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Journal of the Optical Society of America A

Light scattering from a moving atom

Wei Guo

Published Nov 21, 2012• 2 citations
Publisher

Abstract

In this work, scattering of an incident electric field from a moving atom is reexamined classically in two steps: the time-dependent current density created by the field inside the atom is first calculated under the electric-dipole approximation, and is then used to calculate the field scattered from the atom. Unlike the conventional frame-hopping method, the present method does not need to treat the Doppler effect as an effect separated from the scattering process, and it derives instead of simply uses the Doppler effect.

DOI
10.1364/josaa.29.002576

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The power spectrum of the light scattered by a three-level atom driven near resonance between the ground state (|1>) and the second excited state (|3>) by a monochromatic classical electric field is evaluated following the method developed by B. R. Mollow. The incident field is assumed to interact with the dipole moment between the states |1> and |3>, while the emitted light is assumed to interact with that between the state |3> and the first excited state |2> of the atom. The atom is assumed to relax to equilibrium only via radiation damping for the sake of simplicity. The power spectrum of the scattered field is explicitly calculated from the two-time atomic dipole moment correlation function, which is evaluated on a Markoff-type assumption, and various limiting cases are discussed. In Appendix the case is considered in which radiative damping between the higher excited state and the ground state is also present.

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In this work, scattering of an incident electric field from a moving atom is reexamined classically in two steps: the time-dependent current density created by the field inside the atom is first calculated under the electric-dipole approximation, and is then used to calculate the field scattered from the atom. Unlike the conventional frame-hopping method, the present method does not need to treat the Doppler effect as an effect separated from the scattering process, and it derives instead of simply uses the Doppler effect.
The power spectrum of the light scattered by a two-level atom driven near resonance by a monochromatic classical electric field is evaluated. The atom is assumed to relax to equilibrium with the driving field via radiation damping, which is treated by explicitly coupling the atom to the quantized electromagnetic field modes. The power spectrum of the scattered field is directly obtainable from the two-time atomic dipole moment correlation function, which is evaluated by a method based on a Markoff-type assumption analogous to that used to evaluate the time evolution of single-time atomic expectation values.
This thesis concerns the theoretical investigation of interference phenomena related to elastic and inelastic scattering of quantized light. The presented work is naturally divided into two parts, the first is concerning elastic scattering while the second explores inelastic scattering. In the first part we use a scattering-matrix formalism combined with results from random-matrix theory to investigate the interference of quantum optical states on a multiple scattering medium. We investigate a single realization of a scattering medium thereby showing that it is possible to create entangled states by interference of squeezed beams. Mixing photon states on the single realization also shows that quantum interference naturally arises by interfering quantum states. We further investigate the ensemble averaged transmission properties of the quantized light and see that the induced quantum interference survives even after disorder averaging. The quantum interference manifests itself through increased photon correlations. Furthermore, the theoretical description of a measurement procedure is presented. In this work we relate the noise power spectrum of the total transmitted or reflected light to the photon correlations after ensemble averaging. This analysis enables us to describe an experimental observation of the quantum nature of light that survives the averaging over disorder. In the second part we investigate inelastic scattering. This we do by first treating the scattering of light on dipoles embedded in an arbitrary dielectric environment. By considering the two different models for dipole interaction known as the minimal-coupling and electric-dipole interaction Hamiltonians, we find exact relations between the electric field and the dipole operators in the Heisenberg picture, while keeping the model of the dipoles arbitrary. Due to the exact treatment of the electric-field operators, we obtain kernels known from classical scattering theory to describe the propagation of the field from the dipoles. Using the found electric field operators we derive the Heisenberg equations of motion for the dipoles while treating them as quantum two-level systems and using the Born–Markov and rotating-wave approximations. Postponing the rotating-wave approximation to the very end of the formal calculations allows us to identify the different physical parameters of the dipole evolution in terms of physical quantities known from optics. Finally, we use our Heisenberg picture formalism to treat a dilute cloud of two-level atoms, by simplifying the equations of motion using a single-scattering approximation for the interaction between the atoms. This enables us to derive expressions for the steady-state population and fluorescence spectrum, where we find cooperative effects in both the elastic and the inelastic spectra.
The power spectrum of the light scattered by a three-level atom driven near resonance between the ground state (|1>) and the second excited state (|3>) by a monochromatic classical electric field is evaluated following the method developed by B. R. Mollow. The incident field is assumed to interact with the dipole moment between the states |1> and |3>, while the emitted light is assumed to interact with that between the state |3> and the first excited state |2> of the atom. The atom is assumed to relax to equilibrium only via radiation damping for the sake of simplicity. The power spectrum of the scattered field is explicitly calculated from the two-time atomic dipole moment correlation function, which is evaluated on a Markoff-type assumption, and various limiting cases are discussed. In Appendix the case is considered in which radiative damping between the higher excited state and the ground state is also present.