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Excitation of $n$ inhomogenous two-level atom with different detunings? Bloch sphere

Physics Asked by blochman on March 18, 2021

I am learning about the bloch sphere and how it is used to to in two level systems. I have done some research already but I am slightly confused.

Suppose you have an $n$ number of inhomogenous atoms with different detunings and therefore different rabi frequencies, how could you use a combination of pulses to excite all the atoms.

I know one solution is known as "spin-echo" where you carry out a $pi/2$ pulse, wait some time $T$, carry out a pi pulse and wait the same time $T$ at which point the bloch vectors will line up. With them lined up again, another $pi/2$ pulse will send them to an excited state.

Is there another method of doing this where you do not have to wait a time $T$ and can send consecutive pulses to excite all $n$ atoms?

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