Fig. 3: Control fields for complete controllability.
From: Full quantum control of enantiomer-selective state transfer in chiral molecules despite degeneracy
Choice of four, respectively five, microwave fields, which are sufficient to ensure evolution operator-controllability (a) and enantio-selective evolution operator-controllability (b) in the rotational subsystem consisting of the asymmetric top states \(\left|J=0,\tau =0,M=0\right\rangle\), \(\left|J=1,\tau =0,M\right\rangle\). and \(\left|J=1,\tau =1,M\right\rangle\), with quantum numbers J, τ, and M. The orange and pink lines in a indicate the four fields which yield complete controllability of this subsystem for a single enantiomer. The polarization of the fields is denoted by x, y, and z, and μa, μb, and μc are the Cartesian components of the dipole moment responsible for the transitions indicated by the vertical bars. The additional field which is required for enantio-selective control is indicated in b by turquoise lines. The frequencies ω1, ω2, and ω3 of propanediol are given in Table 1.
