Complete transfer of populations from a single state to a preselected superposition of states using piecewise adiabatic passage: Theory

We develop a method for executing robust and selective transfer of populations between a single level and preselected superpositions of energy eigenstates. Viewed in the frequency domain, our method amounts to executing a series of simultaneous adiabatic passages into each component of the target superposition state. Viewed in the time domain, the method works by accumulating the wave function of the target wave packet as it revisits the transition region, in what amounts to an extension of the piecewise adiabatic passage technique [E. A. Shapiro et al., Phys. Rev. Lett. 99, 033002 (2007)] to the multistate regime. The viability of the method is verified by performing numerical tests for the ${\text{Na}}_2$ molecule.

Figure 1

(Color online) Piecewise adiabatic following in ${\text{Na}}_2$. (a) Amplitude spectrum (solid) and frequency-dependent phase (dashed blue) of the driving field. (b) The driving field as a function of time. [(c) and (d)] Populations of various vibrational levels of the ground and excited electronic states. (e) Final populations of $A{{}^1\Sigma }_u^{+}$ states predicted by the theory (full circles, red), and obtained in the numerical simulation (empty squares, blue). (f) Same as (e) for the case when the spectral region corresponding to the transition into one of the excited levels is blocked.

Figure 2

(Color online) Field spectrograms. (a) Absolute values of the overlap integral of the pulse train field with probe Gaussian pulses. The red horizontal lines show the resonance frequencies ${\omega }_n^{\text{res}}$. (b) Spectrogram of a conventional frequency-chirped pulse. (c) Expansion of the pulse train field in short probe pulses. The amplitude of each projection on a probe pulse is shown by brightness, its phase by color. The white dotted line marks the spectral center of the pulse.

Figure 3

(Color online) A calculated sample trajectory of the Bloch vector (thick gray arrow) during the piecewise AP process implemented with a train of 20 ultrashort pulses [38].

Figure 4

(Color online) Population transferred into the target manifold (a), and the projection on the target wave packet (b) as a function of the chirp ${\alpha }_{\omega }$ and field strength ${ϵ}^0$.