Enantiomer-specific state transfer of chiral molecules in cyclic three-level systems with SU(2) structures

We propose a streamlined method of fast enantiomer-specific state transfer (ESST) of chiral molecules in cyclic three-level systems. Such three-level enantiomers are chirality-dependent systems driven by one of the three Rabi frequencies differing with a sign for the left- and right-handed chiral molecules. When the Hamiltonian of the three-level chiral molecules possesses the specific SU(2) algebraic structure, the populations transferred to the two excited states are shown to be exchanged between the left- and right-handed chiral molecules if they are initially prepared in their ground states. By employing unitary SU(2) transformation and inversely engineering time-dependent Hamiltonians with designed Rabi frequencies, we can make the left- and right-handed chiral molecules evolve respectively to different excited states from their initial ground states simultaneously. Thus a fast ESST is achieved.

Figure 1

(a) Left- and (b) right-handed chiral molecules of cyclic three-level systems. Three electromagnetic fields couple, respectively, to the three electric-dipole transitions with ${\mathrm{\Omega }}_x$, $\pm {\mathrm{\Omega }}_y$, and ${\mathrm{\Omega }}_z{e}^{i\varphi }$ the corresponding Rabi frequencies.

Figure 2

(a) The designed Rabi frequencies $\mathrm{\Omega }$(red solid line) and ${\mathrm{\Omega }}_y$ (blue dashed line) in Eq. (29) with the conditions in Eq. (28). (b) The corresponding time evolution of the populations for the left- and right-handed chiral molecules: $P_1^L\left(t\right)=P_1^R\left(t\right)$ (red solid line), $P_2^L\left(t\right)=P_3^R\left(t\right)$ (blue dashed line), and $P_3^L\left(t\right)=P_2^R\left(t\right)$ (black dotted line). Here $\epsilon =0.04$. The initial states are $-{i|1\rangle }_{L,R}$.

Figure 3

(a) The designed Rabi frequencies $\mathrm{\Omega }$ (red solid line) and ${\mathrm{\Omega }}_y$ (blue dashed line) in Eq. (32) with the conditions (31). (b) The corresponding time evolution of the populations for the left- and right-handed chiral molecules: $P_1^L\left(t\right)=P_1^R\left(t\right)$ (red solid line), $P_2^L\left(t\right)=P_3^R\left(t\right)$ (blue dashed line), and $P_3^L\left(t\right)=P_2^R\left(t\right)$ (black dotted line). Here ${\epsilon }^{\prime }=0.04$. The initial states are $-{i|1\rangle }_{L,R}$.

Figure 4

(a) The maximum absolute value of the Rabi frequencies ${\mathrm{\Omega }}_{\max }$ vs the small value ${\epsilon }^{\prime }$ in protocol 2 with $\tau =0.5\mu \mathrm{s}$. (b) The corresponding populations of the target states at the final time vs the small value ${\epsilon }^{\prime }$. The initial states are $-{i|1\rangle }_{L,R}$.