External constraints on optimal control strategies in molecular orientation and photofragmentation: role of zero-area fields

Abstract

We propose a new formulation of optimal and local control algorithms which enforces the constraint of time-integrated zero-area on the control field. The fulfillment of this requirement, crucial in many physical applications, is mathematically implemented by the introduction of a Lagrange multiplier aiming at penalizing the pulse area. This method allows one to design a control field with an area as small as possible, while bringing the dynamical system close to the target state. We test the efficiency of this approach on two control purposes in molecular dynamics, namely, orientation and photodissociation.

Monotonic convergent quantum optimal control method with exact equality constraints on the optimized control fields

“…The time-integrated zero area field constraint for a freely propagating electromagnetic pulse is an important property for exploring coherent interaction of light with matter [30][31][32][33], and is required as a fundamental condition for satisfying the Maxwell's equations [27]. Only have there been limited attempts to take into account such constraint in the contexts of local control theory (LCT) and QOCT [27,34]. However, these previously proposed LCT-and QOCT-based methods in principle do not exactly reduce the field area to zero and, as a result, an additional filtering process is required to accurately render a zeroarea field.…”

Control of molecular dynamics with zero-area fields: Application to molecular orientation and photofragmentation

“…Several modifications of the standard optimal control algorithms have been brought forward to account for experimental constraints [9,11,10,12], such as the non linear interaction of the system with the field [13,14], the question of spectral constraints [15,16,17] and the robustness with respect to one or several model parameters [20,18,19,21]. Recently, we have shown how optimal control strategies can be extended to enforce the constraint of time-integrated zero-area on the control field [22]. This constraint is a fundamental requirement in laser physics, as shown in different experimental and theoretical studies [25,23,24,26,22,27].…”

“…Recently, we have shown how optimal control strategies can be extended to enforce the constraint of time-integrated zero-area on the control field [22]. This constraint is a fundamental requirement in laser physics, as shown in different experimental and theoretical studies [25,23,24,26,22,27]. Basically this effect can be related to the fact that the dc component of the control field is not a solution of Maxwell's equation.…”

“…Our preliminary study on the subject [22] is a methodology-oriented paper, focusing mainly on the technical aspects of the optimization algorithms (local and optimal approaches) as briefly illustrated on two typical molecular processes (orientation and dissociation). The present paper thoroughly expands this initial work [22] by providing an extended numerical investigation and a detailed physical analysis of the dynamics of two specific molecular systems. The article is organized as follows.…”

Optimal control theory with arbitrary superpositions of waveforms

“…In order to gain experimentally realizable control pulses, additional constraints may have to be taken into account, such as restricting the total energy or limiting the control functions [12,13,22,23,24,25,26]. Not all control algorithms follow this requirement equally well; for the effects such constraints have on the convergence behaviour of control algorithms, see [2].…”