Frequency domain quantum optimal control under multiple constraints

Abstract

Optimal control of quantum systems with complex constrained external fields is one of the longstanding theoretical and numerical challenges at the frontier of quantum control research.Here, we present a theoretical method that can be utilized to optimize the control fields subject to multiple constraints while guaranteeing monotonic convergence towards desired physical objectives.This new optimization method is formulated in the frequency domain in line with the current ultrafast pulse shaping technique, providing the possibility for performing quantum optimal control simulations and experiments in a unified fashion. For illustrations, this method is successfully employed to perform multiple constraint spectral phase-only optimization for maximizing resonant multiphoton transitions with desired pulses.

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

“…(14). Finally, the frequency-domain constrained D-MORPH scheme [29] may be solved in conjunction with the present time-domain constrained D-MORPH one for removing the frequency components below ∼ 1000 cm −1 and above ∼ 2000 cm −1 .…”

“…In practice, the dc component along with other unwanted frequencies can also be removed by adding a spectral constraint, e.g., a bandpass filter throughout the optimization [8][9][10], or more systematically, using a hybrid time-frequency D-MORPH scheme that solves simultaneously the current time-domain constrained D-MORPH scheme and its frequencydomain counterpart recently formulated [29].…”

“…The subject of finding reasonable control fields subject to various constraints governed by partial differential equations while maintaining monotonic convergence of the optimization algorithms is among the most challenging problems at the frontier of quantum control research [21][22][23][24][25][26][27][28]. In a recent study [29], we proposed a gradientbased frequency domain quantum optimal control method to optimize the spectral field of laser pulses subject to multiple external constraints. For the present work, we generalize this method to the time domain to directly optimize the temporal control fields while taking into account multiple equality constraints.…”

“…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. The constant fluence constraint on the optimized control field has been considered in our previous work by fixing the spectral amplitude of the control unchanged [29]. Here, we will apply this requirement to the full control field in the time domain.…”

Complete elimination of nonlinear light-matter interactions with broadband ultrafast laser pulses

“…Solutions to analytically unaccessible maximization/mimization problems under consideration can be established in the framework of quantum optimal control theory (QOCT) [30][31][32][33][34][35]. Due to the technical complexity involved in acquiring either monotonic convergence or general applicability of the algorithms, however, the present problem is a challenge to the previously developed QOCT methods.…”