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Modulated pulses compensating classical noise

We consider pulses of finite duration for coherent control in the presence of classical noise. We derive the corrections to ideal, instantaneous pulses for the case of general decoherence (spin-spin relaxation and spin-lattice relaxation) up to and including the third order in the duration τ_p of the pulses. For pure dephasing (spin-spin relaxation only), we design πand π/2 pulses with amplitude and/or frequency modulation which resemble the ideal ones up to and including the second order in τ_p. For completely general decoherence including spin-lattice relaxation the corrections are computed up to and including the second order in τ_p as well. Frequency modulated pulses are determined which resemble the ideal ones. They are used to design a low-amplitude replacement for XY8 cycles. In comparison with pulses designed to compensate quantum noise less conditions have to be fulfilled. Consequently, we find that the classical pulses can be weaker and simpler than the corresponding pulses in the quantum case.