Combining Jaynes-Cummings and anti-Jaynes-Cummings dynamics in a trapped-ion system driven by a laser

We show that, if one combines the Jaynes-Cummings and anti-Jaynes-Cummings dynamics in a trapped-ion system driven by a laser, additional series of collapses and revivals of the vibrational state of the ion can be generated.

Figure 1

Surface and contour plots of the $Q$ function at different times $t=t_1+t_2$, for a switch time equal to one-fourth of the revival time, i.e., $t_1=t_r∕4$. $t_2=$ (a) 0, (b) $t_r∕8$, (c) $t_r∕4$.

Figure 2

(a) Atomic population inversion $W=2P_e-1$, with $P_e=\mathrm{Tr}\left(\mid e⟩⟨e\mid \right)$, and (b) purity function, $\xi =1-\mathrm{Tr}\left\{{\rho }_v^2\right\}$, as a function of the scaled time $\eta \mathrm{\Omega }t$, with a switch time equal to one-fourth of the revival time, $t_1=t_r∕4$.

Figure 3

Surface and contour plots of the $Q$ function at different times $t=t_1+t_2$, for a switch time equal to one-half of the revival time, $t_1=t_r∕2$. $t_2=$ (a) 0, (b) $t_r∕4$, (c) $t_r∕2$.

Figure 4

(a) Atomic population inversion $W$ and (b) purity function $\xi$ as a function of the scaled time $\eta \mathrm{\Omega }t$, with a switch time equal to one-half of the collapse time, $t_1=t_r∕2$.