Locally designed pulse shaping for selective preparation of enantiomers from their racemate

Abstract

We present a method for the design of laser fields to control a selective preparation of enantiomers from their racemate. An expression for two components of the laser pulses [EX(t) and EY(t)] propagating along the Z axis is derived using a locally optimized control theory in the density operator formalism. This expression was applied to a selective preparation of (R-, L-) enantiomers from preoriented phosphinotioic acid (H2POSH) at low temperatures. The target operator was set for the populations to be localized in one side of the double-well potential. First, a simple one-dimensional model was treated. Then, a two-dimensional model in which a free rotation around the preoriented torsional axis is included was briefly considered. In the one-dimensional model, almost complete preparation of the enantiomers was obtained. The optimal electric field consists of a sequence of two linearly polarized pulses with the same phases but with different magnitudes. This means that the resultant electric field is linearly polarized with the polarization for obtaining the R-form nearly parallel to its S–H bond. The optimal electric field transfers the L-form into the R-form while suppressing the reverse process. In the two-dimensional model, the enantiomer selective preparation is controlled by a sequence of circularly polarized pulses.