Creation of arbitrary coherent superposition states by stimulated Raman adiabatic passage

A technique for creation of well-defined preselected coherent superpositions of multiple quantum states is proposed. It is based on an extension of the technique of stimulated Raman adiabatic passage (STIRAP) to degenerate levels. As an example, the nine-state system composed of the magnetic sublevels of three levels with angular momenta $J_g=0$, $J_e=1$, and $J_f=2$ is studied in detail. Starting from the $\mid J_g=0,M_g=0⟩$ state, STIRAP can create an arbitrary preselected coherent superposition between the five $M_f$ sublevels $(M_f=-2,-1,0,+1,+2)$ of the $J_f=2$ level with 100% efficiency in the adiabatic limit. The populations and the phases of the $M_f$ states in this superposition are determined entirely by the polarizations of the two laser fields. It is shown that this technique allows one to create any superposition of the five $M_f$ states, that is, to reach any point in the Hilbert space of the $J_f=2$ manifold, and the corresponding recipes for choosing the laser polarizations are presented.

Figure 1

(Color online) The nine-state $\Lambda$ system. States with $J_g=0$ and $J_f=2$ are coupled through the states with $J_e=1$ by the pump (P) and Stokes (S) laser pulses with ${\sigma }^{\pm }$ and $\pi$ polarizations. The pulses are on two-photon resonance, but may be detuned from the $J_e=1$ states by a certain detuning $\Delta$. Only state ${\psi }_{0,0}$ is populated initially and the objective is to create an arbitrary coherent superposition of the five $J_f=2$ magnetic sublevels.

Figure 2

(Color online) Time evolution of the populations in the STIRAP process characterized by the parameters in the first line of Table . The target state is given by ${\Psi }_1$ in Eq. (31). The populations $P(2,M)$, $M=-2,\dots ,2$, all coincide.