Antisymmetric polarizabilities of rotational sublevels for linear molecules with a non-degenerate ground electronic state

Abstract

Using the semiclassical perturbation theory, we study the antisymmetric polarizabilities of rotational sublevels, the M-dependent splittings and shifts of the sublevels and corresponding rotational spectral lines of a linear molecule induced by a right (+) or left (−) circularly polarized resonant optical field. The deduced theoretical formulas for these quantities indicate that for rotational sublevels M of linear molecules with a non-degenerate ground electronic state, the antisymmetric polarizabilities induced by a resonant polarized optical fields exist and are the same order of magnitude of the symmetric ones. Based on them, M-dependent (both size and sign of M) splitting and shifts of the sublevels and corresponding spectral lines can be produced and the degeneracy for +M and −M sublevels can be completely broken by the circularly polarized resonant optical field. As examples, we have calculated these quantities for H2 and CO molecules. For H2 molecule, the antisymmetric and symmetric polarizabilities of the rotational magnetic sublevels in the ground electronic state X1Σg+(v=0,J=1,M), which are induced by a optical field with frequency v0 resonant with the transition X1Σ+g(v=0,J=1)→B1Σu+(v′=0,J′=2), are the same order of 10 a.u.; and laser-induced M-dependent splittings and shifts for M=1,0,−1 sublevels and the corresponding resonant Rayleigh scattering lines X1Σg+(v=0,J=1,M)↔B1Σu+(v′=0,J′=2,M′) can be the order of 0.1–1 GHz when the intensity of circularly polarized optical field is 100 MW cm−2. Similarly the antisymmetric polarizabilities of CO molecule in the rotational magnetic sublevels X1Σ+(v=0,J=1,M=1) using IR field with the frequency v0 resonant with the transition X1Σ+(v=0,J=1)→X1Σ+(v′=1,J′=2) are the same order (10 a.u.) of the symmetric ones.