Shortcut to Adiabatic Passage in Two- and Three-Level Atoms

We propose a method to speed up adiabatic passage techniques in two-level and three-level atoms extending to the short-time domain their robustness with respect to parameter variations. It supplements or substitutes the standard laser beam setups with auxiliary pulses that steer the system along the adiabatic path. Compared to other strategies, such as composite pulses or the original adiabatic techniques, it provides a fast and robust approach to population control.

Figure 1

Dimensionless energies (in quasi-interaction picture) $\epsilon =E/(\beta \hslash )$ versus dimensionless time $T=t\beta$ for the AE scheme: diabatic energies (dot-dashed blue lines), adiabatic energies (dashed orange lines), average energy evolving with $H_0^I$ (solid purple line), average energy evolving with ${\mathcal{H}}^I=H_1^I$ or ${\mathcal{H}}^I=H_0^I+H_1^I$ (dotted red line), indistinguishable from the adiabatic energy. Parameters: $\omega =5$ and $\tau =1.22$.

Figure 2

Fidelity ($F=P_2$) versus the changes of (a) the Rabi frequency from ${\Omega }_0$ to ${\Omega }_0(1+\eta )$, (b) the detuning by $\delta$. SHAPE, AE scheme (solid red line) with ${\Omega }_a\le {\Omega }_0$, ordinary AE adiabatic passage (dotted black line), Rabi pulse (dashed blue line), composite pulse $\frac{\pi }{2}(x)\pi (y)\frac{\pi }{2}(x)$ (dot-dashed purple line). ${\Omega }_0=2\pi \times 5\mathrm{MHz}$, $t_0=25\mathrm{ns}$, $\beta =2\pi \mathrm{MHz}$.

Figure 3

Level scheme (left) and evolution of Rabi frequencies (right) in a STIRAP sequence of laser pulses, Eq. (7), with ${\Omega }_0=2\pi \times 2\mathrm{MHz}$, $\Delta =2\pi \times 0.1\mathrm{MHz}$, and $T=4\mu \mathrm{s}$, $\tau =0.1T$. ${\Omega }_s/{\Omega }_0$ (dashed blue line), ${\Omega }_p/{\Omega }_0$ (solid red line), ${\tilde{\Omega }}_a/{\Omega }_0$ (dotted orange line).

Figure 4

Time evolution of the populations of levels 1, 2, and 3 for STIRAP: (a) Hamiltonian $H_0^I(t)$, (b) ${\tilde{H}}_1^I(t)$. Same parameters as in Fig. 3.