Population Transfer between Two Quantum States by Piecewise Chirping of Femtosecond Pulses: Theory and Experiment

We propose and experimentally demonstrate the method of population transfer by piecewise adiabatic passage between two quantum states. Coherent excitation of a two-level system with a train of ultrashort laser pulses is shown to reproduce the effect of an adiabatic passage, conventionally achieved with a single frequency-chirped pulse. By properly adjusting the amplitudes and phases of the pulses in the excitation pulse train, we achieve complete and robust population transfer to the target state. The piecewise nature of the process suggests a possibility for the selective population transfer in complex quantum systems.

Figure 1

Two calculated sample trajectories of the Bloch vector (thick gray arrow) during the AP process implemented in atomic Rb with a single continuous chirped pulse (a), and a train of 20 ultrashort pulses (b) (see text).

Figure 2

(a) The amplitudes (oscillatory line, blue) and phases (piecewise parabola, red) of the driving field. (b) The populations of states $|1⟩$ (falling, blue) and $|2⟩$ (rising, green) during the PAP process.

Figure 3

(a) Experimental setup. Ion signal is measured for each excitation pulse (wide blue) followed by an ionizing probe (narrow red); (b) Amplitude (solid blue line) and phase (dashed red line) mask for generating a train of 9 pulses from a transform-limited pulse (dash-dotted black line). (c) FROG retrieval for the above pulse train with the temporal field amplitude (solid blue) and phase (dashed red), compared with the target quadratic phase of the pulses, ${\Phi }_k$ (black dots). All amplitudes are shown in arbitrary units.

Figure 4

Measured (dots) and calculated (lines) population of the excited state for a single pulse (a),(c) and a train of 7 pulses (b),(d). In (a) and (b), the efficiency of the population transfer is shown as a function of the integrated pulse energy. Blue diamonds and solid lines represent Rabi oscillations; red circles and dashed lines correspond to continuously (a) and piecewise (b) chirped excitation with $\alpha =20\times {10}^3{\mathrm{fs}}^2$ and $\overline{\alpha }=1$ radian, respectively. Black crosses in (b) represent an example of random distribution of phases ${\Phi }_k$. In (c) and (d), the efficiency of the population transfer is shown as a function of the continuous and piecewise chirp, respectively. In both cases, the energy of the excitation field corresponds to the first minimum of the respective Rabi oscillation. Experimental signals on all four plots are normalized to the maximum of Rabi oscillations in plot (a).