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arXiv:1204.4972

Rayleigh scattering under light-atom coherent interaction

Akifumi Takamizawa, Kōichi Shimoda

Published Apr 23, 2012• 0 citations
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Abstract

Semi-classical calculation of an oscillating dipole induced in a two-level atom indicates that spherical radiation from the dipole under coherent interaction, i.e., Rayleigh scattering, has a power level comparable to that of spontaneous emission resulting from an incoherent process. Whereas spontaneous emission is nearly isotropic and has random polarization generally, Rayleigh scattering is strongly anisotropic and polarized in association with incident light. In the case where Rabi frequency is much larger than frequency detuning and spontaneous emission rate, while the power of spontaneous emission varies with time at the Rabi frequency, the power of Rayleigh scattering oscillates at twice the Rabi frequency. Moreover, the radiation pressure force acting on an atom due to Rayleigh scattering exceeds that caused by spontaneous emission when frequency detuning is large.

DOI
10.48550/arxiv.1204.4972

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Semi-classical calculation of an oscillating dipole induced in a two-level atom indicates that spherical radiation from the dipole under coherent interaction, i.e., Rayleigh scattering, has a power level comparable to that of spontaneous emission resulting from an incoherent process. Whereas spontaneous emission is nearly isotropic and has random polarization generally, Rayleigh scattering is strongly anisotropic and polarized in association with incident light. In the case where Rabi frequency is much larger than frequency detuning and spontaneous emission rate, while the power of spontaneous emission varies with time at the Rabi frequency, the power of Rayleigh scattering oscillates at twice the Rabi frequency. Moreover, the radiation pressure force acting on an atom due to Rayleigh scattering exceeds that caused by spontaneous emission when frequency detuning is large.
Variations in the spatial intensity distribution of light caused by coherent interaction with two-level atoms are determined by semi-classically calculating a term for interference between incident light and spherical radiation from the atom. The interference term is divided into two components: one oscillates at the Rabi frequency corresponding to absorption and stimulated emission, and the other contributes to dispersion. The spatial distribution of both components involves alternation of constructive and destructive parts in the form of parabolic surfaces where light energy flows. Although the time average over the Rabi oscillation of the former component vanishes at every position, that of the latter remains. The light-related reaction of a dipole force acting on an atom is considered to appear in the non-vanishing latter component.
In order to investigate the effect of perturbation caused by the interaction of a two-level atom with its environment on the coherency of light scattered by the atom when it is irradiated by an intense radiation, Mollow's theory is generalized to include a random modulation of the resonance frequency as well as fluctuations of the incident field. Expressions for the power spectrum, the total intensity, the coherent scattering intensity and the broad Rayleigh scattering intensity are derived. Some general aspects of the problem are discussed.
When two-level atoms interact with laser light which is fully amplitude modulated at frequency omega , it is found that if omega is a particular fraction of the Rabi frequency then the coherence associated with the density matrix element rho 12 , or dipole, can be suppressed, along with the modulation in the inversion, provided omega also greatly exceeds the longitudinal decay rate Gamma . Increasing Gamma , by random collisions for example, induces a non-zero oscillating dipole and a modulation of the inversion, the enhancements of which are directly proportional to Gamma , giving an example of a coherent effect produced by an incoherent perturbation of a random nature.
We investigate the photon statistics of an ensemble of coherently driven non-interacting two-level atoms in the weak driving regime. As it turns out, the system displays unique emission characteristics that are strongly in contrast to the emission of classical oscillating dipoles. By deriving the second-order autocorrelation function, we show that extraordinary two-photon correlations are obtained, ranging from strong antibunching to superbunching. These features are enhanced by disorder in the emitter positions, and the control parameter is the number of excitations in the system. We observe the appearance of bunching and antibunching when the light is scattered by the atoms predominantly coherently, i.e., mimicking classical Rayleigh scattering, whereas thermal photon statistics is obtained when the light is scattered via spontaneous decay, a well-known quantum effect. The underlying mechanism is the interplay between coherent scattering, which exhibits spatial fluctuations due to interference, and dissipation in the form of isotropic spontaneous decay.
Our theoretical model of forced dipole oscillation demonstrates that when the amplitude of the forcing field is changing fast, the oscillations of the bound electron in the atom or molecule initially proceed at two frequencies: the frequency of the natural electron oscillations and the frequency of the forcing field. Particularly, applied to the science of scattering, this model of transient forced atomic and molecular oscillations suggests that accurate interpretation of the laser scattering experiments using short laser pulses must include both the conventionally known scattering at the laser frequency (Rayleigh) and the predicted by our theoretical spectral emission that corresponds to the natural frequency of the electronic oscillations. This article presents the results of numerical simulations using our model performed for the hydrogen atom. The characteristics of the components of scattered radiation, their polarization, and Doppler thermal broadening are discussed.