Weak localization of light by cold atoms: The impact of quantum internal structure

Abstract

Since the work of Anderson on localization, interference effects for the propagation of a wave in the presence of disorder have been extensively studied, as exemplified in coherent backscattering (CBS) of light. In the multiple scattering of light by a disordered sample of thermal atoms, interference effects are usually washed out by the fast atomic motion. This is no longer true for cold atoms where CBS has recently been observed. However, the internal structure of the atoms strongly influences the interference properties. In this paper, we consider light scattering by an atomic dipole transition with arbitrary degeneracy and study its impact on coherent backscattering. We show that the interference contrast is strongly reduced. Assuming a uniform statistical distribution over internal degrees of freedom, we compute analytically the single and double scattering contributions to the intensity in the weak localization regime. The so-called ladder and crossed diagrams are generalized to the case of atoms and permit to calculate enhancement factors and backscattering intensity profiles for polarized light and any closed atomic dipole transition.

Spectrum of coherently backscattered light from two atoms

“…A much weaker sensitivity of the quality of the CBS signal was observed for Rb atoms [9]. In this latter case, inelastic processes occur on degenerate transitions [10,11,12,13,14], while Sr atoms offer dipole transitions with a nondegenerate ground state [15].…”

Double scattering of intense laser light by two atoms

“…While a thorough theory of CBS of light from degenerate atoms in the regime of elastic scattering already exists [11,12], a theory of CBS from saturated atoms is still in a rudimentary state, several years after the "saturation" experiments with strontium [10] and rubidium [13] atoms. The main obstacle for developing such a theory is that CBS becomes a multi-wave interference effect in the nonlinear scattering regime [14,15], with more than two interfering amplitudes.…”

Multiple scattering of photons by atomic hyperfine multiplets

“…In units where = c = 1, the energy or angular frequency of this state is ω = k. The scattering of these one-photon states by atomic dipole transitions will be described following the lines of [14,15] while generalizing to multilevel transitions.…”

“…Previous analytical studies of the CBS double scattering contribution from an infinite atomic medium [14] as well as the case of multiple scattering inside an infinite medium [15] treated an arbitrary single, isolated, degenerate atomic dipole transition. This description is a priori accurate if the hyperfine optical resonance under consideration is sufficiently far away from neighboring transitions and if the laser detuning is sufficiently small.…”

“…In general, however, photons probe dipole transitions with rather high Zeeman degeneracy due to large total angular momentum. It was shown theoretically that an average over all possible angular momentum orientations then leads to an antisymmetric component of the atomic scattering tensor which reduces the interference contrast of coherent backscattering considerably [13,14]. Indeed, in the absence of an external magnetic field, photons are scattered elastically by freely orientable atomic dipoles just like electrons propagating in a sample of magnetic impurities (spin-flip scattering), and in this case interference corrections to the diffusive transport picture are cut off very efficiently [15].…”