Nuclear-state population transfer by a train of coincident pulses

Population transfer of three-level $\mathrm{\Lambda }$-like nuclei interacting with x-ray free electron lasers (XFEL) via a train of coincident pulses has been investigated theoretically. This study uses copropagating beams in which the frequency of the pump laser is different from that of the Stokes laser. We calculate the required laser intensities for each step which satisfy the condition of coincident-pulse technique in different nuclei. By employing the master equation and considering the effect of spontaneous emission, we show that complete nuclear population transfer occurs by choosing the appropriate number of pulse pairs. It is shown that the effect of laser intensity fluctuation is suppressed by increasing the number of pulse pairs. In this scheme, after each step, the populations of system are in stable states and the time delays between the neighboring pulses do not affect the transmission efficiency.

Figure 1

Linkage pattern of a three-level $\mathrm{\Lambda }$-like system. All initial population is in state $|1\rangle$.

Figure 2

Two-color scheme (copropagating beams) in the laboratory frame. The frequency of pump laser is different from that of the Stokes laser. The nuclear beam is accelerated such that $\gamma (1+\beta ){\omega }_{P\left(S\right)}=c{k}_{31\left(2\right)}$ is fulfilled.

Figure 3

Rabi frequencies in nuclear rest frame (a) and density matrix elements (b) vs time for ${}^{97}\mathrm{Tc}$ using SXFEL parameters in master equation (12). As can be seen, complete population transfer occurs using one step of coincident pulses. See Tables 2, 3, 4 for numerical parameters.

Figure 4

Rabi frequencies in nuclear rest frame (a) and density matrix elements (b) vs time for ${}^{154}\mathrm{Gd}$ by using SXFEL parameters in master equation (12). As can be seen, complete population transfer occurs by using five steps of coincident pulses. See Tables 2, 3, 4 for numerical parameters.

Figure 5

Contour plot of the final population of state $|2\rangle$ as a function of $I_p^{\text{eff}}/{sin}^2{\phi }_k$ and $I_S^{\text{eff}}/{cos}^2{\phi }_k$ for $N=2,5,10,$ a sequence of pulse pairs which is implemented in ${}^{97}\mathrm{Tc}$ by using XFELO laser parameters.