Digitizing ultrafast adiabatic passage with a pulse train

Abstract

We present a digitized implementation of rapid adiabatic passage based on a train of weak, frequency-varying ultrafast pulses. Analytic conditions on the subpulse Rabi frequencies and detunings are derived to reproduce the continuous-time population dynamics of a conventional long-pulse excitation. We find that the reproduced dynamics achieves high fidelity even for pulse trains with a small number of subpulses, provided that each subpulse remains within the perturbative regime. The subpulses act as discrete samples of the underlying continuous evolution; consequently, more complex population dynamics, characterized by multiple oscillations prior to the onset of adiabaticity, require a larger number of subpulses for accurate reproduction. In addition, we demonstrate how the sidebands of a frequency comb can be exploited for resonant excitation at large carrier detuning and for the precise preparation of superposition states.

Figures (6)

• Figure 1: (a) Energy level diagram of a two-level system. (b) Time-dependent Rabi frequency of the pulse train. For simplicity in the drawing, we show the case with $T=0$, whereas in most cases $T$ is much larger than the duration of each subpulse, $\tau$.
• Figure 2: Population dynamics by a continuous pulse with total pulse area of $5\pi$ and chirp $\alpha\tilde{\tau}^2 = 291.6$ (a) and (b) or $\alpha\tilde{\tau}^2 =64.8$ (c) and (d). The sampling (number of subpulses) in the digitized version is $N = 20, 100, 50$ and $100$ for subfigures (a) to (d) respectively.
• Figure 3: Time-averaged population error, defined as square quadratic deviation of the population in the target state in the continuous $\tilde{P}_1(t)$ pulse from its digitized version $P_1(t)$, with $N = 100$ subpulses, for dynamics with different pulse areas and chirp ratios. The precision of the copy improves as the dynamics is more adiabatic, as it requires less subpulses to respond to all the population wiggles.
• Figure 4: Yield of population inversion at final time as a function of the energy difference $\Delta E$ between the levels, in units of the sideband of the train $n$. Whenever $T\Delta_E/2\pi$ is an integer number, there is resonance between a sideband of the train (for $n \neq 1$) and the molecular transition, leading to full population transfer. The yield decays for large $n$ due to the decay in the amplitude of the spectra with the sideband. The main figure shows the envelope of the yield. With higher resolution, the inset zooms in the yield when the transition is resonant with a few sidebands.
• Figure 5: Decay of the yield of population transfer as a function of the detuning from the resonant frequency for different sidebands, $n = 0, 10, 100, 150$ and $200$, which further zooms in the spikes shown in the inset of Fig. 4. Final populations follow the same behavior as a function of detuning, regardless of the sideband order.