Composite Pulses

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Composite pulses are sequences of consecutive radiofrequency pulses which are self-compensated for various classes of pulse imperfection. The first composite pulse (909018009090) was invented by myself (Malcolm Levitt) during an undergraduate research project in Ray Freeman's group at Oxford in 1978. The name "composite pulse" was invented by Ray Freeman. This three-pulse sequence was published in 1979:

"NMR Population Inversion Using a Composite Pulse", M.H.Levitt and R.Freeman, J.Magn.Reson. 33, 473 (1979).

Around 100 different sorts of composite pulse were developed subsequently. Some review articles are:

"Composite Pulses", M.H.Levitt, Prog. NMR Spectroscopy 18, 61 (1986).

and

M. H. Levitt, "Composite Pulses" in "Encyclopedia of Nuclear Magnetic Resonance", Eds. D. M. Grant and R. K. Harris (Wiley, 1996). PDF

Composite pulses have recently (2005) experienced a revival in interest from the Control Theory community, since they represent a particularly simple case of quantum control in a 2-level system. See, for example, the work by Navin Khaneja and Steffen Glaser.

The operation of composite pulses may readily be visualized by animations of the motion of magnetization vectors on a unit sphere. The animation above shows the effect of a 909018009090 composite pulse on magnetization vectors which are initially at the +z-axis, in the case of three different rf field values. The blue arrow represents sample elements with the nominal value of rf field, while the green arrow represents sample elements experiencing an rf field which is 15% too high, and the red arrow represents sample elements experiencing an rf field which is 15% too low.

Note that all three arrows end up close to the -z-axis, showing that the 909018009090 composite pulse is equivalent to a single 1800 pulse, compensated for rf field errors.

More composite pulse animations are given here.

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