Phase control of nonadiabatic optical transitions

We theoretically study the interaction of two time delayed, phase-locked, and nonresonant pulses with a two-level system in the strong field regime. The population transfer is shown to be extremely sensitive to the phase shift $\varphi$ between the pulses, with efficient population transfer taking place only for $\varphi$ close to $\pi$. This effect is explained in terms of nonadiabatic jump and rapid adiabatic passage phenomena.

Figure 1

(a) Nonadiabatic coupling $\mid {\partial }_T\theta \mid$; it presents a maximum at $T=0$, two local maxima at $T=\pm T_m$, and is zero at $T=\pm T_0$. (b) Field profile $f_d(\pi ,T)$ (solid line) and adiabatic energy levels $\frac{\Delta \pm \Omega \left(T\right)}{2}$ (dashed line). (c) Excited adiabatic state population ${\mid {\alpha }_{+}\mid }^2$ showing NAJ. Parameters are $\Delta =8$, ${\theta }_d=400$ $(r=50)$, $\tau =1$, and $\varphi =\pi$.

Figure 2

Adiabatic excited state population profile at time $(T=0.1)$ just after the nonadiabatic jump (for $\varphi =\pi$). Other parameters are the same as those in Fig. 1.

Figure 3

Asymptotic excited state population. Parameters are the same as those in Fig. 1. In the inset a zoom is made to show the width of the peak.

Figure 4

Dynamics of adiabatic excited state population with $\varphi =\pi$ (solid line), $\varphi =\pi +0.04$ (dashed line), and $\varphi =\pi +0.05$ (dotted line). Other parameters are the same as those in Fig. 1.

Figure 5

(a) Modified adiabatic energy levels showing one crossing at $T=0$, and another near $T=2.5$; the second crossing is shown magnified in the inset. (b) Population in adiabatic excited state. The phase shift is $\varphi =0$; other parameters are the same as those in Fig. 1.