Figure 1

Occupation probability of the target state as a function of time for a qubit interacting with a single pulse. The heavy solid line corresponds to $\tau =1\mathrm{ps}$ (almost an ideal kick), the thin dashed line to $\tau =10\mathrm{ps}$ (where small deviations from an ideal kick occur), and the thin dotted line to $\tau =100\mathrm{ps}$ (where the kicked approximation is breaking down). The Rabi time for the oscillation between the states is $972\mathrm{ps}$.Reuse & Permissions

Figure 2

Occupation probability of the target state as a function of time for a double pulse that returns the system to its initial state in the kicked limit. The heavy solid line corresponds to $\tau =1\mathrm{ps}$ (almost ideal kicks), the thin dashed line to $\tau =10\mathrm{ps}$ (where small deviations from ideal kicks occur), and the thin dotted line to $\tau =100\mathrm{ps}$ (where the kicked approximation is breaking down).Reuse & Permissions

Figure 3

Occupation probability of the target state as a function of time for a double pulse that fully transfers population in the kicked limit. The heavy solid line corresponds to $\tau =1\mathrm{ps}$ (almost ideal kicks), the thin dashed line to $\tau =10\mathrm{ps}$ (where small deviations from ideal kicks occur), and the thin dotted line to $\tau =100\mathrm{ps}$ (where the kicked approximation is breaking down).Reuse & Permissions

Figure 4

Target state probability as a function of the pulse width $\tau$ (on the left), and as a function of the observation time $T_f$ (on the right). Here $T_{\Delta E}=2\pi \hslash ∕\Delta E=\pi ∕\omega$ is the Rabi time for oscillations between the states, where $\Delta E=E_{2p}-E_{2s}$. The heavy line denotes probability including time ordering, the dashed line denotes the probability in the intermediate picture without time ordering, and the dotted line represents the probability in the Schrödinger picture without time ordering. On the right, the lines begin at the midpoint of the pulse, $T_f=T_k$. The Schrödinger results damp out for large $T_f$ on the right as explained in the text.Reuse & Permissions

Figure 5

Target state probability as a function of the separation time $T_s=T_2-T_1$ between the two pulses, for integrated pulse strength $\alpha =\pi ∕2$, $\pi ∕4$, and $3\pi ∕8$. On the left the pulse width is a rather narrow $10\mathrm{ps}$, while on the right the pulse width is $100\mathrm{ps}$, where the kicked approximation is breaking down. Again the heavy line denotes the exact result including time ordering, while the thin dashed line denotes the intermediate picture result without time ordering. The Schrödinger picture result without time ordering is identically zero for all values of $T_s$ and $\alpha$.Reuse & Permissions