Laser distillation

In Section 8.3, we introduce a coherent control scheme for enhancing the fraction of one desired enantiomer, given a racemic mixture of molecules. This scheme, called laser distillation, is of great practical interest because the effect obtained is substantial, even in the presence of decoherence. An alternative scheme, due to Fujimura and co-workers [263, 264] is also briefly described. 

Fig. 8.1 Laser distillation control scenario discussed in detail in Section 8.3. Two ljtsfi with pulse envelopes ,(0 and e2(0 couple, by virtue of the dipole operator, the states and L enantiomers to two vibrotational states 1) and 2) (denoted If ,) and E2) in the.t i the excited electronic manifold. A third laser pulse with envelope r.0(i) couples the ex E)) and E2) states to one another. The system is allowed to absorb a photon and relax hack the ground state. After many such excitation-relaxation cycles, a significant cnantionneh excess is obtained, as explained in Section 8.3. ...

The essence of the laser distillation process lies in choosing the laser of central frequency ay so that it excites the system to a state IF,). which is symmetric with. respect to the reflection operation nh, and to a state E2), which is antisymmetric with.) respect to ah and coupling these states with an additional co0 laser. By contrast, IEq) and EL) do not share these symmetries but are related to one another through, reflection [i.e., ah Eu) — L), ah EL) = D) whereas ah Ex) = IE,), ah E2) =(... 

Ig jEig. 8.7 Results for laser distillation after a convergent series of steps comprised of radiative I excitation, and collisional and radiative relaxation. Shown are the results at three different field, strengths j = e2 = o = c. 

In order to avoid the need to cycle repeatedly the excitation-relaxation process, we present in Sec. VII an alternative approach to the laser distillation scheme of Sec. IV in which one can affect enantioselectivity of the sample by a single laser pulse. The method exploits the coexistence, owing to the lack of an inversion center, of one- and two-photon transitions between the same chiral... 

The procedure that we propose in order to enhance the concentration of a particular enantiomer when starting with a racemic mixture, i.e., to "purify the mixture, is as follows. The statistical (racemic) mixture of L and D is irradiated with a specific sequence of three coherent laser pulses, as described below. These pulses excite a coherent superposition of symmetric and antisymmetric vibrational states of G. After each pulse the excited system is allowed to relax back to the ground electronic state by spontaneous emission or any other nonradiative process. By allowing the system to go through many irradiation and relaxation cycles, we show below that the concentration of the selected enantiomer L or D can be enhanced, depending on the laser characteristics. We call this scenario laser distillation of chiral enantiomers. 

To outline the computation associated with laser distillation we describe, for notational simplicity, the case where there is no p degeneracy (e.g., the asymmetric top). Computations below are, however, for the symmetric top, where the p degeneracy is added as noted later below. Consider the system initiated in a racemic mixture of L, M)s and D, M) of fixed 7. Here we have explicitly indicated the M quantum number of the ground state. In the first step, the system is excited with a laser pulse sequence as described above. In the second step, the system collisionally and radiatively relaxes so that all the population returns to the ground state to produce an incoherent mixture of L, M)s and Z), M)s. This pair of steps is then repeated until the populations of L, M) and D, M) reach convergence. 

Enantiomeric control is more difficult if the excited molecular potential energy surfaces do not possess an appropriate minimum at the o hyperplane configurations (see Figs. 1 and 2). In this case the method introduced in this section is not applicable. One may however be able to apply the laser distillation procedure by adding a molecule B to the initial L, D mixture to form weakly bound L — B and B - D, which are themselves right- and left-handed enantiomeric pairs [83]. The molecule B is chosen so that electronic excitation of B — D and L — B forms an excited species G, which has stationary rovibrational states that are either symmetric or antisymmetric with respect to reflection through t7>,. The species L - B and B - D now serve as the L and D enantiomers in the general scenario above, and the laser distillation procedure described above then applies. Further, the molecule B serves as a catalyst that may be removed from the final product by traditional chemical means. 

Rather than going through many excitation-relaxation cycles as in the laser distillation scenario, described in Sec. IV, it is possible to affect the enantio-selectivity... 

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