Control Of Quantum Dynamics Research Articles

Systematically Identifying Mechanisms in the Control of Quantum Dynamics

This paper introduces a method to quantitatively determine the various pathways taken by a quantum system in going from the initial state to the final target. The mechanism is revealed by encoding a signal in the system Hamiltonian and decoding the resultant nonlinear distortion of the signal in the system time evolution operator. The relevant interfering pathways determined by this analysis give insight into the physical mechanisms operative during the evolution of the quantum system. The mechanism analysis tools reveal the roles of multiple interacting quantum pathways to maximally take advantage of constructive and destructive interference

Identifying mechanisms in the control of quantum dynamics through Hamiltonian encoding

A variety of means are now available to design control fields for manipulating the evolution of quantum systems. However, the underlying physical mechanisms often remain obscure, especially in the cases of strong fields and high quantum state congestion. This paper proposes a method to quantitatively determine the various pathways taken by a quantum system in going from the initial state to the final target. The mechanism is revealed by encoding a signal in the system Hamiltonian and decoding the resultant nonlinear distortion of the signal in the system time-evolution operator. The relevant interfering pathways determined by this analysis give insight into the physical mechanisms operative during the evolution of the quantum system. A hierarchy of mechanism identification algorithms with increasing ability to extract more detailed pathway information is presented. The mechanism identification concept is presented in the context of analyzing computer simulations of controlled dynamics. As illustrations of the concept, mechanisms are identified in the control of several simple, discrete-state quantum systems. The mechanism analysis tools reveal the roles of multiple interacting quantum pathways to maximally take advantage of constructive and destructive interference. Similar procedures may be applied directly in the laboratory to identify control mechanisms without resort to computer modeling, although this extension is not addressed in this paper.

Femtosecond learning control of quantum dynamics in gases and liquids: Technology and applications

Obtaining active control over quantum-mechanical systems is a fascinating prospect in modern physics. In recent years, quantum control has developed as a means of actively controlling the outcome of light-matter interactions. The basic principles of adaptive femtosecond quantum control are discussed. Specifically shaped femtosecond laser pulses are used to direct the dynamical evolution of quantum wavefunctions into desired target channels. This is achieved in a ‘closed-loop’ implementation wherein experimental feedback signals are evaluated by a learning algorithm. In this iterative optimization scheme, knowledge of the Hamiltonian is not required. Specific experimental examples are automated compression of amplified femtosecond laser pulses and control of gas-phase molecular photodissociation in Fe(CO)5, CpFe(CO)2Cl and CH3CHOHCOOH. Additionally, selective control of molecular excitation is demonstrated under liquid-phase conditions. As a further technological development, the technique of femtosecond polarization pulse shaping is discussed briefly, which makes it possible to vary the polarization state of light, intensity and oscillation frequency in a flexible manner on an ultrashort timescale.

SHORT-TIME DECOHERENCE AND DEVIATION FROM PURE QUANTUM STATES

In systems considered for quantum computing, i.e., for control of quantum dynamics with the goal of processing information coherently, decoherence and deviation from pure quantum states, are the main obstacles to error correction. At low temperatures, usually assumed in quantum computing designs, some of the accepted approaches to evaluation of relaxation mechanisms break down. We develop a new formalism for the estimation of decoherence at short times, appropriate for evaluation of quantum computing architectures.

The role of microscopic and macroscopic coherence in laser control

In this article, we discuss microscopic and macroscopic coherences resulting from multiple pulse excitation of molecular samples. The wave packet formalism is applied to describe the interference of wave packets within a single molecule (microscopic coherence) and the macroscopic interference between the polarizations resulting from optical responses of a single molecule or from different molecules (macroscopic coherence). Experimental virtual echo and stimulated photon echo measurements with noncollinear, degenerate femtosecond pulses are presented where both of these coherences are shown to control the observed dynamics. Theoretical simulations of the rovibronic dynamics observed experimentally on iodine vapor are presented. The role of these coherences in laser control of quantum dynamics is discussed.

Design and interpretation of laser pulses for the control of quantum systems

An extended theory of optimal control strategies for the design of feasible laser pulses is presented. The theoretical framework includes the control of population-transfer and expectation values. Selected studies for two-dimensional model systems providing aspects of uni- and bimolecular reactions are presented. Subsequent analysis of the obtained laser fields is performed to gain insight into the underlying reaction mechanisms. The effect of non-uniform spatial laser profiles and the orientation of the molecules versus the laser beam on controlling quantum dynamics is investigated with the main interest focussed on the achievable quantum yield and information on variable pathways stored in the laser field.

Optimal control of quantum dynamics: a new theoretical approach

A New theoretical formalism for the optimal quantum control has been presented. The approach stems from the consideration of describing the time-dependent quantum system in terms of the real physical observables, viz., the probability density rho(x,t) and the quantum current j(x,t) which is well documented in the Bohm's hydrodynamical formulation of quantum mechanics. The approach has been applied for manipulating the vibrational motion of HBr in its ground electronic state under an external electric field.

Compensating for spatial laser profile effects on the control of quantum systems

This paper investigates the influence of experimentally nonuniform spatial laser profiles on controlling quantum dynamics. The influence of Gaussian $({\mathrm{TEM}}_{00}),$ donut $({\mathrm{TEM}}_{01}^{*}),$ and uniform laser profiles upon quantum control yield is considered. Nonuniform laser profiles can reduce the control yield, but it is shown that this effect can be diminished, by designing optimized laser pulses explicitly taking into account the spatial laser profile. These laser pulses are of significantly different structure than the ones for uniform profiles. This result suggests that an analysis of experimental laser fields to gain information on the resultant physical processes will be more difficult for pulses with nonuniform profiles. The simulations indicate that direct closed loop control in the laboratory can learn to operate effectively with nonuniform profiles.

Theoretical perspectives on spintronics and spin-polarized transport

Selected problems of fundamental importance for spintronics and spin-polarized transport are reviewed, some of them with a special emphasis on their applications in quantum computing and coherent control of quantum dynamics. The role of the solid-state environment in the decoherence of electron spins is discussed. In particular, the limiting effect of the spin-orbit interaction on spin relaxation of conduction electrons is carefully examined in the light of recent theoretical and experimental progress. Most of the proposed spintronic devices involve spin-polarized transport across interfaces in various hybrid structures. The specific example discussed here, of a magnetic semiconductor/superconductor interface, displays many intricacies which a complex spin-dependent interface introduces in the spin-polarized transport. It is proposed that pairs of entangled electrons in a superconductor (Cooper pairs) can be transfered to a non-superconducting region, and consequently separated for a transport study of the spin entanglement. Several important theoretical proposals for quantum computing are based on electronic and nuclear spin entanglement in a solid. Physical requirements for these proposals to be useful are discussed and some alternative views are presented. Finally, a recent discovery of optical control of nuclear spins in semiconductors is reviewed and placed in the context of a long-standing search for electronic control of nuclear dynamics.

Two-color control of localization: From lattices to spin systems

We demonstrate control of quantum dynamics in a finite model system described by a tight-binding Hamiltonian, through interaction with a multifrequency external field. Effective defects can be introduced into the lattice by a two-frequency field, and the character of the defects can be controlled by the relative phase between the two field components. These field-induced defects imply robust localization of dressed (Floquet) states on lattice sites. Implications for a spin system in crossed magnetic fields are discussed.

Adaptive real-time femtosecond pulse shaping

Experimental results of a practical self-learning pulse-shaping system are presented. Real-time adaptive pulse shaping of uncharacterized pulses is achieved. A cross-correlation feedback measurement of the output pulses is used by a simulated-annealing algorithm to modify the pulses iteratively toward target shapes. This scheme can readily be used for coherent control of quantum dynamics.

Theory of controlled quantum dynamics

We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general linear, and it amounts to introduce additional quadratic and linear time-dependent terms to the given potential. In this way one can construct for general systems either coherent packets moving with constant dispersion, or dynamically squeezed packets whose spreading remains bounded for all times. In the standard operatorial framework our scheme corresponds to a suitable generalization of the displacement and scaling operators that generate the coherent and squeezed states of the harmonic oscillator.

Dispersion-free wave packets and feedback solitonic motion in controlled quantum dynamics

This paper considers the feasibility of creating dispersion-free solitary quantum-mechanical wave packets. The analysis is carried out within a general framework of quantum-optimal control theory. A key to the realization of solitary quantum wave packets is the ability to create traveling wave potentials U(x-\ensuremath{\nu}t) with coordinated space and time dependence where \ensuremath{\nu} is a characteristic speed. As an illustration, the case of an atom translating in a designed optical trap is considered. Three examples are treated within this framework: (A) the motion of a dispersion-free traveling bound state, (B) feedback-stabilized solitonic motion, and (C) feedback-stabilized solitonic motion in the presence of auxiliary physical objectives. The quantum solitons of (B) and (C) satisfy a nonlinear Schr\"odinger-type equation with laboratory feedback in the form of an observation of the probability density. This feedback is essential for maintaining the solitonic-type motion. Some generalizations and potential applications of these concepts are also discussed.

Relation between quantum computing and quantum controllability.

It is demonstrated that the universality of any quantum computing element can be understood and verified via a precise mathematical criterion which tests for the controllability of an associated quantum control system. This relation between quantum computing and quantum control is deeper in that tools of coherent control of quantum dynamics may be used to arrive at specific designs for quantum computing devices. \textcopyright{} 1996 The American Physical Society.

A simplified approach to optimally controlled quantum dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously [J. Botina, H. Rabitz, and N. Rahman, J. Chem. Phys. 102, 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory [S. Shi and H. Rabitz, Comp. Phys. Comm. 63, 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reaction induced by an external optical electric field.

Control of quantum dynamics by a locally optimized laser field. Multi-photon dissociation of hydrogen fluoride

We present a theoretical method for laser-control of a quantum system with open channels. The framework is based on the local optimization theory proposed in a previous paper (J. Chem. Phys. 100 (1994) 5646). The optimization theory is extended by introducing an optimization parameter q(ϵ) relevant to a continuum channel with kinetic energy ϵ. As an example of application, the control theory is used in multi-photon dissociation of hydrogen fluoride in the ground electronic state. The optimized laser field is analyzed with the help of a window Fourier transform and is shown to approximate a sequence of linear chirped pulses with different chirping rates. Such a form of the optimized laser field originates from the breakdown of the selection rule for optical transition in a Morse oscillator model. The time variation of multi-photon processes in the presence of the optimized laser field and a dissociation fraction are calculated based on the nuclear wave packet theory.

Control of quantum dynamics by a locally optimized laser field. Application to ring puckering isomerization

We presented a theoretical method for controlling quantum dynamics by locally optimized nonstationary laser fields, within the semiclassical theory of the molecule–radiation field interaction. The external laser field is optimized based on the control theory of a linear time-invariant (LTI) system, so that both the summation of the population of the nontarget states and the total energies of the laser fields are minimized. The optimization procedure involves operation of the so-called feedback gain matrix to the time-dependent state vector. This procedure is carried out at every successive short stage, in which the time-dependent Schrödinger equation can be approximated to the equation of motion of the LTI system. As an example, the control theory was applied to laser-induced ring-puckering isomerization, the dynamics of which can be described as the wave packet in the one-dimensional double minimum potential under locally optimized laser fields. The result indicated that nearly 100% of the population can be transferred to the final product state by irradiation of the optimized laser fields. The optimized laser fields were analyzed to obtain information on the carrier frequencies or the frequency modulation by using the fast Fourier transform method. These results were then compared with the result of isomerization induced by nonoptimized laser fields.

Coherent Control of Quantum Dynamics: The Dream Is Alive

Current experimental and theoretical progress toward the goal of controlling quantum dynamics is summarized. Two key developments have now revitalized the field. First, appropriate ultrafast laser pulse shaping capabilities have only recently become practical. Second, the introduction of engineering control concepts has put the required theoretical framework on a rigorous foundation. Extrapolations to determine what is realistically possible are presented.