Monotonically convergent optimal control theory of quantum systems under a nonlinear interaction with the control field

We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured by a non-standard choice of the cost which is not quadratic in the field. These algorithms can be constructed for pure and mixed-state quantum systems. The efficiency of the method is shown numerically on molecular orientation with a non-linearity of order 3 in the field. Discretizing the amplitude and the phase of the Fourier transform of the optimal field, we show that the optimal solution can be well-approximated by pulses that could be implemented experimentally.Comment: 24 pages, 11 figure

Monotonically convergent optimal control theory of quantum systems with spectral constraints on the control field

We propose a new monotonically convergent algorithm which can enforce spectral constraints on the control field (and extends to arbitrary filters). The procedure differs from standard algorithms in that at each iteration the control field is taken as a linear combination of the control field (computed by the standard algorithm) and the filtered field. The parameter of the linear combination is chosen to respect the monotonic behavior of the algorithm and to be as close to the filtered field as possible. We test the efficiency of this method on molecular alignment. Using band-pass filters, we show how to select particular rotational transitions to reach high alignment efficiency. We also consider spectral constraints corresponding to experimental conditions using pulse shaping techniques. We determine an optimal solution that could be implemented experimentally with this technique.Comment: 16 pages, 4 figures. To appear in Physical Review

Field-free molecular orientation by nonresonant and quasiresonant two-color laser pulses

International audienceWe analyze the control of molecular orientation by nonresonant and quasiresonant two-color laser pulses (2+1 process). The laser pulses are assumed to be short with respect to the rotational period. In the nonresonant case, we show that the efficiency of this strategy crucially depends on the polarizability and the hyperpolarizability of the molecule. In the quasiresonant case, i.e., if the 2ω frequency is in quasiresonance with a vibrational frequency, one can improve the orientation by adjusting the detuning. The best orientation is obtained for an optimal value of the detuning, which is different from zero

Snapshot imaging of postpulse transient molecular alignment revivals

International audienceLaser induced field-free alignment of linear molecules is investigated by using a single-shot spatial imaging technique. The measurements are achieved by femtosecond time-resolved optical polarigraphy FTOP . Individual alignment revivals recorded at high resolution in CO2, as well as simultaneous observation of several alignment revivals produced within the rotational period of the O2 molecule are reported. The data are analyzed with a theoretical model describing the alignment experienced by each molecule standing within the interaction region observed by the detector. The temporal dynamics, intensity dependence, and degree of alignment are measured and compared with the awaited results. The technique is simple and can be easily implemented in a large class of molecular samples. Improvement to extend the performance of the method is discussed. The reported study is a decisive step toward feedback optimization and optimal control of field-free molecular alignment

Laser induced field-free molecular alignment

Talk given by O. FaucherInternational audienc

Control and optimization of postpulse molecular alignment by shaped laser pulse

Talk given by O. FaucherInternational audienc