Resonant atomic factors: multipole expansion

The resonant interaction of optical radiation with atomic vapors can excite the atoms into anisotropic states with long lifetimes. The conventional description of these states uses an expansion in a basis of multipole moments, which are represented by irreducible tensor operators. We demonstrate an experimental method that permits the excitation of these atomic multipole moments in specific, experimentally controllable spatial orientations. Complementary optical methods permit the observation of multipole moments of arbitrary order and a direct measurement of their spatial orientation. We demonstrate these procedures in the ground state of atomic sodium, using optical pumping to polarize the angular-momentum substates. We show how the experimental results can be used to separate signal contributions that originate from different multipole moments.The resonant interaction of optical radiation with atomic vapors can excite the atoms into anisotropic states with long lifetimes. The conventional description of these states uses an expansion in a basis of multipole moments, which are represented by irreducible tensor operators. We demonstrate an experimental method that permits the excitation of these atomic multipole moments in specific, experimentally controllable spatial orientations. Complementary optical methods permit the observation of multipole moments of arbitrary order and a direct measurement of their spatial orientation. We demonstrate these procedures in the ground state of atomic sodium, using optical pumping to polarize the angular-momentum substates. We show how the experimental results can be used to separate signal contributions that originate from different multipole moments.

Journal of the Optical Society of America BJan 1, 19947 citations

Atomic Multipoles

W. E. Baylis

Springer handbooksJan 1, 20230 citations

Atomic Multipoles

W. E. Baylis

Springer handbooksJan 1, 20060 citations

Multipole analysis of radio-frequency reactions in ultracold atoms

Betzalel Bazak, Evgeny Z. Liverts, Nir Barnea

Using the multipole expansion, we analyze photoinduced reactions in an ultracold atomic gas composed of identical neutral bosons. While the Franck-Condon factor dominates the photoinduced spin-flip reactions, we have found that for a frozen-spin process in which the atomic spins are conserved, the reaction rate is governed by the monopole ${r}^{2}$ and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number $k$ acquires an extra ${k}^{4}$ factor in comparison to the spin-flip process. Comparing the relative strength of the ${r}^{2}$ and quadrupole modes in dimer photoassociation, we predict that the mutual importance of these two modes changes with temperature and scattering length.Using the multipole expansion, we analyze photoinduced reactions in an ultracold atomic gas composed of identical neutral bosons. While the Franck-Condon factor dominates the photoinduced spin-flip reactions, we have found that for a frozen-spin process in which the atomic spins are conserved, the reaction rate is governed by the monopole ${r}^{2}$ and the quadrupole terms. Consequently, the dependence of the frozen-spin reaction rate on the photon wave number $k$ acquires an extra ${k}^{4}$ factor in comparison to the spin-flip process. Comparing the relative strength of the ${r}^{2}$ and quadrupole modes in dimer photoassociation, we predict that the mutual importance of these two modes changes with temperature and scattering length.

arXiv:1207.5936Physical Review AOct 10, 20126 citations