25-30 August 2019
Henry Ford Building
Europe/Berlin timezone

Second order dispersion by optimised rotation pulses

27 Aug 2019, 11:05
Lecture Hall B (Henry Ford Building)

Lecture Hall B

Henry Ford Building

Talk Computation Computation


Dr David Goodwin (Karlsruhe Institute of Technology)


The GRAPE method of optimal control can attempt to find the maximum overlap between a desired rotation propagator and the effective propagator of the pulse sequence [1], termed the fidelity. In finding optimal rotation pulses, numerical optimisation methods use the gradient of the fidelity to give super-linear convergence to a maximum overlap [2].

Building on past research that creates broadband pulses performing unitary propagators (BURBOP) [3,4], the research presented in this communication advances a step forward to create a new class of pulses with a defined second order phase dispersion.

One of the problems associated with universal rotation solutions, named BURBOP pulses [3,4], is the resulting high irradiation energy compared with the easier control problem of optimising state-to-state problems. A novel method is presented which will show this energy can be lowered by defining target rotation propagators as a function of phase dispersion. A customised version of the Spinach [5] optimal control toolbox [2,6,7] is used to simulate an ensemble of two-level quantum systems. This new class of pulse is named SORDOR pulses by the authors.

This optimal control method uses a defined quadratic phase dispersion, similar to the chirped pulses, for the targets of optimal control methods to find pulses that produce a rotation around an axis [3,4] at each frequency offset. Results for $90^{\circ}$ and $180^{\circ}$ SORDOR pulses are compared the achievable fidelity to the equivalent BURBOP pulse.

[1] J Magn. Reson., 172, 296 (2005)
[2] J Magn. Reson., 212, 412 (2011)
[3] J. Magn. Reson. 225, 142 (2012)
[4] J. Magn. Reson. 216, 78 (2012)
[5] J. Magn. Reson., 208, 179 (2011)
[6] J. Chem. Phys., 143, 084113 (2015)
[7] J. Chem. Phys., 144, 204107 (2016)

Primary authors

Dr David Goodwin (Karlsruhe Institute of Technology) Dr Martin Koos (Carnegie Mellon University) Prof. Burkhard Luy (Institute for Biological Interfaces 4 - Magnetic Resonance and Institute for Organic Chemistry, Karlsruhe Institute of Technology)

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