Motivation and background

One of the major problems of NMR (nuclear magnetic reonance) spectroscopy is its relatively low sensitivity which implies long measurement times (often several hours or even days) and/or relatively large quantities (mg to g) of sample. So far, for many experiments, it was not clear whether a further sensitivity enhancement can be achieved by better pulse sequences or if there are theoretical bounds that limit the efficiency of the experiment.

For example, consider an experiment to measure heteronuclear NOEs (nuclear Overhauser effect) between proton (1H) and carbon (13C) spins I and S (Nirmala & Wagner,1988; Kay et al., 1989; Palmer et al., 1991; Sattler et al., 1995). The sensitivity of the experiment is proportional to the effciciency of each individual building block of the pulse sequence. Consider for example the yellow building block that is responsible for the transfer of in-phase coherence S- of e.g. a 13C nuclear spin to in-phase coherence F- of attached 1H nuclear spins. For I2S and I3S spin systems (corresponding to CH2 and CH3 moeities, respectively), the theoretical least upper bound for this transfer efficiency was not known.

In I3S spin systems the transfer effciciency |f| between S- and F- has been improved considerably over the years by using new techniques, such as HEHAHA (Hartmann, Hahn 1962), refocussed INEPT (Burum, Ernst 1980), HIHAHA (Sattler et al. (1995), Glaser, Quant 1996) and yxz-ICOS-CT (Sattler et al. 1995). However, it was not clear whether further improvements can be achieved by developing more sophisticated techniques as the theoretical upper limit for this transfer was not known.

This situation is comparable to the development of the high jump record: Better training methods but also new techniques - such as the western roller, the Osborn roller, the straddle, or the Fosbory flop (introduced during the 1968 olympics) - have led to significant improvements. However, it is not clear if the "biomechanical" optimum has been reached or if the world record can be further improved by some revolutionary new jump technique.

In the field of NMR we are now able to determine the maximum possible efficiency of unitary transformations between arbitrary initial and final coherences. This was made possible by a procedure that yields the theoretical upper bound as well as optimal unitary operators that achieve this bound (Science 280, 421-424 (1998)).

For example, for the transfer of S- to F- in I3S spin systems we determined the theoretical bound to be 0.79. Hence, it became clear that there was still considerable room for improvement. In fact, in the following we were able to develop new pulse sequences that actually achieve this theoretical bound (T. Untidt, T. Schulte-Herbrüggen, B. Luy, S. J. Glaser, C. Griesinger, O. W. Sørensen, N. C. Nielsen, Mol. Phys., 95, 787-796, 1998).

Unfortunately (or perhaps fortunately), we still cannot state a theoretical upper limit for this discipline ...