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The Journal of Chemical Physics

Optimal dynamic discrimination of similar quantum systems with time series data

Baiqing Li, HERSCHEL A. RABITZ, Jean‐Pierre Wolf

Published Apr 15, 2005• 38 citations
Publisher

Abstract

Optimal dynamic discrimination (ODD) was proposed [Li et al., J. Phys. Chem. B 106, 8125 (2002)] as a paradigm for discriminating noninteracting similar quantum systems in a mixture. This paper extends the ODD concept to optimize a laser control pulse for guiding similar quantum systems such that each exhibits a distinct time series signal for maximum discrimination. The use of temporal data addresses various experimental difficulties, including noise in the laser pulse, signal detection errors, and finite time resolution in the signal. Simulations of ODD with time series data are presented to explore these effects. It is found that the use of an optimally chosen control pulse can significantly enhance the discrimination quality. The ODD technique is also adapted to the case where the sample contains an unknown background species.

DOI
10.1063/1.1883170

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Optimal dynamic discrimination (ODD) was proposed [Li et al., J. Phys. Chem. B 106, 8125 (2002)] as a paradigm for discriminating noninteracting similar quantum systems in a mixture. This paper extends the ODD concept to optimize a laser control pulse for guiding similar quantum systems such that each exhibits a distinct time series signal for maximum discrimination. The use of temporal data addresses various experimental difficulties, including noise in the laser pulse, signal detection errors, and finite time resolution in the signal. Simulations of ODD with time series data are presented to explore these effects. It is found that the use of an optimally chosen control pulse can significantly enhance the discrimination quality. The ODD technique is also adapted to the case where the sample contains an unknown background species.
Optimal dynamic discrimination (ODD) of a mixture of similar quantum systems with time series signals enables the extraction of the associated concentrations with reasonable levels of laser-pulse noise, signal detection errors, and imperfect signal detector resolution [Li et al., J. Chem. Phys. 122, 154103 (2005)]. The ODD paradigm is reexpressed in the density-matrix formulation to allow for the consideration of environmental decoherence on the quality of the extracted concentrations, along with the above listed factors. Simulations show that although starting in a thermally mixed state along with decoherence can be detrimental to discrimination, these effects can be counteracted by seeking a suitable optimal control pulse. Additional sampling of the temporal data also aids in extracting more information to better implement ODD.
A paradigm for discriminating similar quantum systems in the laboratory is presented based on optimal control principles with the aid of closed loop learning algorithms. The optimal dynamic discrimination (ODD) process is simulated for a noninteracting mixture of up to three similar finite-dimensional quantum systems. The optimal control field giving rise to species discrimination, that considers the presence of field and observation noise, is deduced with a genetic algorithm (GA). The similar quantum systems yield distinct dynamics and detection signals, although influenced by the same control laser pulse. The ODD process is shown to operate by drawing on constructive and destructive interference effects to simultaneously maximize or minimize the signals from each of the species in the mixture. The ODD technique may have applications to the analysis and separation of possibly even complex chemical species.
Similar molecules or materials have comparable composition, structure, and other properties thus making them difficult to discriminate for purposes of detection. Although the species may be spectrally similar, they each could have significantly different (quantum) dynamical behavior for detection. Optimal dynamic discrimination (ODD) aims to maximally draw out the differences among similar species by manipulating their molecular dynamics with optimized radiation resources. The highest degrees of discrimination arise upon exploiting control of the quantum dynamics of the species. Theoretical analysis shows that quantum systems differing even infinitesimally in character may be distinguished by means of their dynamics when acted upon by a suitably shaped control field. Simulations have demonstrated the capabilities of optimal discrimination in the presence of laser-pulse noise, signal detection errors, and imperfect signal detection resolution. Recent experiments have demonstrated the feasibility of ODD.
Optimal dynamic discrimination (ODD) uses closed-loop learning control techniques to discriminate between similar quantum systems. ODD achieves discrimination by employing a shaped control (laser) pulse to simultaneously exploit the unique quantum dynamics particular to each system, even when they are quite similar. In this work, ODD is viewed in the context of multiobjective optimization, where the competing objectives are the degree of similarity of the quantum systems and the level of controlled discrimination that can be achieved. To facilitate this study, the D-MORPH gradient algorithm is extended to handle multiple quantum systems and multiple objectives. This work explores the trade-off between laser resources (e.g., the length of the pulse, fluence, etc.) and ODD's ability to discriminate between similar systems. A mechanism analysis is performed to identify the dominant pathways utilized to achieve discrimination between similar systems.
Optimal dynamic discrimination (ODD) was recently introduced as a technique for maximally drawing out and detecting the differences between similar quantum systems by exploiting their controllable dynamical properties. As a simulation of ODD, optimal fields were found that successfully discriminated among similar species, but the underlying mechanisms of the process remained obscure. Hamiltonian encoding (HE) has been introduced as a technique for identifying the mechanisms of controlled quantum dynamics. The results of a HE based simulation analysis of ODD are presented in this paper. Different types and degrees of constructive and destructive interference are shown to underly the controlled discrimination processes. In general, it is found that successful discrimination relies on more complex interfering pathways for increasingly similar systems or increasing numbers of similar quantum systems.