Bright-state expansion and optimal control of highly excited polyatomics

This paper reports the results of a study of the robustness of the field required to generate the isomerization reaction HCN→CNH as a function of number of degrees of freedom and the complexity of the description of the dynamics. The particular reduced state representation of the control process that is tested in this paper is the reaction path method proposed by Zhao and Rice. We show that if the description of the system dynamics includes vibrational motions perpendicular to the one-dimensional reaction path and both the interactions between those vibrations and between them and the reaction path, the fields found by the conventional computational scheme represent local optima, and none of these correspond to generating a transfer of 100% of the population from the ground vibrational state of HCN to a mixture of vibrational states of CNH. Moreover, it is very difficult to find fields that will efficiently transfer population from the ground vibrational state of HCN to particular vibrational states of CNH. Comparing the optimized control fields reported in this paper with those previously obtained using simplified versions of the reaction path reduction, one finds that the complexity ͑measured by the power spectra͒ of optimal control fields increases as the dynamical description includes more degrees of freedom and then the interactions between all of the degrees of freedom. The optimal control field generated using a simpler dynamical description is not a good guide to the optimal control field associated with a more complex dynamical description. We conclude that the reaction path method of reduction of the complexity of calculation of the optimal field required to drive a particular reaction is not likely to be useful for the design of fields with which to actively control reactions of polyatomic molecules.

Section: Introductionmentioning

confidence: 58%

A test of the dependence of an optimal control field on the number of molecular degrees of freedom: HCN isomerization

Shah

Rice

2000

“…In our previous investigations 11,4 we demonstrated selective excitation of any mode of linear acetylene ͑HCCH͒ as well as breaking of the CH bond with at most a pair of femtosecond, transform-limited infrared pulses of limited intensity. Although we showed a generic way to selectively excite the infrared-inactive CC stretch by a number of quanta ͑3 and 4 were demonstrated͒ with only a few infrared laser pulses, we do not envision a way to selectively break the very strong CC triple bond in acetylene with infrared laser pulses.…”

Section: Selective Ch-bond Excitation With a Single Frequency-swmentioning

confidence: 97%

Bond selective infrared multiphoton excitation and dissociation of linear monodeuterated acetylene

Kaluža

Muckerman

1996

Self Cite

Energetics and spin selectivity in the infrared multiphoton dissociation HN3(X1A')→N2(X1Σ g +)+NH(X3Σ−,a1Δ) AIP Conf.Quantum mechanical simulations of vibrational excitation of monodeuterated linear acetylene ͑HCCD͒ with linearly polarized, frequency-swept, intense but nonionizing infrared laser pulses are performed. The aim is selective dissociation of either H or D atoms by optimal shaping of the laser pulses. We use a discrete variable representation and a compact (Ͻ400 states͒ bright-state expansion to represent the wave function during and after the pulse. Wave packet propagations in the bright-state expansion are at least an order of magnitude faster than discrete variable representation wave packet propagations. This enables optimal-control calculations to find the best parameters for the laser pulses. The dynamics of CH-bond breaking with infrared pulses are very different from the dynamics of CD-bond breaking. This is a direct consequence of CH being the highest-frequency mode in the molecule. Selective CH-bond breaking is possible with two synchronized pulses, the first being quasi-resonant with the ⌬vϭ1 transitions in the CH stretch between vϭ0 and vϭ8, and the second being quasiresonant with ⌬vϭ2 transitions at higher v. H-atom yields as high as 7.7%, with H to D yield ratio as high as 2.1, are demonstrated. Selective CD-bond breaking is possible using a single, subpicosecond, frequency-swept pulse. D-atom yields as high as 3%, or D to H atom yield ratios as high as 3.9, are calculated.

“…[21][22][23][24][25] If the dynamics admit a significant reduction in N to an effective dimension N eff , the detriment of the factorial dimensional scaling of the suboptimal critical regions may be mitigated. The determination of the difference between the effective dimension N eff and the true Hilbert space dimension N of the system is necessarily dependent on the nature of the coupling of the system levels, the resolution and range of the controls, and the structure of the observable being optimized.…”

Section: A the Effective Dynamical Dimensionmentioning

confidence: 98%

Topology of the quantum control landscape for observables

Hsieh

Rabitz

2009

A broad class of quantum control problems entails optimizing the expectation value of an observable operator through tailored unitary propagation of the system density matrix. Such optimization processes can be viewed as a directed search over a quantum control landscape. The attainment of the global extrema of this landscape is the goal of quantum control. Local optima will generally exist, and their enumeration is shown to scale factorially with the system's effective Hilbert space dimension. A Hessian analysis reveals that these local optima have saddlepoint topology and cannot behave as suboptimal extrema traps. The implications of the landscape topology for practical quantum control efforts are discussed, including in the context of nonideal operating conditions.