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

The development of femtosecond time-resolved methods for the study of gas-phase molecular dynamics is founded upon the seminal studies of Zewail and co-workers, as recognized in 1999 by the Nobel Prize in Chemistry.1 This methodology has been applied to chemical reactions ranging in complexity from bond-breaking in diatomic molecules to dynamics in larger organic and biological molecules, and has led to breakthroughs in our understanding of fundamental chemical processes. Photoexcited polyatomic molecules and anions often exhibit quite complex dynamics involving the redistribution of both charge and energy.2-6 These processes are the primary steps in the photochemistry of many polyatomic systems,7 are important in photobiological processes such as vision and photosynthesis,8 and underlie many concepts in molecular electronics.9 Femtosecond time-resolved methods involve a pump-probe configuration in which an ultrafast pump pulse initiates a reaction or, more generally, creates a nonstationary state or wave packet, the evolution of which is monitored as a function of time by means of a suitable probe pulse. Time-resolved or wave packet methods offer a view complementary to the usual spectroscopic approach and often yield a physically intuitive picture. Wave packets can behave as zeroth-order or even classical-like states and are therefore very helpful in discerning underlying dynamics. The information obtained from these experiments is very much dependent on the nature of the final state chosen in a given probe scheme. Transient absorption and nonlinear wave mixing are often the methods of choice in condensed-phase experiments because of their generality. In studies of molecules and clusters in the gas phase, the most popular methods, laser-induced fluorescence and resonant multiphoton ionization, usually require the probe laser to be resonant with an electronic transition in the species being monitored. However, as a chemical reaction initiated by the pump pulse evolves toward products, one expects that both the electronic and vibrational structures of the species under observation will change. Hence, these probe methods can be * To whom corresondence should be addressed. A.S.: telephone (613) 993-7388, fax (613) 991-3437, E-mail albert.stolow@nrc.ca. D.M.N.: telephone (510) 642-3505, fax (510) 642-3635, E-mail dan@radon.cchem.berkeley.edu. 1719 Chem. Rev. 2004, 104, 1719−1757

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Femtosecond time-resolved photoelectron spectroscopy.

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

Femtosecond time-resolved photoelectron imaging (TRPEI) is a variant of time-resolved photoelectron spectroscopy used in the study of gas-phase photoinduced dynamics. A new observable, time-dependent photoionization-differential cross section provides useful information on wave-packet motions, electronic dephasing, and photoionization dynamics. This review describes fundamental issues and the most recent works involving TRPEI.

Femtosecond time-resolved photoelectron imaging.

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.

Nonadiabatic laser alignment of an asymmetric top molecule is studied using the combination of a quantum dynamical theory and time-resolved photofragment imaging experiments. In particular, the degree of alignment of iodobenzene, induced by an intense, linearly polarized picosecond laser pulse, is calculated and measured. Pronounced alignment is obtained under field-free conditions.

Nonadiabatic Alignment of Asymmetric Top Molecules: Field-Free Alignment of Iodobenzene

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.

Nonadiabatic alignment of asymmetric top molecules: Rotational revivals

Nonadiabatic alignment of symmetric top molecules induced by a linearly polarized, moderately intense picosecond laser pulse is studied theoretically and experimentally. Our studies are based on the combination of a nonperturbative solution of the Schr\"odinger equation with femtosecond time-resolved photofragment imaging. Using methyliodide and tert-butyliodide as examples, we calculate and measure the alignment dynamics, focusing on the temporal structure and intensity of the revival patterns, including their dependence on the pulse duration, and their behavior at long times, where centrifugal distortion effects become important. Very good agreement is found between the experimental and numerical results. This allows us to use our theory and numerical results to provide additional insight into the origin of the experimental findings.

Alignment of symmetric top molecules by short laser pulses

Nonadiabatic alignment of an asymmetric top molecule induced by a short, moderately intense laser pulse is studied theoretically and experimentally. Numerically, we solve nonperturbatively the time-dependent Schr\"odinger equation for a general asymmetric top molecule subject to a moderately intense laser field, and analyze the dependence of the alignment dynamics on the field strength and on the rotational temperature. Experimentally, we use time-resolved photofragment imaging to measure the time-dependent angular distributions of the spatial orientation of the molecules. Our studies, using iodobenzene as a test molecule, focus on the short-time alignment dynamics, during and after the pulse.

Mikael D. Poulsen

Papers

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

Nonadiabatic Alignment of Asymmetric Top Molecules: Field-Free Alignment of Iodobenzene

Nonadiabatic alignment of asymmetric top molecules: Rotational revivals

Alignment of symmetric top molecules by short laser pulses

Nonadiabatic laser-induced alignment of iodobenzene molecules