We show that the weak electric field optical activity of a molecule in a complex superposition of mirror image amplitudes need not vanish. In addition, we show that the optical activity is a direct measure of left-right coherence.
Recently we investigated molecules in superpositions of localized chiral states which can be written in the form [ll,
I~)=C,IL)+eiT,JR).
(1) 1 L) and 1 R) are real, mirror images of one another, and C,_ and C, are also real. When tunnelling may be ignored instantaneously and I L) and I R) are the lowest energy vibronic states, we showed that pairs of phaselocked pulses could both prepare 1 y) and measure its left-right coherence. We termed the measurement process parity-insensitive in that parity did not directly enter into the measurement process.
In a companion work we proved for a homogenous, isotropic ensemble of noninteracting molecules, no paritysensitive experiment could measure the left-right coherence of states such as 1 y) if sin v)= 0 [ 21. A paritysensitive experiment is one in which the operator representing the experiment is odd under parity. Optical activity is the ur parity-sensitive experiment. However, because it is unable to detect left-right coherence, we suggested a set of simple polarized light scattering experiments which obtained the coherence.
In this note we resurrect the simplest of all parity-sensitive experiments when an external field is present, namely linear electric field optical activity. We prove that electric field optical activity can provide an all-ornone measure of chiral coherence in states such as I v) .
It is well known that, unlike the Faraday effect, optical activity in a weak, static homogeneous electric field is zero [ 3-61. The assumption is that the state being measured is real. Here we consider the possibility of complex states.
As is regularly done, we approach the optical activity through the forward scattering amplitude [ 3 I. In the long wavelength limit the amplitude is
where Q is the polarization of the radiation, a and b are molecular quantities, and E is the field. From overall conservation of parity we have a=ap,