Feedback control optimisation of ESR experiments

Abstract

Numerically optimised microwave pulses are used to increase excitation efficiency and modulation depth in electron spin resonance experiments performed on a spectrometer equipped with an arbitrary waveform generator. The optimisation procedure is samplespecific and reminiscent of the magnet shimming process used in the early days of nuclear magnetic resonance -an objective function (for example, echo integral in a spin echo experiment) is defined and optimised numerically as a function of the pulse waveform vector using noise-resilient gradient-free methods. We found that the resulting shaped microwave pulses achieve higher excitation bandwidth and better echo modulation depth than the pulse shapes used as the initial guess. Although the method is theoretically less sophisticated than simulation based quantum optimal control techniques, it has the advantage of being free of the linear response approximation; rapid electron spin relaxation also means that the optimisation takes only a few seconds. This makes the procedure fast, convenient, and easy to use. An important application of this method is at the final stage of the implementation of theoretically designed pulse shapes: compensation of pulse distortions introduced by the instrument. The performance is illustrated using spin echo and out-of-phase electron spin echo envelope modulation experiments. Interface code between Bruker SpinJet arbitrary waveform generator and Matlab is included in versions 2.2 and later of the Spinach library.

Light-induced dipolar spectroscopy – A quantitative comparison between LiDEER and LaserIMD

“…In addition, given the dramatic improvement in modulation depth for LiDEER with a broadband pump pulse, it would certainly be worth it to investigate the impact of a larger set of inversion pulse shapes and parameters on the experiment. For LaserIMD, the modulation depth can be tuned via the triplet excitation,an enhancement of the SNR e. g. with optimal control theory-derived pulses as observer pulses can be envisioned [31,32].…”

Chirped ordered pulses for ultra-broadband ESR spectroscopy

“…Since the limitations of the ESR hardware, including the receiver and resonator bandwidth, hinder the CHORUS sequence from reaching its full potential, future improvements in ESR hardware design should enable an even better performance. Additionally, the CHO-RUS method could be combined with feedback loop optimization, 75 where multiple aspects of the problems posed by the ESR hardware can be addressed at once. The CHORUS sequence has the potential to find applications in many ESR experiments, especially where experiments already consist of three pulses.…”

Second order phase dispersion by optimized rotation pulses

“…The piecewise-constant time slices used in calculations are a very good approximation in nuclear magnetic resonance (NRM) spectroscopy. In cases where this piecewise-constant approximation is not valid, such as applications to electron paramagnetic resonance (EPR) spectroscopy, a feedback control method [39,40] or a transfer-matrix method [41][42][43] can be used to calibrate pulses due to these hardware-specific cavity effects. Further to this, optimal control can be designed to include a robustness to pulse amplitude miscalibration [29].…”