Piecewise Adiabatic Passage with a Series of Femtosecond Pulses

We develop a method of executing complete population transfers between quantum states in a piecewise manner using a series of femtosecond laser pulses. The method can be applied to a large class of problems as it benefits from the high peak powers and large spectral bandwidths afforded by femtosecond pulses. The degree of population transfer is robust to a wide variation in the absolute and relative intensities, durations, and time ordering of the pulses. The method is studied in detail for atomic sodium where piecewise adiabatic population transfer, as well as the induction of Ramsey-type interferences, is demonstrated.

Figure 1

Four types of PAP processes: (a),(c),(e),(g)—the pulse sequences; dashed blue—the pump, firm red—the dump. (b),(d),(f),(h)—the populations ($|b_i(t){|}^2$); dashed blue—$i=1$, dotted green—$i=2$, firm red—$i=3$. (a,b) The reference AP; (c),(d) PAP with sharp turn-ons and turn-offs; (e),(f) and (g),(h) PAP with smooth overlapping and nonoverlapping pulses.

Figure 2

Ramsey interference in PAP. (a),(c) The field envelopes of the pump (dashed blue) and dump (red) pulse sequences. The green dotted lines in panel (a) mark the onset of the turn-off period(s). (b),(d) The final $|b_3{|}^2$ population as a function of the duration of the turn-off period(s).

Figure 3

(a) Depiction of the state vector $\mathbf{a}$. (b) Two sample trajectories of the $\mathbf{a}$ vector during the PAP process. Both the pump and the dump sequences of small rotations rotate the vector by an overall angle of $10\times 2\pi$. The left (right) trajectory corresponds to 50 (100) pulses in each sequence.

Figure 4

Field envelopes of the ($2+1$) PAP, and the final population of the target state as a function of the dump detuning in PAP (black), and in the reference conventional STIHRAP (dashed red).