used to determine the S-matrix elements. The time propagation of the reactant wave packet is performed by the semiclassical method of Herman and Kluk, which is an initial value, uniformly converged method. The agreement between the quantum and semiclassical results is far better than that obtained previously for this system by other semiclassical methods.

Dynamics of triatomic photodissociation in the interaction representation. I. Methodology

This paper presents a new, quantum mechanical, time dependent approach to the photodissociation of triatomic molecules in Jacobi coordinates. The algorithm is based on a nested interaction representation, designed to make the representation of the time evolving wave packet as compact as possible. The new equations of motion are solved numerically using a synthesis of grid techniques: the fast Fourier transform (FFT) method is used in Cartesian‐like coordinates, and the discrete variable representation (DVR) method in the angular or bending coordinate. A variant on the short iterative Lanczos (SIL) procedure is used for the temporal propagation of the wave packet. Rotational state distributions obtained from this new algorithm are presented for the single surface photodissociation of ClCN and for the two surface photodissociation of ICN. The ClCN results are in good agreement with the semiclassical results of Barts and Halpern [J. Phys. Chem. 93, 7346 (1989)] and in excellent agreement with the time indepe...