Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article discusses how TDDFT is much broader in scope, and yields predictions for many more properties. We discuss some of the challenges involved in making accurate predictions for these properties.Kohn-Sham density functional theory [1,2,3] is the method of choice to calculate ground-state properties of large molecules, because it replaces the interacting manyelectron problem with an effective single-particle problem that can be solved much faster. Time-dependent density functional theory (TDDFT) applies the same philosophy to time-dependent problems. We replace the complicated many-body time-dependent Schrödinger equation by a set of time-dependent single-particle equations whose orbitals yield the same time-dependent density n(r, t). We can do this because the Runge-Gross theorem [4] proves that, for a given initial wavefunction, particle statistics and interaction, a given time-dependent density n(r, t) can arise from at most one time-dependent external potential v ext (r, t). We define time-dependent Kohn-Sham (TDKS) equations that describe N non-interacting electrons that evolve in v S (r, t), but produce the same n(r, t) as that of the interacting system of interest. Development and applications of TDDFT have enjoyed exponential growth in the last few years [5,6,7,8], and we hope this merry trend will continue.The scheme yields predictions for a huge variety of phenomena, that can largely be classified into three groups: (i) the non-perturbative regime, with systems in laser fields so intense that perturbation theory fails, (ii) the linear (and higher-order) regime, which yields the usual optical response and electronic transitions, and (iii) back to the ground-state, where the fluctuation-dissipation theorem produces ground-state approximations from TDDFT treatments of excitations.In the first, non-perturbative regime, we have systems in intense laser fields with electric field strengths that are comparable to or even exceed the attractive Coulomb field of the nuclei [5]. The time-dependent field cannot be treated perturbatively, and even solving the time-dependent Schrödinger equation for the evolution of two interacting electrons is barely feasible with present-day computer technology [9]. For more electrons in a time-dependent field, wavefunction methods are prohibitive, and in the regime of (not too high) laser intensities, where the electron-electron interaction is still of importance TDDFT is essentially the only practical scheme available. With the recent advent of atto-second laser pulses, the electronic time-scale has become accessible. Theoretical tools to analyze the dynamics of excitation processes on the attosecond time scale will become more and more important. An example of such a tool is the time-dependent electron localization function (TDELF) [10,11]. This quantity allows the time-resolved observation of ...

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.

Complete control of single-electron states in a two-dimensional semiconductor quantum-ring model is established, opening a path into coherent laser-driven single-gate qubits. The control scheme is developed in the framework of optimal-control theory for laser pulses of two-component polarization. In terms of pulse lengths and target-state occupations, the scheme is shown to be superior to conventional control methods that exploit Rabi oscillations generated by uniform circularly polarized pulses. Current-carrying states in a quantum ring can be used to manipulate a two-level subsystem at the ring center. Combining our results, we propose a realistic approach to construct a laser-driven single-gate qubit that has switching times in the terahertz regime. DOI: 10.1103/PhysRevLett.98.157404 PACS numbers: 78.67.ÿn, 73.23.Ra, 78.20.Bh In recent years there has been wide interest in quantum control of nanoscale systems. One of the main motivations behind these studies arises from the possibilities of using tailored laser-pulse sequences for logic operations [1]. Semiconductor quantum dots and quantum rings (QRs) [2] are likely to play an important role in these far-reaching developments. Their atomlike properties together with a high flexibility in size and shape construct an ideal playground for quantum control.A fundamental question in laser control of a general N-level quantum system is controllability, i.e., if the control target such as a certain eigenstate can be reached even in principle. The first steps toward laser control of QRs were recently taken by analyzing the current generation in mesoscopic rings by time-delayed linear pulses [3], and in narrow QRs subjected to circularly polarized laser pulses [4]. A similar approach has been used also to generate ring currents in circular biomolecules such as Mg-porphyrin [5]. Quantum optimal-control theory (OCT) [6] is a powerful tool to find optimal laser pulses for controlling a quantum system. The iterative scheme developed within OCT [7] converges monotonically to an optimal laser pulse for reaching the prescribed target, such as a desired final quantum state, at the end of the pulse.In this Letter we apply OCT to semiconductor QRs of finite ring width. We construct optimal two-component laser pulses that drive the QR from a given initial state to any predefined target state. These terahertz pulses generate the desired transitions in significantly shorter times and higher accuracies than previously used circularly polarized continuous waves (cw) of finite lengths. Finally, we sketch how the full control of current-carrying states in QRs enables the construction of a coherent laser-driven singlegate qubit.The time evolution of our system is described by the time-dependent Schrödinger equationwhere t x t; y t is the two-component laser field propagating in the z direction. The interaction between the field and the electron is modeled in the dipole approximation (length gauge) with the dipole operator ÿer. The static effective Hamiltonian for the semiconductor ...

In this work, we investigate how and to which extent a quantum system can be driven along a prescribed path in Hilbert space by a suitably shaped laser pulse. To calculate the optimal, i.e., the variationally best pulse, a properly defined functional is maximized. This leads to a monotonically convergent algorithm which is computationally not more expensive than the standard optimalcontrol techniques to push a system, without specifying the path, from a given initial to a given final state. The method is successfully applied to drive the time-dependent density along a given trajectory in real space and to control the time-dependent occupation numbers of a two-level system and of a one-dimensional model for the hydrogen atom.