Evolution of polarization in an atomic vapour with negative refractive index

A three-level Lambda-configuration atomic vapour may exhibit simultaneously negative permittivity and permeability in the optical frequency band, and an isotropic left-handed vapour medium could therefore be realized within the framework of quantum optics. One of the most remarkable features of the present scheme is that both the refractive index and the photon helicity reversal inside the vapour can be controllably manipulated by an external coupling light field. The phenomenological Hamiltonian that describes the process of helicity reversal is constructed and the time-dependent Schroedinger equation governing the time evolution of the polarization states of the lightwave is solved by means of the Lewis-Riesenfeld invariant theory. The transition between the polarization states (and hence the accompanied photon helicity reversal), which is exactly analogous to the transition operation between bits in digital circuit, may be valuable for the development of new techniques in quantum optics and would have potential applications in information technology