The Fantastic Four: A plug ‘n’ play set of optimal control pulses for enhancing NMR spectroscopy

Abstract

We present highly robust, optimal control-based shaped pulses designed to replace all 90° and 180° hard pulses in a given pulse sequence for improved performance. Special attention was devoted to ensuring that the pulses can be simply substituted in a one-to-one fashion for the original hard pulses without any additional modification of the existing sequence. The set of four pulses for each nucleus therefore consists of 90° and 180° point-to-point (PP) and universal rotation (UR) pulses of identical duration. These 1ms pulses provide uniform performance over resonance offsets of 20kHz ((1)H) and 35kHz ((13)C) and tolerate reasonably large radio frequency (RF) inhomogeneity/miscalibration of ±15% ((1)H) and ±10% ((13)C), making them especially suitable for NMR of small-to-medium-sized molecules (for which relaxation effects during the pulse are negligible) at an accessible and widely utilized spectrometer field strength of 600MHz. The experimental performance of conventional hard-pulse sequences is shown to be greatly improved by incorporating the new pulses, each set referred to as the Fantastic Four (Fanta4).

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“…A number of novel pulse shapes with exceptional properties have been determined by optimal control methods [14]. Fig.…”

Training Schrödinger’s cat: quantum optimal control

“…In general, UR pulses are significantly longer than PP pulses for the same error resilience, which was exploited in a new strategy to build complete sequences based on standardized UR pulses when necessary and standardized PP pulses whenever they are sufficient [376]. The recent application of optimal control methods to the problem of heteronuclear decoupling yields not only significantly improved performance [377,378] but also unprecedented flexibility in the design of tailored decoupling sequences [379][380][381].…”

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.…”