We analyze the simultaneous time-optimal control of two-spin systems. The two
non coupled spins which differ in the value of their chemical offsets are
controlled by the same magnetic fields. Using an appropriate rotating frame, we
restrict the study to the case of opposite shifts. We then show that the
optimal solution of the inversion problem in a rotating frame is composed of a
pulse sequence of maximum intensity and is similar to the optimal solution for
inverting only one spin by using a non-resonant control field in the laboratory
frame. An example is implemented experimentally using techniques of Nuclear
Magnetic Resonance.Comment: 13 pages, 3 figure
