Jair Botina

Rapidly convergent iteration methods for quantum optimal control of population

A family of new iteration methods is presented for designing quantum optimal controls to manipulate the transition probability. Theoretical analysis shows that these new methods exhibit quadratic and monotonic convergence. Numerical calculations verify that for these new methods, within very few steps, the optimized objective functional comes close to its convergent limit.

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 reacti...

Nonstationary optimal paths and tails of prehistory probability density in multistablestochastic systems

The tails of prehistory probability density in nonlinear multistable stochastic systems driven by white Gaussian noise, which has been a subject of recent study, are analyzed by employing the concepts of nonstationary optimal fluctuations. Results of numerical simulations evidence that the prehistory probability density is non-Gaussian and highly asymmetrical that is an essential feature of noise driven fluctuations in nonlinear systems. We show also that in systems with the detail balance the prehistory probability density is the conventional transition probability that obeys the backward Kolmogorov equation.

Determining regular orbits in the presence of irregular trajectories using optimal control theory

Two general algorithms are presented to determine regular orbits in the presence of irregular trajectories in a phase space of n degrees of freedom. The first algorithm searches for regular orbits with the energy as a free‐floating parameter. The second algorithm seeks regular orbits at constant energy. These two approaches utilize optimal control theory to employ a small external control field that permits a search among the irregular motion for the regular orbits. The optimizing algorithm naturally seeks regular orbits with the control field turned off. Numerical results with a chaotic Hamiltonian show the method to be effective in determining regular trajectories. If the system is completely chaotic in some region, the method determines which initial condition is the best one in order to achieve a nearly regular orbit.

Optimal control of laser induced transient birefringence in liquid crystals

Abstract Optimal control theory is applied to design a laser pulse to produce an anisotropic change of the refraction index in the vicinity of the isotropicnematic phase transition in liquid crystals. The laser induced birefringence originates from the orientational anisotropy induced by the laser field that is enhanced significantly due to the excluded volume effect. The shape of the optimal pulse is analyzed for different values of relaxation time and different molecule concentrations.