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Journal of Physics A Mathematical and General

Optimal discrimination of multiple quantum systems: controllability analysis

Gabriel Turinici, Viswanath Ramakhrishna, Baiqing Li, HERSCHEL A. RABITZ

Published Dec 9, 2003• 41 citations
Publisher

Abstract

A theoretical study is presented concerning the ability to dynamically discriminate between members of a set of different (but possibly similar) quantum systems. This discrimination is analysed in terms of independently and simultaneously steering about the wavefunction of each component system to a target state of interest using a tailored control (i.e. laser) field. Controllability criteria are revealed and their applicability is demonstrated in simple cases. Discussion is also presented in some uncontrollable cases.

DOI
10.1088/0305-4470/37/1/019

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A theoretical study is presented concerning the ability to dynamically discriminate between members of a set of different (but possibly similar) quantum systems. This discrimination is analysed in terms of independently and simultaneously steering about the wavefunction of each component system to a target state of interest using a tailored control (i.e. laser) field. Controllability criteria are revealed and their applicability is demonstrated in simple cases. Discussion is also presented in some uncontrollable cases.
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.
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.
In this article, we present an overview of theory and technique for optimal control of molecular dynamics using tailored light fields. The goal of this research is to design an optical field, which can drive a system to a desired target state with a fairly high probability and low power expenditure. For the laboratory implementation of the designed field, it is desirable that it has simple frequency structure and that the control outcome is robust in the presence of noise which will always accompany the field. The ability of the control field to cooperate with noise in the manipulation of quantum dynamics is also discussed.
We investigate the problem of control of quantum systems. Various notions of controllability of quantum systems are discussed and Lie algebraic techniques are employed to derive necessary and sufficient conditions for the resulting degrees of controllability. The results are employed to study the degree of controllability for various model systems. The problem of optimal control is formulated as a problem of maximisation of the expectation value of an observable of the system subject to dynamical constraints and costs. A class of iterative algorithms is discussed, and shown to converge to a solution of the Euler-Lagrange equations, which is a necessary condition for optimality of a solution. A numerical realisation of the algorithm is presented and potential implementation of the resulting control fields in the laboratory is discussed. The algorithm is applied to find optimal control fields for a variety of applications including selective and simultaneous excitation of individual quantum dots in a globally addressed ensemble, creation of superposition states, and selective excitation of certain vibrational modes of a simple molecule such as Hydrogen Fluoride. In each case we systematically explore the parameter space of the algorithm to select solutions with desirable physical features from the multitude of possible choices. As there are many possible optimal control fields which give similar yields the question of whether some are more robust than others is investigated. A number of optimal fields are analysed quantitatively in terms of robustness with regard to temporal and spectral noise affecting the fields, uncertainty in the model parameters and the effect of experimental limitations such as restrictions on the bandwidth of the fields. It is shown that whilst the solutions tend to be sensitive to uncertainty in the energy levels chosen for the model, they appear to be surprisingly tolerant to even severe bandwidth limitations.
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.
The ability to optimally control quantum systems in the presence of environmentally-induced decoherence is important for many physical and chemical problems.We discuss both theoretical and experimental aspects of optimal control of open quantum systems. The theoretical analysis is based on fundamental concepts of open-system controllability and control landscapes. These theoretical advances lay the groundwork for practical applications, including numerical simulations and experimental implementations of adaptive feedback control. In particular, the adaptive approach was utilized to implement coherent control of decoherence, which uses coherent (unitary) preparation and manipulation of an open quantum system to significantly alter its incoherent (non-unitary) dynamics caused by coupling to an environment. We also discuss other applications, including optimal dynamic discrimination of similar quantum systems and optimal control of high-fidelity quantum gates in the presence of decoherence.