Quantum control is concerned with active manipulation of physical and chemical processes on the atomic and molecular scale. This work presents a perspective of progress in the field of control over quantum phenomena, tracing the evolution of theoretical concepts and experimental methods from early developments to the most recent advances. Among numerous theoretical insights and technological improvements that produced the present state-of- the-art in quantum control, there have been several breakthroughs of foremost importance. On the technology side, the current experimental successes would be impossible without the development of intense femtosecond laser sources and pulse shapers. On the theory side, the two most critical insights were (i) realizing that ultrafast atomic and molecular dynamics can be controlled via manipulation of quantum interferences and (ii) understanding that optimally shaped ultrafast laser pulses are the most effective means for producing the desired quantum interference patterns in the controlled system. Finally, these theoretical and experimental advances were brought together by the crucial concept of adaptive feedback control (AFC), which is a laboratory procedure employing measurement-driven, closed-loop optimization to identify the best shapes of femtosecond laser control pulses for steering quantum dynamics towards the desired objective. Optimization in AFC experiments is guided by a learning algorithm, with stochastic methods proving to be especially effective. AFC of quantum phenomena has found numerous applications in many areas of the physical and chemical sciences, and this paper reviews the extensive experiments. Other subjects discussed include quantum optimal control theory, quantum control landscapes, the role of theoretical control

https://iopscience.iop.org/article/10.1088/1367-2630/12/7/075008/pdf

Control of quantum phenomena: past, present and future

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

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Training Schrödinger’s cat: quantum optimal control

Molecular aggregates are abundant in nature; they form spontaneously in concentrated solutions and on surfaces and can be synthesized by supramolecular chemistry techniques.1-3 Assemblies of chromophores play important roles in many biological processes such as light-harvesting and primary * To whom correspondence should be addressed. E-mail: smukamel@uci.edu. † University of California Irvine. ‡ Universität Würzburg. § Charles University. Chem. Rev. 2009, 109, 2350–2408 2350

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Coherent Multidimensional Optical Spectroscopy of Excitons in Molecular Aggregates; Quasiparticle versus Supermolecule Perspectives

It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a system from a given initial state into a desired target state with minimized expenditure of energy and resources -- as famously applied in the Apollo programme. 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. --- Here state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium uniting expertise in optimal control theory and applications to spectroscopy, imaging, quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap to future developments.

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Training Schr\"odinger's cat: quantum optimal control

The control of quantum dynamics via specially tailored laser pulses is a long-standing goal in physics and chemistry. Partly, this dream has come true, as sophisticated pulse-shaping experiments allow us to coherently control product ratios of chemical reactions. The theoretical design of the laser pulse to transfer an initial state to a given final state can be achieved with the help of quantum optimal control theory (QOCT). This tutorial provides an introduction to QOCT. It shows how the control equations defining such an optimal pulse follow from the variation of a properly defined functional. We explain the most successful schemes to solve these control equations and show how to incorporate additional constraints in the pulse design. The algorithms are then applied to simple quantum systems and the obtained pulses are analysed. Besides the traditional final-time control methods, the tutorial also presents an algorithm and an example to handle time-dependent control targets.

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Quantum optimal control theory

We report on selective optimization of different isotopes in an ionization process by means of spectrally broad shaped fs-laser pulses. This is demonstrated for $^{39,39}K_{2}$ and $^{39,41}K_{2}$ by applying evolution strategies in a feedback loop, whereby a surprisingly high enhancement of one isotope versus the other and vice versa is achieved (total factor $\ensuremath{\approx}140$). Information about the dynamics on the involved vibrational states is extracted from the optimal pulse shapes, which provides a new spectroscopical approach of yielding distinct frequency pattern on fs-time scales. The method should, in principle, be feasible for all molecules.

Isotope selective ionization by optimal control using shaped femtosecond laser pulses.

We report on coherent control of excitation processes of translationally ultracold rubidium dimers in a magneto-optical trap by using shaped femtosecond laser pulses Evolution strategies are applied in a feedback loop in order to optimize the photoexcitation of the ${\mathrm{Rb}}_{2}$ molecules, which subsequently undergo ionization or fragmentation A superior performance of the resulting pulses compared to unshaped pulses of the same pulse energy is obtained by distributing the energy among specific spectral components The demonstration of coherent control to ultracold ensembles opens a path to actively influence fundamental photoinduced processes in molecular quantum gases

https://arxiv.org/pdf/physics/0509056.pdf

Coherent control with shaped femtosecond laser pulses applied to ultracold molecules

We present a shaper scheme that fully controls the spectral phase, amplitude,
and polarization of femtosecond laser pulses. In particular, it enables independent manipulation over the major axis orientation and the axis ratio of the polarization ellipse. This is accomplished by integrating a 4f-shaper setup in both arms of a Mach-Zehnder interferometer and rotating the polarization by 90° in one of the arms before overlaying the beams. The generated pulses are resolved in a simple and intuitive detection scheme.

Phase, amplitude, and polarization shaping with a pulse shaper in a Mach-Zehnder interferometer

We demonstrate the photoassociation of ultracold rubidium dimers using coherent femtosecond pulses. Starting from a cloud of ultracold rubidium atoms, electronically excited rubidium molecules are formed with shaped photoassociation pump pulses. The excited state molecules are projected with a time-delayed probe pulse onto molecular ion states which are detected in a mass spectrometer. Coherent transient oscillations of the excited state population are observed in the wings of the pump pulse, in agreement with the time-dependent solution of the Schrodinger equation of the excitation process.

Coherent transients in the femtosecond photoassociation of ultracold molecules.

We report a good agreement between the shapes of tailored pulses obtained theoretically and experimentally by using the optimal-control theory and the closed-loop learning technique to maximize the ionization yield in NaK. The theoretical pulse shapes are found to be robust regarding the choice of the initial guess. We assign the leading features of the pulse shapes to processes underlying the optimal control and reveal the mechanism which involves an electronic transition followed by a direct two-photon process and sequential one-photon processes at later times. We show that the optimal control not only serves for maximizing the desired yield but also as a tool for the analysis and the identification of the responsible processes.

Stefan M. Weber

Papers

Isotope selective ionization by optimal control using shaped femtosecond laser pulses.

Coherent control with shaped femtosecond laser pulses applied to ultracold molecules

Phase, amplitude, and polarization shaping with a pulse shaper in a Mach-Zehnder interferometer

Coherent transients in the femtosecond photoassociation of ultracold molecules.

Optimal control of ionization processes in NaK: Comparison between theory and experiment