Quantum Optimally Controlled Transition Landscapes

Design of infrared laser pulses for the deexcitation of highly excited homonuclear diatomic molecules

We explore the possibility of using shaped infrared laser pulses to deexcite a homonuclear diatomic molecule from its highest vibrational state down to its ground vibrational state. The motivation for this study arises from the need to deexcite alkali metal dimers in a similar way so as to stabilize molecular Bose-Einstein condensates. We demonstrate that for the case of the H(2) molecule, where it is possible to evaluate all the necessary high accuracy ab initio data on the interaction of the molecule with an electric field, we are able to successfully design a sequence of infrared laser pulses to accomplish the desired deexcitation process in a highly efficient manner.

Coherent spectroscopy in dissipative media: Time-domain studies of channel phase and signal interferometry

We extend a recently formulated coherence spectroscopy of dissipative media [J. Chem. Phys. 122, 084502 (2005)] from the stationary excitation limit to the time domain. Our results are based on analytical and numerical solutions of the quantum Liouville equation within the Bloch framework. It is shown that the short pulse introduces a new, controllable time scale that allows better insight into the relation between the coherence signal and the phase properties of the material system. We point to the relation between the time-domain coherence spectroscopy and the method of interferometric two-photon photoemission spectroscopy, and propose a variant of the latter method, where the two time-delayed excitation pathways are distinguishable, rather than identical. In particular, we show that distinguishability of the two excitation pathways introduces the new possibility of disentangling decoherence from population relaxation.

Modeling the influence of a laser pulse on the potential energy surface in optimal molecular control theory

Understanding and modeling the interaction between light and matter is essential to the theory of optical molecular control. While the effect of the electric field on a molecule's electronic structure is often not included in control theory, it can be modeled in an optimal control algorithm by a set or toolkit of potential energy surfaces indexed by discrete values of the electric field strength where the surfaces are generated by Born-Oppenheimer electronic structure calculations that directly include the electric field. Using a new optimal control algorithm with a trigonometric mapping to limit the maximum field strength explicitly, we apply the surface-toolkit method to control the hydrogen fluoride molecule. Potential energy surfaces in the presence and absence of the electric field are created with two-electron reduced-density-matrix techniques. The population dynamics show that adjusting for changes in the electronic structure of the molecule beyond the static dipole approximation can be significant for designing a field that drives a realistic quantum system to its target observable.

Optimal control landscapes for quantum observables

The optimal control of quantum systems provides the means to achieve the best outcome from redirecting dynamical behavior. Quantum systems for optimal control are characterized by an evolving density matrix and a Hermitian operator associated with the observable of interest. The optimal control landscape is the observable as a functional of the control field. The features of interest over this control landscape consist of the extremum values and their topological character. For controllable finite dimensional quantum systems with no constraints placed on the controls, it is shown that there is only a finite number of distinct values for the extrema, dependent on the spectral degeneracy of the initial and target density matrices. The consequences of these findings for the practical discovery of effective quantum controls in the laboratory is discussed.

Quantum optimal control: Hessian analysis of the control landscape

Seeking an effective quantum control entails searching over a landscape defined as the objective as a functional of the control field. This paper considers the problem of driving a state-to-state transition in a finite level quantum system, and analyzes the local topology of the landscape of the final transition probability in terms of the variables specifying the control field. Numerical calculation of the eigenvalues of the Hessian of the transition probability with respect to the control field variables reveals systematic structure in the spectra reflecting the existence of a generic and simple control landscape topology. An illustration shows that the number of nonzero Hessian eigenvalues is determined by the number of quantum states in the system. The Hessian eigenvectors associated with its nonzero eigenvalues are shown to give insight into the cooperative roles of the control variables. The practical consequences of these findings for quantum control are discussed.

General Method for the Dimension Reduction of Adaptive Control Experiments

Adaptive femtosecond control experiments are expanding the possibilities for using laser pulses as photophysical and photochemical reagents. However, because of the large number of variables necessary to perform these experiments (usually 100-200), it has proven difficult to elucidate the underlying control mechanisms from the optimized pulse shapes. If adaptive control is to become a widespread tool for examining chemical dynamics, methods must be developed that reveal latent control mechanisms. This manuscript presents a generally applicable method for dimension reduction of adaptive control experiments based on partial least squares regression analysis (PLS) of the normalized covariance matrix of the total data set. When applied to experimental results obtained in our laboratory, it shows that only seven fundamental dimensions from an original 208-dimension search space are needed to account for approximately 90% of the variance in the observed fitness of 11,700 laser-pulse shapes explored during the optimization experiment. Furthermore, the seven dimensions have a remarkable regularity in their functional form. It is anticipated that this work will facilitate theoretical treatments directly linking the optimal fields to control mechanisms, allow quantitative comparisons of independent control results, and suggest new experimental methods for rapid adaptive searches.

Pulse shaping for optimal control of molecular processes

In this paper, a new method is proposed to design optimized control fields with desired temporal and/or spectral properties. The method is based on penalizing the difference between an optimized field obtained from an iterative scheme and a reference field with desired temporal and/or spectral properties. Compared with the standard optimal control theory, the current method allows a simple, experimentally accessible field be found on the fly; while compared with parameter space searching optimization, the iterative nature of this method allows automatic exploration of the intrinsic mechanism of the population transfer. The method is illustrated by examing the optimal control of vibrational excitation of the Cl-O bond with both temporally and spectrally restricted pulses.

Phase and polarization control as a route to plasmonic nanodevices

We extend the concepts of phase, polarization, and feedback control of matter to develop a general approach for guiding light in the nanoscale via nanoparticle arrays. The phase and polarization of the excitation source are first introduced as tools for control over the pathway of light at array intersections. Genetic algorithms are next applied as a systematic design tool, wherein both the excitation field parameters and the structural parameters of the nanoparticle array are optimized to make devices with desired functionality. Implications to research fields such as single molecule spectroscopy, spatially confined chemistry, optical logic, and nanoscale sensing are envisioned.

Detection and automatic repair of nucleotide base-pair mutations by coherent light

We show that phase-coherent optical techniques allow for the detection and automatic repair of mutations in nucleotide pairs. We demonstrate computationally that there is a laser pulse sequence that can detect the occurrence of a mutation caused by a double proton transfer between hydrogen-bonded nucleotide pairs and automatically repair it by converting the mutated nucleotide pair to the nonmutated one. The specific system chosen for this demonstration is the hydrogen-bonded 2-pyridone.2-hydroxypyridine dimer at typical internucleotide distances, a well-established model for tautomeric acid base pairs.

Spectral phase optimization of femtosecond laser pulses for narrow-band, low-background nonlinear spectroscopy

We use experimental search space mapping to examine the problem of selective nonlinear excitation with binary phase shaped femtosecond laser pulses. The search space maps represent a graphical view of all the possible solutions to the selective nonlinear excitation problem along with their experimental degrees of success. Using the information learned from these maps, we generate narrow lines with low background in second harmonic generation and stimulated Raman scattering spectra.

Systematic Control of Nonlinear Optical Processes Using Optimally Shaped Femtosecond Pulses

This article reviews experimental efforts to control multiphoton transitions using shaped femtosecond laser pulses, and it lays out the systematic study being followed by us for elucidating the effect of phase on nonlinear optical laser-molecule interactions. Starting with a brief review of nonlinear optics and how nonlinear optical processes depend on the electric field inducing them, a number of conclusions can be drawn directly from analytical solutions of the equations. From a Taylor expansion of the phase in the frequency domain, we learn that nonlinear optical processes are affected only by the second- and higher-order terms. This simple result has significant implications on how pulse-shaping experiments are to be designed. If the phase is allowed to vary arbitrarily as a continuous function, then an infinite redundancy that arises from the addition of a linear phase function across the spectrum with arbitrary offset and slope could prevent us from carrying out a closed-loop optimization experiment. The early results illustrate how the outcome of a nonlinear optical transition depends on the cooperative action of all frequencies in the bandwidth of a laser pulse. Maximum constructive or destructive interference can be achieved by programming the phase using only two phase values, 0 and pi. This assertion has been confirmed experimentally, where binary phase shaping (BPS) was shown to outperform other alternative functions, sometimes by at least on order of magnitude, in controlling multiphoton processes. Here we discuss the solution of a number of nonlinear problems that range from narrowing the second harmonic spectrum of a laser pulse to optimizing the competition between two- and three-photon transitions. This Review explores some present and future applications of pulse shaping and coherent control.

Quantum observable homotopy tracking control

This paper presents a new tracking method where the target observable O(s,T) at the final dynamical time T follows a predefined track P(s) with respect to a homotopy tracking variable s>or=0. The procedure calculates the series of control fields E(s,t) required to accomplish observable homotopy tracking by solving a first-order differential equation in s for the evolution of the control field. Controls produced by this technique render the desired track for all s without encountering field singularities. This paper also extends the technique to the case where the field-free Hamiltonian and dipole moment operator change with s in order to explore the control of new physical systems along the track. Several simulations are presented illustrating the various uses for this quantum tracking control technique.

Optimal dynamic discrimination of similar quantum systems with time series data

Optimal dynamic discrimination (ODD) was proposed [Li et al., J. Phys. Chem. B 106, 8125 (2002)] as a paradigm for discriminating noninteracting similar quantum systems in a mixture. This paper extends the ODD concept to optimize a laser control pulse for guiding similar quantum systems such that each exhibits a distinct time series signal for maximum discrimination. The use of temporal data addresses various experimental difficulties, including noise in the laser pulse, signal detection errors, and finite time resolution in the signal. Simulations of ODD with time series data are presented to explore these effects. It is found that the use of an optimally chosen control pulse can significantly enhance the discrimination quality. The ODD technique is also adapted to the case where the sample contains an unknown background species.

Transformations to diagonal bases in closed-loop quantum learning control experiments

This paper discusses transformations between bases used in closed-loop learning control experiments. The goal is to transform to a basis in which the number of control parameters is minimized and in which the parameters act independently. We demonstrate a simple procedure for testing whether a unitary linear transformation (i.e., a rotation amongst the control variables) is sufficient to reduce the search problem to a set of globally independent variables. This concept is demonstrated with closed-loop molecular fragmentation experiments utilizing shaped, ultrafast laser pulses.

Coherence spectroscopy in dissipative media: A Liouville space pathway approach

We address the possibility of using coherent control tools to extract useful information about the interaction of a system with a dissipative environment. To that end we extend previous work, which developed a coherence spectroscopy based on two-pathway excitation phase control, from the isolated molecule limit to dense media. Specifically, we explore the properties of the channel phase, an observable of energy-domain two-pathway excitation experiments that was shown in the isolated molecule limit to carry information about the phase properties of the material system. Our analysis is based on the combination of steady state and time-dependent analytical perturbative approaches within the density matrix formalism, complemented by nonperturbative numerical simulations. We find that the channel phase carries significantly richer information in the presence of decoherence mechanisms than in their absence. In particular, rescattering events in the structured continuum introduce new features in the channel phase spectrum, whose structure conveys information about both the molecular continuum and the system bath interaction.

Gaining mechanistic insight from closed loop learning control: The importance of basis in searching the phase space

This paper discusses different routes to gaining insight from closed loop learning control experiments. We focus on the role of the basis in which pulse shapes are encoded and the algorithmic search is performed. We demonstrate that a physically motivated, nonlinear basis change can reduce the dimensionality of the phase space to one or two degrees of freedom. The dependence of the control goal on the most important degrees of freedom can then be mapped out in detail, leading toward a better understanding of the control mechanism. We discuss simulations and experiments in selective molecular fragmentation using shaped ultrafast laser pulses.

Efficient algorithms for the laboratory discovery of optimal quantum controls

The laboratory closed-loop optimal control of quantum phenomena, expressed as minimizing a suitable cost functional, is currently implemented through an optimization algorithm coupled to the experimental apparatus. In practice, the most commonly used search algorithms are variants of genetic algorithms. As an alternative choice, a direct search deterministic algorithm is proposed in this paper. For the simple simulations studied here, it outperforms the existing approaches. An additional algorithm is introduced in order to reveal some properties of the cost functional landscape.

Accuracy of gates in a quantum computer based on vibrational eigenstates

A model is developed to study the properties of a quantum computer that uses vibrational eigenstates of molecules to implement the quantum information bits and shaped laser pulses to apply the quantum logic gates. Particular emphasis of this study is on understanding how the different factors, such as properties of the molecule and of the pulse, can be used to affect the accuracy of quantum gates in such a system. Optimal control theory and numerical time-propagation of vibrational wave packets are employed to obtain the shaped pulses for the gates NOT and Hadamard transform. The effects of the anharmonicity parameter of the molecule, the target time of the pulse and of the penalty function are investigated. Influence of all these parameters on the accuracy of qubit transformations is observed and explained. It is shown that when all these parameters are carefully chosen the accuracy of quantum gates reaches 99.9%.