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International Conference on Recent Advances in Engineering & Computational Sciences

Optimal quantum control: Designing lasers for controlling quantum systems

Renuka Rai

Published Mar 1, 2014• 1 citation
Publisher

Abstract

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.

DOI
10.1109/raecs.2014.6799567

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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 discuss recent advances in optimal control theory (OCT) related to the investigation of the impact of control field noise on controllability of quantum dynamics. Two numerical methods, the gradient method and the iteration method, are paid particular attention. We analyze the problem of designing noisy control fields to maximize the vibrational transition probability in diatomic quantum systems, e.g. the HF and OH molecules. White noise is used as an additive random variable in the amplitude of the control field. It is demonstrated that the convergence is faster in the presence of noise and population transfer is increased by 0.04% for small values of noise compared to the field amplitude.
Quantum control refers to our ability to manipulate quantum systems. This tutorial-style chapter focuses on the use of classical electromagnetic fields to steer the system dynamics. In this approach, the quantum nature of the control stems solely from the underlying dynamics, through the exploitation of destructive and constructive interference to reach the control target. We first discuss two basic control principles -- coherent control which uses manipulation in frequency or time to design these interferences, and adiabatic following where access to the control target is enabled by tracking the time-dependent ground state. For complex control targets and system dynamics that exceed the scope of these basic principles, optimal control theory provides a powerful suite of tools to design the necessary protocols. A key consideration for the successful application of optimal control theory is a proper choice of the optimization functional. All concepts are illustrated using recent work from my research group, with a focus on controlling atoms and superconducting qubits. The chapter concludes with an outlook on integrating coherent control with engineered dissipation and a discussion of open questions in the field.
Advances in quantum control theory and optimization techniques have made possible a new phenomena of quantum engineering. Chemical reactions can now be dynamically manipulated using first-principles quantum chemical models, in which a laser field, rather than a catalyst, serve as photonic reagents to selectively break a chemical bond and yield products via intramolecular rearrangement. A field pulse may also be designed to perform ultrasensitive spectroscopy, where compounds with very similar chemical properties are differentiated through their unique interaction with resonant and off-resonant photons. Despite significant progress in theoretical and laboratory quantum control, however, quantum engineering remains principally challenging due to manifestation of noise and uncertainties associated with the input and system parameters. Specifically, a small magnitude of variation in the field and Hamiltonian parameters would cause an otherwise optimal field to deviate from controlling desired quantum state transitions and reaching a particular objective. Thus, an accurate analysis of robustness of controlled quantum dynamics followed by a robust control framework is essential in achieving quantum control in a practical setting. In this work, theoretical foundations for quantum control robustness analysis are presented from both a distributional perspective - in terms of moments of the transition amplitude, interferences, and transition probability - and a worst-case perspective. In addition, an evolutionary control strategy for achieving robust control via open- and closed-loop approach are described with its mechanism of convergence elucidated using the robustness analysis method.
It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments.
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.