A concept from the field of quantum mechanics, spin is a property of particles that has no direct counterpart in everyday experience. Since the early twentieth century researchers have learned to manipulate it deliberately by means of precisely shaped electromagnetic pulses. This has resulted in two technologies that are widespread today: magnetic resonance imaging (MRI) is commonplace in hospitals, and nuclear magnetic resonance spectroscopy (NMR) is used to determine the structures of proteins and to develop new drugs. The mathematical framework of optimal control theory can be used to improve these technologies.
“The question it answers is a practical one,” explains Christiane Koch, professor of theoretical physics at Freie Universität Berlin. “Given a quantum system and the fields I can apply to it, how do I reach the state I want as quickly, as reliably, and as accurately as possible – and how well can it be done at all, in principle?”
The gains are considerable: Pulses designed in this way invert nuclear spins about ten times faster than the conventional pulses previously in use, and in magnetic resonance imaging they make it possible to build the constraints of a real scanner directly into the design of the experiment.
The review article shows that the same methods now reach well beyond magnetic resonance; even molecules can be precisely controlled using tailored electromagnetic pulses. This is particularly interesting in chiral molecules, which occur in left- and right-handed forms and can differ markedly in their biological effect. Tailored sequences of microwave pulses can transfer one of the two forms into a selected quantum state while leaving the other unaffected – a prerequisite for separating them.
Related methods have been used to navigate individual atoms through a large range of possible states. For example, methods from optimal control could be used to significantly improve the preparation of certain atomic states in experiments, and it has also been possible to achieve nonclassical superposition, a quantum state in which the atom occupies several very different configurations at once. No protocol for this purpose had existed at all prior to this.
“Improving a protocol that already works is useful,” says Koch, “The more interesting case is a state that no one had been able to prepare before.”
The researchers also point to the limitations of this approach: Optimal control requires an accurate model of the respective quantum system and a well-calibrated experiment. Looking ahead, the authors see the combination of optimal control with machine learning as the most promising direction. While control methods use precise physical models and fast convergence, machine learning can infer compact descriptions from experimental data.
However, much less data is available in quantum physics. “Quantum measurements are scarce and expensive,” says Koch. “Quantum physics is not big data. That is why the two approaches have to be combined, rather than one replacing the other.”
The review article was written in cooperation with researchers from the Technical University of Munich, Aarhus University, Université de Bourgogne, and Dortmund University. It appeared in a special edition of Science Advances dedicated to the next one hundred years of spin.
Optimal Control of Spin Systems
16-Sep-2026