Past exam of the quantum physics course of the University of Oxford / 2016 / 10 / e

On Rabi resonance, $\omega ={\omega }_0$ and $\Omega =0$, soFor nonzero drive the probability starts at zero, reaches unity at $t=\pi /(2|\gamma |)$, and repeats with period $\pi /|\gamma |$. The population oscillation therefore has angular frequency $2|\gamma |$. This is complete resonant Rabi transfer; a drive of zero strength gives no transition.

For nonzero Rabi detuning,The sketch starts at zero and oscillates between zero and ${\gamma }^2/({\gamma }^2+{\Omega }^2)<1$, with period $\pi /\sqrt{{\gamma }^2+{\Omega }^2}$ when the coupling is nonzero. Relative to resonance, the oscillations have a smaller maximum and a shorter period at fixed coupling. The sign of the Rabi detuning changes the amplitudes' phases but leaves this transition probability unchanged. For $|\Omega |\gg |\gamma |$, its maximum is approximately ${\gamma }^2/{\Omega }^2$, so population transfer is strongly suppressed. The plotted detuned example has $|\Omega |=|\gamma |$, giving maximum $1/2$.