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

An experimental study shows how a polar molecule can be oriented in three dimensions by using a combination of laser and electrostatic fields. The approach should help to obtain molecular-frame information about strong-field ionization processes in molecules for which the orientation cannot be determined after ionization.

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Photoelectron angular distributions from strong-field ionization of oriented molecules

A strong inhomogeneous static electric field is used to spatially disperse a supersonic beam of polar molecules, according to their quantum state. We show that the molecules residing in the lowest-lying rotational states can be selected and used as targets for further experiments. As an illustration, we demonstrate an unprecedented degree of laser-induced one-dimensional alignment ðhcos 2 � 2D i¼ 0:97Þ and strong orientation of state-selected iodobenzene molecules. This method should enable experiments on pure samples of polar molecules in their rotational ground state, offering new opportunities in molecular science.

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Laser-induced alignment and orientation of quantum-state-selected large molecules

We review the theory of intense laser alignment of molecules and present a survey of the many recent developments in this rapidly evolving field. Starting with a qualitative discussion that emphasizes the physical mechanism responsible for laser alignment, we proceed with a detailed exposition of the underlying theory, focusing on aspects that have not been presented in the past. Application of the theory in several pedagogical illustrations is then followed by a review of the recent experimental and theoretical advances in the field. We conclude with a discussion of new directions, future opportunities, and areas where we expect intense laser alignment to play a role in the future. Throughout we emphasize the recent evolution of the method of nonadiabatic alignment from isolated diatomic molecules to complex media.

Nonadiabatic Alignment by Intense Pulses. Concepts, Theory, and Directions

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 one 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, 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.

Quantum control of molecular rotation

We show experimentally that field-free alignment of iodobenzene molecules, induced by a single, intense, linearly polarized 1.4-ps-long laser pulse, can be strongly enhanced by dividing the pulse into two optimally synchronized pulses of the same duration. For a given total energy of the two-pulse sequence the degree of alignment is maximized with an intensity ratio of 1:3 and by sending the second pulse near the time where the alignment created by the first pulse peaks.

Observation of enhanced field-free molecular alignment by two laser pulses.

We demonstrate that strong laser pulses can induce torsional motion in a molecule consisting of a pair of phenyl rings. A nanosecond laser pulse spatially aligns the carbon-carbon bond axis, connecting the two phenyl rings, allowing a perpendicularly polarized, intense femtosecond pulse to initiate torsional motion accompanied by an overall rotation about the fixed axis. We monitor the induced motion by femtosecond time-resolved Coulomb explosion imaging. Our theoretical analysis accounts for and generalizes the experimental findings.

Manipulating the torsion of molecules by strong laser pulses.

One-dimensional alignment of molecules in the adiabatic limit, where the pulse duration greatly exceeds the molecular rotational periods, is studied experimentally Four different asymmetric top molecules (iodobenzene, p-diiodobenzene, 3,4-dibromothiophene, and 4,4′-dibromobiphenyl), rotationally cooled through a high pressure supersonic pulsed valve, are aligned by a 9-ns-long pulse Their orientations are measured through Coulomb explosion, induced by a 130-fs-long pulse, and by recording the direction of the recoiling ions The paper focuses on the crucial role of the initial rotational temperature for the degree of alignment In particular, we show that at molecular temperatures in the 1K range very strong alignment is obtained already at intensities of a few times 1011W∕cm2 for all four molecules At the highest intensities (∼1012W∕cm2) the molecules can tolerate without ionizing ⟨cos2θ⟩⩾092 in the case of iodobenzene This is the strongest degree of alignment ever reported for any molecule

Role of rotational temperature in adiabatic molecular alignment

Laser-aligned carbondisulfide (${\mathrm{CS}}_{2}$) molecules are singly ionized by multiphoton absorption from intense, linearly polarized 25 fs laser pulses. The angular distribution of the photoelectrons exhibits a significant dependence on the angle between the polarizations of the aligning and ionizing laser fields. The widely used strong-field approximation predicts angular distributions in qualitative agreement with the experimental data but fails at a quantitative level.

Multiphoton Electron Angular Distributions from Laser-Aligned CS 2 Molecules

The rotational revival structure of asymmetric top molecules, following irradiation by an intense picosecond laser pulse, is explored theoretically and experimentally. Numerically we solve nonperturbatively for the rotational dynamics of a general asymmetric top subject to a linearly polarized intense pulse, and analyze the dependence of the dynamical alignment on the field and system parameters. Experimentally we use time-resolved photofragment imaging to measure the alignment of two molecules with different asymmetry, iodobenzene, and iodopentafluorobenzene. Our numerical results explain the experimental observations and generalize them to other molecules. The rotational revival structure of asymmetric tops differs qualitatively from the intensively studied linear top case. Potentially it provides valuable structural information about molecules.

Simon S. Viftrup

Papers

Observation of enhanced field-free molecular alignment by two laser pulses.

Manipulating the torsion of molecules by strong laser pulses.

Role of rotational temperature in adiabatic molecular alignment

Multiphoton Electron Angular Distributions from Laser-Aligned CS 2 Molecules

Nonadiabatic alignment of asymmetric top molecules: Rotational revivals