Session L26: Focus Session: Quantum Control II

Hiking Over Quantum Control Landscapes

Seeking the best control over a posed quantum dynamic objective entails climbing over the associated control landscape, which is defined as the quantum mechanical observable as a function of the controls. The topology and general structure of quantum control landscapes as input output maps dictate the final attainable yield, the efficiency of the search for an effective control, the possible existence of multiple dynamically equivalent controls, and the robustness of any viable control solution. Normal optimization problems in virtually any area of engineering and science typically have landscape topologies that remain a mystery. Quantum mechanics appears out to be quite special in that the topology of quantum control landscapes can be established generically based on minimal physical assumptions. Various features of these landscapes will be discussed and illustrated for circumstances where the controls are either an external field or the time independent portions of the Hamiltonian; the latter circumstance corresponds to subjecting the material or molecules to systematic variation and hence viewed in the context of being controls. Both theoretical and experimental findings on control landscapes and their consequences will be discussed, including issues of robustness to noise, search algorithm efficiency, existence of multiple control solutions, prospects for identifying reduced sets of control variables, simultaneous control of multiple quantum systems (optimal dynamic discrimination (ODD)), and mechanism analysis.   

Non-resonant, non-perturbative Dynamic Stark Control of Quantum Dynamics.

One of the most important non-resonant interactions is the dynamic Stark effect. In the non-perturbative but non-ionizing limit, an effective Hamiltonian can be constructed based upon a hierarchy of approximations (the Born-Oppenheimer Approximation, Slowly Varying Envelope Approximation, the Rotating Wave Approximation). In this situation, the effective Hamiltonian contains first order (dipole) and second order (polarizability) matter-field interactions which can lead to significant yet reversible changes to the molecular Hamiltonian. The first order term leads to a fast evolution which follows each optical cycle. The second order term causes an evolution which follows, by contrast, the envelope of the laser pulse. We discuss the use of the non-resonant second order Dynamic Stark Effect as a tool for controlling quantum systems without any net absorption of light. We illustrate this by examples chosen from problems in: (i) Control of branching ratios during non-adiabatic photodissociation; (ii) Control of 3D field free molecular frame alignment of asymmetric tops.   

Controlling and Understanding Laser Filamentation in the Solution and Gas Phase Molecular Systems

The process of laser filamentation is highly nonlinear, yet amenable to control using laser pulse shaping techniques. Investigations of our ability to control the spatial position of a filament in a water tank and measurements of the forward and back scattered amplified spontaneous emission (resulting from the strong field excitation in the resulting plasma) will be presented. Our time resolved measurements of the dynamics of the filamentation process in various gases will also be reviewed. Finally, a model of the plasma formation will be presented.   

New Developments in Quantum Control: Phase Space Learning Algorithms and Uncontrollable Quantum Systems

This talk has two parts. The first deals with a new representation of shaped ultrafast laser pulses based on a von Neumann time-frequency lattice. We show that a pulse defined in terms of an amplitude and a phase at $N$ frequency points can be represented on the von Neumann lattice using $\surd N$ points in frequency and $\surd N$ in time without loss of information. The transformation from the frequency (or time) representation to the von Neumann representation is one-to-one and therefore invertible. We discuss three possible applications of the von Neumann representation of pulses: 1) for cleaning and interpreting complex pulses; 2) for performing systematic scans of the effect of timing and frequency on molecular control; 3) as genes to be used in mutations and crossover in evolutionary algorithms. The second part of the talk deals with the classification of uncontrollable quantum systems. It is well-known that for a quantum system to be controllable the Lie algebra spanned by iterated commutators of H$_{0}$ and H$_{1}$ must span the full space of the dynamical algebra. We pose the following questions: When a system is \textbf{not} completely controllable, can we classify different families of uncontrollable systems? If so, can we associate these different types of mathematical structures with different underlying physics (for example, dark states or generalized entangled states)? We show that uncontrollable quantum systems fall into two categories: reducible and irreducible. The former is associated with dark states and the latter with generalized entangled states. Based on Lie subalgebras we give a complete characterization of irreducible uncontrollable systems for systems up to 9 levels. Finally, we show that an earlier intuitive concept of connectivity only incompletely captures this Lie algebraic structure of uncontrollable systems.   

Quantum information processing with a minimal control

Various physical and practical constraints limit the amount and type of control we have in quantum information processing systems, leading to complicated or unreliable implementations. To try and circumvent these problems, we take the most restricted candidate systems where only a single energy transition can be controlled by a piecewise-constant field, and show that even this is sufficient for efficient execution of a range of useful QIP tasks. We show that it is in principle possible to achieve global control with a single, simple, fixed, local actuator, and show how such minimal control could significantly improve information processing in terms of speed, fidelity and transfer efficiency. The scheme presented has a natural application to spin-chain systems, where only one interaction between two spins can be controlled, and the effects of the position of the controller in the 'quantum wire' and the system's symmetries are explored. It may also be relevant for gate-controlled solid-state systems where it is desirable or necessary to limit the number of control electrodes due to the constraints of size, decoherence and cross-talk, and where complex temporal variation of the control voltages is difficult.   

A Simulation of Strong-Field Attosecond Electron Dynamics: Effects of Pulse Shape

As the complexity of systems increases from atoms to molecules, the exploration of non-adiabatic electron dynamics in strong fields requires a leap in understanding and in the principles of description. Recently, a time-dependent Hartree-Fock approach (TDHF) was developed to study the dynamics of individual electrons in multielectron systems. We have used this TDHF approach to numerically simulate the non-adiabatic electron dynamics of a few small molecules and polyacenes using basis sets ranging from AUG-cc-pVTZ for smaller molecules to 6-31G(d,p) for larger molecules. The electric field was applied in the direction of the long molecular axis and the attosecond response of the electrons during and after the laser pulse has been obtained. To determine the effects of ionization, electron dynamics for both neutrals and ions was also simulated. As a function of pulse shape, there are significant differences in the excitation spectrum and volume for each molecule.