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Canadian Journal of Physics

The effect of collisions on the coherent scattering from strongly driven two level atoms

Haider R. Zaidi, M. P. Chaubey

Published Aug 1, 1981• 0 citations
Publisher

Abstract

The existence of a coherent mode in phase with the near resonant driving field is reconsidered using the resolvent operator technique in Liouville space. A result, previously obtained from Green function technique, is rederived. It is shown that such a mode does not exist in the general case of collisional relaxation in a gas. As a result, the coherent scattering component acquires a nonzero width in the strong field region. This width depends on some non-Markovian collision parameters.

DOI
10.1139/p81-130

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The existence of a coherent mode in phase with the near resonant driving field is reconsidered using the resolvent operator technique in Liouville space. A result, previously obtained from Green function technique, is rederived. It is shown that such a mode does not exist in the general case of collisional relaxation in a gas. As a result, the coherent scattering component acquires a nonzero width in the strong field region. This width depends on some non-Markovian collision parameters.
A theory of resonant light scattering from two level atoms in a gas is developed for an arbitrarily strong pump field. The Doppler effect and two body foreign gas collisions are considered. Elastic, inelastic (upward and downward), and the velocity changing collisions are retained in the general formulation. The impact approximation is not made, and the expressions for all (field dependent) collision rates are generated internally. Particular attention is paid to the lower state interaction, and a more complete parameterization of the theory is achieved. The general theory is non-Markovian and the quantum regression theorem is not used; it reduces to existing theories in special cases. It is shown that the coherent scattering is not a general property of the system if the lower state interaction is present; the "coherent" component acquires a small, but nonzero, width in the strong field region. This width could provide information about some new collision parameters.
Using a diagram technique, the equations of motion for the density matrix and the field inside the medium are derived for a system of driven two-level atoms. It is pointed out that these equations do not necessarily imply that the local driving field is perfectly coherent even if the external field is. In fact, by calculating the emission spectrum, it is shown that the coherent-scattering component acquires a small nonzero width in the strong-field region. It is concluded that the local driving field is only quasi-coherent. The physical origin of this effect lies in the peculiar nature of resonant interaction between two atoms. The results are compared with the previously obtained results for the foreign gas broadening type of collisions. It is found that there are qualitative as well as quantitative differences between the two results.
Resonant scattering (redistribution) of weak monochromatic light by atoms in the presence of collisions has been considered by Omont et al., who allowed for the broadening of both upper and lower levels of the transition. Mollow (who also has considered this problem for intense radiation) has shown that their results are applicable only if collisional repopulation of the levels (in contrast to collisional depopulation) is ignored. We here consider in detail the effect of repopulation. It leads, in the weak-field limit, to a true-coherent component ($\ensuremath{\delta}$-function spectrum) at the driving frequency, as well as a component at this frequency whose width is essentially the inelastic collisional rate of the lower state. An additional redistributed component due to repopulation of the upper level is also obtained.
A set of coupled non-Markovian equations of motion is derived for the Green's function of a driven two-level atom. These equations can be expressed in terms of the density-matrix elements only in the Markovian limit, in which case the set reduces to optical Bloch equations. The non-Markovian effect arises from correlations between successive photon emissions, an effect which is neglected in the existing equations of motion. The resulting correction is of the order of ${\ensuremath{\gamma}}_{0}$/${\ensuremath{\Omega}}_{0}$ in the strong-field region (${\ensuremath{\gamma}}_{0}$${\ensuremath{\Omega}}_{0}$) and it vanishes in the weak-field region, where ${\ensuremath{\gamma}}_{0}$ is the Einstein A coefficient and ${\ensuremath{\Omega}}_{0}$ is the Rabi frequency.
The response of a collision-broadened gas sample to driving coherent radiation is studied theoretically, taking into account effects of coherent excitations of two or more atoms (or molecules). In analogy to the Bloch-type master equation for one-atom coherences, describing the motion of a single atom "dressed" by the relevant (incident and detected) field modes, a master equation is derived for two-atom coherences, including an effective interaction of the Bethe-Salpeter---type, accounting for the mutual interaction of the coherently driven pair. The master equation includes also all symmetrization effects owing to resonance exchange between identical atoms, and is limited to nonreactive gas atoms (or molecules) undergoing binary collisions, including otherwise all (internal and translational) relaxation effects. The self-energy kernels are expressed in a nonperturbative fashion, in terms of binary-collision scattering amplitudes, and include renormalization effects due to coincidence of radiative couplings with the collisions (optical and radiative collisions). The concept of two-atom coherences is generalized to higher coherence ranks by constructing a hierarchy of master equations, including vertex operators that upgrade or downgrade the coherence rank, as a prelude to a diagrammatic method for calculating continuous-wave spectra. This hierarchy is compared with prevalent Agarwal-type master equations, based on the Dicke pseudospin method, and used in the study of two-level atoms.