Quantum control of molecular rotation

The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian with only a few accurately known parameters, and transitions between rotational levels can be driven by external fields from various parts of the electromagnetic spectrum. Control over the rotational motion can be exerted in one-, two- and many-body scenarios, thereby allowing to probe Anderson localization, target stereoselectivity of bimolecular reactions, or encode quantum information, to name just a few examples. The corresponding approaches to quantum control are pursued within separate, and typically disjoint, subfields of physics, including ultrafast science, cold collisions, ultracold gases, quantum information science, and condensed matter physics. It is the purpose of this review to present the various control phenomena, which all rely on the same underlying physics, within a unified framework. To this end, we recall the Hamiltonian for free rotations, assuming the rigid rotor approximation to be valid, and summarize the different ways for a rotor to interact with external electromagnetic fields. These interactions can be exploited for control --- from achieving alignment, orientation, or laser cooling in a one-body framework, steering bimolecular collisions, or realizing a quantum computer or quantum simulator in the many-body setting.Comment: 52 pages, 11 figures, 607 reference

On the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space

We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be approximated in a finite dimensional Hilbert space. For a given threshold error, we estimate this finite dimension in terms of the used control field. As illustrative examples, we consider the cases of a rigid rotor and of a harmonic oscillator.Comment: Journal of Mathematical Chemistry, Springer Verlag (Germany), 201

Exploring the limits of the generation of non-classical states of spins coupled to a cavity by optimal control

We investigate the generation of non-classical states of spins coupled to a common cavity by means of a collective driving of the spins. We propose a control strategy using specifically designed series of short coherent and squeezing pulses, which have the key advantage of being experimentally implementable with the state-of-the art techniques. The parameters of the control sequence are found by means of optimization algorithms. We consider the cases of two and four spins, the goal being either to reach a well-defined target state or a state maximizing a measure of non-classicality. We discuss the influence of cavity damping and spin offset on the generation of non-classical states. We also explore to which extent squeezing fields help enhancing the efficiency of the control process.Comment: 13 pages, 7 figure

An introduction into optimal control for quantum technologies

In this series of lectures, we would like to introduce the audience to quantum optimal control. The first lecture will cover basic ideas and principles of optimal control with the goal of demystifying its jargon. The second lecture will describe computational tools (for computations both on paper and in a computer) for its implementation as well as their conceptual background. The third chapter will go through a series of popular examples from different applications of quantum technology.Comment: Lecture notes for the 51st IFF Spring Schoo

Fundamental bounds on qubit reset

Qubit reset is a key task in the operation of quantum devices which, for many quantum hardware platforms, presently limits device clock speed. While it is known that coupling the qubit to an ancilla on demand allows for the fastest qubit reset, the limits on reset accuracy and speed due to the choice of ancilla have not yet been identified-despite the great flexibility in device design for most quantum hardware platforms. Here, we derive bounds on qubit reset in terms of maximum fidelity and minimum time, assuming control over the qubit and no control over the ancilla. For two-level ancillas, we find a provably time-optimal protocol which consists of purity exchange between qubit and ancilla brought into resonance. The globally minimal time can only be realized for specific choices of coupling and control which we identify. When increasing the size of the ancilla Hilbert space, the maximally achievable fidelity increases, whereas the reset time remains constant. Our results translate into device design principles for realizing, in a given quantum architecture, the fastest and most accurate protocol for qubit reset

Floquet operator engineering for quantum state stroboscopic stabilization

Optimal control is a valuable tool for quantum simulation, allowing for the optimized preparation, manipulation, and measurement of quantum states. Through the optimization of a time-dependent control parameter, target states can be prepared to initialize or engineer specific quantum dynamics. In this work, we focus on the tailoring of a unitary evolution leading to the stroboscopic stabilization of quantum states of a Bose-Einstein condensate in an optical lattice. We show how, for states with space and time symmetries, such an evolution can be derived from the initial state-preparation controls; while for a general target state we make use of quantum optimal control to directly generate a stabilizing Floquet operator. Numerical optimizations highlight the existence of a quantum speed limit for this stabilization process, and our experimental results demonstrate the efficient stabilization of a broad range of quantum states in the lattice.Comment: (10 pages, 3 figures

All-optical regeneration of polarization of a 40-Gbit/s return-to-zero telecommunication signal

10We report all-optical regeneration of the state of polarization of a 40 Gbit∕s return-to-zero telecommunication signal. The device discussed here consists of a 6.2-km-long nonzero dispersion-shifted fiber, with low polarization mode dispersion, pumped from the output end by a backward propagating wave coming from either an external continuous source or a reflection of the signal. An initially scrambled signal acquires a degree of polarization close to 100% toward the polarization generator output. All-optical regeneration is confirmed by means of polarization and bit-error-rate measurements as well as real-time observation of the eye diagrams. We show that the physical mechanism underlying the observed four-wave-mixing-based polarization attraction phenomenon can be described in terms of the geometric approach developed for the study of Hamiltonian singularities.openopenJ. Fatome; D. Sugny; S. Pitois; P. Morin; M. Guasoni; A. Picozzi; H. R. Jauslin; C. Finot; G. Millot; S. WabnitzJ., Fatome; D., Sugny; S., Pitois; P., Morin; Guasoni, Massimiliano; A., Picozzi; H. R., Jauslin; C., Finot; G., Millot; Wabnitz, Stefa

Beating the limits with initial correlations

Fast and reliable reset of a qubit is a key prerequisite for any quantum technology. For real world openquantum systems undergoing non-Markovian dynamics, reset implies not only purification, but inparticular erasure of initial correlations between qubit and environment. Here, we derive optimal resetprotocols using a combination of geometric and numerical control theory. For factorizing initialstates, we find a lower limit for the entropy reduction of the qubit as well as a speed limit. The timeoptimalsolution is determined by the maximum coupling strength. Initial correlations, remarkably,allow for faster reset and smaller errors. Entanglement is not necessary.</p

Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe

Quantum optimal control, a toolbox for devising and implementing the shapes of external fields that accomplish given tasks in the operation of a quantum device in the best way possible, has evolved into one of the cornerstones for enabling quantum technologies. The last few years have seen a rapid evolution and expansion of the field. We review here recent progress in our understanding of the controllability of open quantum systems and in the development and application of quantum control techniques to quantum technologies. We also address key challenges and sketch a roadmap for future developments