Pump-probe approach to multiple scattering of intense laser light from cold atoms
Final Report Abstract
The key challenge of a theoretical treatment of multiple scattering of intense laser light in cold, dilute atomic clouds using traditional quantum optical methods is the exponential growth of the complexity of the problem with the number of atoms. Recently, to overcome this problem, we have put forward a novel pump-probe approach. Within the pump-probe approach, a multiple scattering signal is obtained from single-atom building blocks representing elastic and inelastic spectral responses of a single atom to a classical, polychromatic random probe field. The major goal of the present project was to further develop the pump-probe approach, and to apply it to describing coherent backscattering (CBS) of intense light from saturated atoms in the bulk medium. One of our main questions was how the quantum nature of the atomic scatterers manifests in the inelastic multiphoton scattering processes, and how internal degeneracy affects the interference effects giving rise to CBS. In the first part of the project, we have developed the pump-probe approach for two(three) twolevel (scalar) atoms, in which case the basic equation of our approach is the optical Bloch equation (OBE) under classical bi(tri)chromatic driving. We proposed a diagrammatic representation of the single-atom building blocks and formulated rules for the self-consistent combination thereof. Moreover, we have also found a physical interpretation of the single-atom responses in terms of effective nonlinear susceptibilities. Further on, we considered triple scattering and established the condition under which the analytical solutions of the three-atom master equation and of the pump-probe equations are equivalent. Finally, we derived general expressions for the building blocks corresponding to an arbitrary number of probe field components. In the second part of the project, we generalized our method to vector atoms with degenerate electronic levels. We showed that the diagrammatic representation of the single-atom building blocks retains the same structure as in the case of scalar atoms, only garnished by the field’s polarisation degree of freedom. The assessment of the building blocks in the vector case requires the solution of a generalized OBE, on a vector space with a dimension which reflects the internal atomic structure. We found that the ground state degeneracy leads to a reduced enhancement of CBS from saturated atoms. We also calculated a third-order scattering-induced correction to CBS from strontium atoms, leading to better agreement with the experiment than within a treatment based on double scattering alone. Finally, using the pump-probe approach we developed a multiple scattering theory of intense laser light in a bulk medium of two-level atoms. We derived the integral transport equations for the incoherent propagation of light in a slab geometry. The frequency-dependent integral kernels of these equations were obtained from solutions of a stochastic OBE under polychromatic driving. Our results prove the potential to overcome the problem of the exponential growth of Hilbert space, and to efficiently describe multiple inelastic scattering of intense light in clouds of cold atoms.
Publications
- Diagrammatic pump-probe approach to coherent backscattering of laser light by cold atoms: Double scattering revisited, J. Phys. B 45, 215501 (2012)
V. Shatokhin, T. Wellens, A. Buchleitner
- Rigorous derivation of the triple scattering signal from singleatom responses, Phys. Rev. A 86, 043808 (2012)
V. Shatokhin, T. Wellens
(See online at https://doi.org/10.1103/PhysRevA.86.043808)
