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We analyze the simultaneous time-optimal control of two-spin systems. The twonon coupled spins which differ in the value of their chemical offsets arecontrolled by the same magnetic fields. Using an appropriate rotating frame, werestrict the study to the case of opposite shifts. We then show that theoptimal solution of the inversion problem in a rotating frame is composed of apulse sequence of maximum intensity and is similar to the optimal solution forinverting only one spin by using a non-resonant control field in the laboratoryframe. An example is implemented experimentally using techniques of NuclearMagnetic Resonance.

Simultaneous time-optimal control of the inversion of two spin 1/2 particles