= Weak resonant driving
{title2=$\varepsilon\omega T/a_0\ll1$}
A sinusoidal trap displacement with amplitude $\varepsilon$ and duration $T$ produces a resonant first-order excitation amplitude proportional to $\varepsilon\omega T/a_0$, where $a_0$ is the <oscillator length>. Keeping its square much smaller than one is the long-time condition for weak excitation. The small-displacement condition $\varepsilon/a_0\ll1$ alone does not ensure uniform validity as $T$ grows. Exact linear driving remains solvable as a <coherent state> after this first-order approximation fails.
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