Piecewise Adiabatic Population Transfer in a Molecule via a Wave Packet

We propose a class of schemes for robust population transfer between quantum states that utilize trains of coherent pulses, thus forming a generalized adiabatic passage via a wave packet. We study piecewise stimulated Raman adiabatic passage with pulse-to-pulse amplitude variation, and piecewise chirped Raman passage with pulse-to-pulse phase variation, implemented with an optical frequency comb. In the context of production of ultracold ground-state molecules, we show that with almost no knowledge of the excited potential, robust high-efficiency transfer is possible.

Figure 1

Sequences of femtosecond pulses in piecewise STIRAP (a) and piecewise CRP (b) between states $|1⟩=3S$, $|2⟩=4P$, and $|3⟩=5S$ of Na [19]. Dashed blue: pump field envelope; solid red: dump field envelope; gray: the carrier phase in piecewise CRP with ${\alpha }_P={\alpha }_D=0.2$.

Figure 2

KRb potentials, basis states, and PAP arrangements discussed in the text.

Figure 3

Time-dependent field of the pump (a), and dump (b) pulses. The field in each pulse is normalized relative to the maximum of the pump field.

Figure 4

Dynamics of the STIRAP-like (a),(b) and CRP-like (c),(d) PAP in KRb. (a),(c) Envelopes of the pump (dashed blue) and dump (solid red) pulses, and the carrier phase in piecewise CRP [gray in (c)]. Each point shows the factor by which the field shown in Fig. 3 is scaled. The carrier phase ${\varphi }^{(0)}$ in the piecewise CRP, same for the pump and dump, is shown by the gray staircase in (c). (b),(d) Population dynamics of all the levels in the system. Time is given at the “compressed” set of points: output is shown only for the times when the field is on.

Figure 5

(a) Efficiency of the STIRAP-like PAP with unshaped laser pulses in dependence on the interpair delay $\Delta T$ and the intrapair delay $\delta T$. Positive $\delta T$ indicates that the pump comes after the dump; i.e., the population remains in the excited wave packet until the next dump comes (suffering more spontaneous emission losses). (b) Section of the density plot (a) taken at $\Delta T=1310.62\mathrm{ps}$ [blue dotted line in (a)]. (c) Fourier transform of (b). The green dotted line marks the beat frequency between $E_2^{(1)}$ and $E_2^{(2)}$.