J. Werschnik

Time-dependent density functional theory: Past, present, and future

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.

Quantum optimal control theory

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.

Optimal control of quantum rings by terahertz laser pulses

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.

Optimal control of time-dependent targets

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 optimal-control 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.

Controlling the dynamics of many-electron systems from first principles: a combination of optimal control and time-dependent density-functional theory.

Quantum optimal control theory (QOCT) provides the necessary tools to theoretically design driving fields capable of controlling a quantum system towards a given state or along a prescribed path in Hilbert space. This theory must be complemented with a suitable model for describing the dynamics of the quantum system. Here, we are concerned with many electron systems (atoms, molecules, quantum dots, etc.) irradiated with laser pulses. The full solution of the many-electron Schrödinger equation is not feasible in general, and therefore, if we aim for an ab initio description, a suitable choice is the time-dependent density-functional theory (TDDFT). In this Letter, we establish the equations that combine TDDFT with QOCT and demonstrate their numerical feasibility.

Tailoring laser pulses with spectral and fluence constraints using optimal control theory

Within the framework of optimal control theory we develop a simple iterative scheme to determine optimal laser pulses with spectral and fluence constraints. The algorithm is applied to a one-dimensional asymmetric double well where the control target is to transfer a particle from the ground state, located in the left well, to the first excited state, located in the right well. Extremely high occupations of the first excited state are obtained for a variety of spectral and/or energetic constraints. Even for the extreme case where no resonance frequency is allowed in the pulse the algorithm achieves an occupation of almost 100%.

Optimal laser control of double quantum dots

Coherent single-electron control in a realistic semiconductor double quantum dot is studied theoretically. Using optimal-control theory we show that the energy spectrum of a two-dimensional double quantum dot has a fully controllable transition line. We find that optimized picosecond laser pulses generate population transfer at significantly higher fidelities (> 0.99) than conventional sinusoidal pulses. Finally we design a robust and fast charge switch driven by optimal pulses that are within reach of terahertz laser technology. Double quantum dots (DQDs), i.e., coupled twodimensional (2D) electron traps, have been under recent and extensive studies both experimentally 1,2,3 and theoretically. 4,7,8 The main interest in DQDs arises from their potential for solid-state quantum computation that could be achieved in principle by rapidly switching voltages of electrostatic gates. The gates permit to tune at will the system geometry and hence the electronic properties of DQDs. Coherent manipulation of a single charge 2 and coupled spins 1 has already been achieved, and recently a coherence time of ∼ 200 ns was obtained for a well isolated silicon DQD. 3 Theoretical studies on single-electron transport inside the DQD driven by linear switches and linearly polarized continuous waves (CWs) were reported very recently. 4 In the latter case the transport is rather sensitive to possible anharmonicity of the potential and limited to uncoupled dots far apart from each other. Electron control in DQDs has been studied also using genetic algorithms 5 as well as rotating-wave and resonant approximations leading to a reduction to a threelevel system. 6 To the best of our knowledge, however, a general N-level control scheme by using direct external electric fields has not been introduced for 2D-DQDs until now. In this paper we discuss the controllability criteria for single-electron states of DQDs by means of external laser pulses. We show that at certain interdot distances some of the single-electron states allow full population transfer from the ground state to those states. We apply quantum optimal-control theory (OCT) 9 which yields the optimal laser pulses for predefined transitions. We obtain high occupations (& 99%) of the target states in a realistic DQD in a few picoseconds, which is well in the coherent regime. If the initial and final states are chosen to have full localization of the electron in one or the other dot, this scheme enables rapid and controlled transport which is not sensitive to the interdot distance or to the inevitable anharmonicities in the confining potential.

Optimal control of charge transfer

In this work, we investigate how and to which extent a quantum system can be driven along a prescribed path in space by a suitably tailored laser pulse. The laser field is calculated with the help of quantum optimal control theory employing a time-dependent formulation for the control target. Within a two-dimensional (2D) model system we have successfully optimized laser fields for two distinct charge transfer processes. The resulting laser fields can be understood as a complicated interplay of different excitation and de-excitation processes in the quantum system.