Optimal control design of constant amplitude phase-modulated pulses: Application to calibration-free broadband excitation

Controlling open quantum systems: tools, achievements, and limitations

“…Moreover, Hamiltonians and relaxation parameters may be known much more accurately than is currently the case in photoinduced chemical reactions. A prominent example is NMR where the development of optimal control in theory and experiment went hand in hand, yielding beautiful results, for example on arbitrary excitation profiles [22], or robust broadband excitation [23,24]. Given these observations, quantum information processing (QIP) and related technologies offer themselves as an obvious playground for quantum optimal control: In these applications, typically the quantum system to be controlled is well characterized, and timescales are sufficiently slow to use electronics for pulse shaping.…”

New strategies for designing robust universal rotation pulses: Application to broadband refocusing at low power

“…The optimal control methodology for generating PP transformations in two-level systems has been described in detail previously [22,23,24,25,26,27,28,29,30,31,32,33,34,35], with progressive modification to enhance pulse performance by incorporating various experimental constraints. In each iteration of the algorithm, one starts with a given initial magnetization M 0 , applies the RF derived for the current iteration, and compares the resulting final state M f with a desired target state F .…”

“…The de novo design of UR pulses for NMR spectroscopy has received comparatively little attention [9,21], so it is an open question whether the composite constructions using PP pulses achieve the best possible performance. Yet, the demonstrated capabilities of optimal control for designing PP pulses [22,23,24,25,26,27,28,29,30,31,32,33,34,35] are equally applicable to the design of UR pulses [36,37,38]. The required modifications to the basic optimal control algorithm are fairly straightforward [36,39,40] and maintain the same flexibility for incorporating tolerance to variations in experimentally important parameters, such as RF homogeneity or relaxation.…”

Smooth optimal control with Floquet theory

“…shapes of laser or microwave pulses that drive a system towards desired properties. A particularly astonishing property of pulses designed by optimal control techniques is their robustness against experimental imperfections [16,17]; for example inhomogeneous broadening in ensembles of quantum systems can be compensated essentially completely through suitably designed control pulses [18][19][20].A disadvantage of these pulses is that they typically contain many frequency components; besides potential experimental challenges to generate such pulses, the complicated structure of these pulses renders it essentially impossible to understand why they result in their astonishing performance. In particular if we want to push the envelope to large many-body systems, the answer to the question of 'why' will become more and more important rather than the observation 'that' one can identify suitable pulses.…”

“…These ordinary derivatives can be obtained rather efficiently, which results in the astonishing performance of Krotov and GRAPE. This decomposition of the control fields' time-dependence in piecewise constant segments, however, often results in pulseshapes that contain high-frequency components [20].In this work, we will follow a parametrization of the control pulse in terms of Fourier modes [24,26]. By doing this, high-frequency components can be excluded by construction.…”