Mechanisms of molecular response in the optimal control of photoisomerization

We report on adaptive feedback control of photoinduced barrierless isomerization of 1,1'-diethyl-2,2'-cyanine in solution. We compare the effect of different fitness parameters and show that optimal control of the absolute yield of isomerization (photoisomer concentration versus excitation photons) can be achieved, while the relative isomerization yield (photoisomer concentration versus number of relaxed excited-state molecules) is unaffected by adaptive feedback control. The temporal structure of the optimized excitation pulses allows one to draw clear mechanistic conclusions showing the critical importance of coherent nuclear motion for the control of isomerization.     

Mechanisms in adaptive feedback control: photoisomerization in a liquid

The underlying mechanism for Adaptive Feedback Control in the experimental photoisomerization of 3,3'-diethyl-2,2'-thiacyanine iodide (NK88) in methanol is exposed theoretically. With given laboratory limitations on laser output, the complicated electric fields are shown to achieve their targets in qualitatively simple ways. Further, control over the cis population without laser limitations reveals an incoherent pump-dump scenario as the optimal isomerization strategy. In neither case are there substantial contributions from quantum multiple-path interference or from nuclear wave packet coherence. Environmentally induced decoherence is shown to justify the use of a simplified theoretical model.     

Step photoisomerization of dicarbocyanine dyes

Step photostereoisomerization of solutions of dicarbocyanine dyes was studied by laser photolysis. It is shown that, due to excitation, primary mono-cis-photoisomers are formed (a one-step process), whose excitation results in the formation of a γβ-di-cis-isomer (a two-step process). It was proved that the γβ-di-cis-isomer is formed mainly from a γ-mono-cis-isomer. The relaxation of the ground state of the γβ-di-cis-isomer to the ground state of a stable all-trans-isomer occurs in steps via two channels, in which γ-and β-mono-cis-isomers arise as intermediate products. The relaxation rates of both channels are different. The shift of the wavelength related to the maximum of absorption in the spectra of the primary and secondary isomers relative to that of the all-trans-isomer depends on the electron-donor ability of terminal groups. Quantum-chemical calculations of changes in the energies of the ground and first excited singlet states of a molecule, caused by the rotation around several bonds in the methine chain, were carried out.     

Optimal control of quantum revival

Increasing fidelity is the ultimate challenge of quantum information technology. In addition to decoherence and dissipation, fidelity is affected by internal imperfections such as impurities in the system. Here we show that the quality of quantum revival, i.e., periodic recurrence in the time evolution, can be restored almost completely by coupling the distorted system to an external field obtained from quantum optimal control theory. We demonstrate the procedure with wave-packet calculations in both one- and two-dimensional quantum wells, and analyze the required physical characteristics of the control field. Our results generally show that the inherent dynamics of a quantum system can be idealized at an extremely low cost.     

Optimal control of neuronal activity

We investigate the optimal control of neuronal spiking activity for neurons receiving a class of random synaptic inputs, characterized by a positive parameter alpha. Optimal control signals and optimal variances are found exactly for the diffusion process approximating an integrate and fire model. When synaptic inputs are "sub-Poisson" (alpha<0.5), we find that the optimal synaptic input is a delta function (corresponding to bang-bang control) and the optimal signal is not unique. Poisson synaptic input is the critical case: The control signal is unique, but the control signal is still a delta function. For "supra-Poisson" (alpha>0.5) inputs, the optimal control is smooth and unique. The optimal variance obtained in the current paper sets the lowest possible bound in controlling the stochasticity of neuronal activity. We also discuss how to implement the optimal control signal for certain model neurons.     

A vision for ultrafast photoisomerization

We propose a simple physical mechanism to explain the ultrafast first step of vision, a photoinduced cis to trans rotation of retinal. In the ground state, the torsional stability of π bonds is countered by Coulomb interactions acting between the π lobes; the torsional dependence for Coulomb interactions is absent in the often-used Ohno approximation, but restored with our formula. After photoexcitation, the bonding weakens causing the destabilizing terms to dominate. The twist in the ground state due to steric interactions surrounding the 11-cis bond increases the initial torque and thus the speed of the reaction.     

Optimal control of resonance radiation processes

Optimal control methods are applied to solve some quantum electronics problems. Some specific problems involving a two-level system state control by optimal resonance radiation pulse shapes are considered.     

Isotope separation by selective unimolecular photoisomerization

The selectivity of a photochemical isotope separation process may be preserved in steps subsequent to photoexcitation through the use of unimolecular photoisomerization.     

Optimal control of vibrational transitions of HCl

Control of fundamental and overtone transitions of a vibration are studied for the diatomic molecule, HCl. Specifically, the results of the effect of variation of the penalty factor on the physical attributes of the system (i.e., probabilities) and pulse (i.e., amplitudes) considering three different pulse durations for each value of the penalty factor are shown and discussed. We have employed the optimal control theory to obtain infrared pulses for selective vibrational transitions. The optimization of initial guess field with Gaussian envelope, phrased as maximization of cost functional, is done using the conjugate gradient method. The interaction of the field with the molecule is treated within the semiclassical dipole approximation. The potential and the dipole moment functions used in the calculations of control dynamics are obtained from high level ab-initio calculations.     

Optimal control for Multi-Conjugate Adaptive Optics

Classic adaptive optics (AO) is now a proven technique that provides a closed loop real time correction of the turbulence. It is generally based on simple and efficient control algorithms. The next AO generation (Multi-Conjugate AO (MCAO) in its various forms and Extreme AO (XAO)) will require more sophisticated control approaches, especially in the case of wide field AO. We present here the concepts behind optimal control. The advantages compared to more standard approaches are stressed. A first experimental validation is presented. To cite this article: C. Petit et al., C. R. Physique 6 (2005).     

Optimal chaos control through reinforcement learning

A general purpose chaos control algorithm based on reinforcement learning is introduced and applied to the stabilization of unstable periodic orbits in various chaotic systems and to the targeting problem. The algorithm does not require any information about the dynamical system nor about the location of periodic orbits. Numerical tests demonstrate good and fast performance under noisy and nonstationary conditions. (c) 1999 American Institute of Physics.     

Optimal dynamical decoherence control of a qubit

We present a theory of dynamical control by modulation for optimal decoherence reduction. The theory is based on the non-Markovian Euler-Lagrange equation for the energy-constrained field that minimizes the average dephasing rate of a qubit for any given dephasing spectrum.     

Mathematical modeling of photoisomerization with intramolecular proton transfer

A system of equations describing time changes in the matrix elements of the density operator of a seven-level model of a molecule interacting with a light pulse taking into account spontaneous (including collective) decays of molecule excited states is suggested. Model parameters were selected to allow us to perform modeling of the photoisomerization of a molecule with two isomeric states with different stable proton positions on an intramolecular H-bond by numerically solving the suggested system of equations for density operator matrix elements. An analysis of the characteristic time dependences of the population of states of the model under consideration showed that proton phototransfer in the collective decay of various isomeric states of a molecule in an excited electronic state can be one of effective mechanisms of the photoisomerization of molecules whose structure is described by the model.     

Optimal control of wave-packets: a semiclassical approach

We studied the optimal quantum control of a molecular rotor in tilted laser fields using the time-sliced Herman–Kluk propagator for the evaluation of the optimal pulse and the light–dipole interaction as the control mechanism. The proposed methodology was used to study the effects of an optimal pulse on the evolution of a wave-packet in a double-well potential and in the effective potential of a molecular rotor in a collinear tilted fields setup. The amplitude and frequency of the control pulse were obtained in such a way that the transition probability between two rotational wave-packets was maximised.     

Optimal control technique for many-body quantum dynamics

We present an efficient strategy for controlling a vast range of nonintegrable quantum many-body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods such as the density matrix renormalization group. To demonstrate its potential, we employ it to solve a major issue in current optical-lattice physics with ultracold atoms: we show how to reduce by about 2 orders of magnitude the time needed to bring a superfluid gas into a Mott insulator state, while suppressing defects by more than 1 order of magnitude as compared to current experiments [T. St?ferle et al., Phys. Rev. Lett. 92, 130403 (2004)]. Finally, we show that the optimal pulse is robust against atom number fluctuations.     

Optimal control of structures with semiactive-tuned mass dampers

In this paper, the optimal performance of a magnetorheological (MR) damper which is used in a tuned mass damper in reducing the peak responses of a single-degree-of-freedom structure subjected to a broad class of seismic inputs including the harmonic, pulse, artificially generated and recorded earthquake excitations are studied. The optimal semiactive control strategy minimizes an integral norm of the main structure squared absolute accelerations subject to the constraint that the non-linear equations of motion are satisfied and is determined through a numerical solution to the Euler-Lagrange equations. The optimal performance evaluated for an MR damper is compared to an equivalent passive-tuned mass damper with optimized stiffness and damping coefficients. It is shown numerically that the optimal performance of the MR damper is always better than the equivalent passive-tuned mass damper for all the investigated cases and the MR damper has a great potential in suppressing structural vibrations over a wide range of seismic inputs.     

Optimal control approach to suppression of radiationless transitions

We propose a general approach for eliminating radiationless transitions in polyatomic molecules and illustrate it through the example of the S2-->S1 internal conversion of pyrazine. Essential to our approach is the phenomenon of electronically localized eigenstates of strongly vibronically coupled Hamiltonians. The occurrence of such states, observed here for the first time, and its generality are traced to the origin of scars of periodic orbits.