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Physical Review A

Resonant Interaction between Two Neutral Atoms

C. S. Chang, P. Stehle

Published Aug 1, 1971• 33 citations
Publisher

Abstract

A standard formalism of quantum electrodynamics is used to investigate the interaction between two neutral atoms. The study is based on an approximate solution of the two-particle Green's function. The frequency distribution of the photon scattering is obtained. We also consider the self-stimulation effect when both atoms are in excited states.

DOI
10.1103/physreva.4.630

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A standard formalism of quantum electrodynamics is used to investigate the interaction between two neutral atoms. The study is based on an approximate solution of the two-particle Green's function. The frequency distribution of the photon scattering is obtained. We also consider the self-stimulation effect when both atoms are in excited states.
The Green's function method is applied to investigate the magnetic spin resonance spectra of three-dimensional and two-dimensional spin-polarized quantum gases. The Hartree-Fock approximation is employed to calculate the one-particle Green's function of the atoms, then this one-particle Green's function is used for the calculation of the vertex part of the Green's function. Such a combination yields a self-consistent result. The absorption spectra are obtained from the calculation of the susceptibility in terms of the two-particle Green's function (bubble diagram). Some general expressions for the dispersion relation, for the effective mass of a spin wave, and for the dipolar frequency shift are given in the calculation. In order to estimate the shift of the electron-spin-resonance (ESR) frequency, the effective dipole-dipole interactions among the hydrogen atoms are included in the calculation. These effective interactions are deduced from the ladder approximation, and hence are characterized by the scattering amplitude. The scattering amplitude is calculated numerically. The result shows that the theoretical value of the shift is smaller than the experimentally observed value by about 35%.
Spontaneous-radiation processes associated with a number of multiatom systems are studied. Green's-function techniques are used in conjunction with a model of NNN two-level atoms interacting with a quantized radiation field to investigate the assumption of the independence of the spontaneous-radiation properties of a given atom from the states of the other atoms in the system. It is shown that the natural linewidth of an excited atom in the presence of a deexcited atom is different from that of an isolated excited atom. For interatomic separations smaller than a critical separation, the two-atom system is best considered as a collective unit with regard to its spontaneous-radiation properties. The influence of these "radiative cooperative effects" is studied also for the systems of two initially excited atoms. Also the influence of radiative cooperative effects in the scattering of a photon by a system of two deexcited atoms is studied. It is shown that the frequency distribution of the scattered radiation exhibits a double-peak structure for interatomic separations smaller than $\frac{3}{4}\ensuremath{\lambda}$. The techniques of Green's functions are then applied to the study of radiative cooperative effects in several many-atom systems. It is shown that within the context of the model certain information is obtained exactly via the Green's-function techniques as applied to the manyatom problems of a single excited atom in the presence of $N\ensuremath{\gg}1$ deexcited atoms and the scattering of a photon by a system of $N\ensuremath{\gg}1$ deexcited atoms. The necessity of treating manyatom systems from a "collective" point of view is easily seen from our results.
We have considered the excitation spectra arising from stimulated two-photon transitions between two atomic levels of the same parity. The system consists of a three-level atom in the cascade configuration interacting with two strong electromagnetic fields whose initially populated modes ωa and ωb are in resonance with the two atomic transition frequencies, respectively. The Green function formalism is used to calculate the spectral function of the system near the frequencies ω=ωa+ωb, in the limit of high photon densities. The excitation spectra consist of Lorentzian lines peaked at the frequencies ω−ωa−ωb=0, ±Ωa/√2, ±Ωb/√2, ±Ω, and ±2Ω, where Ω2=(Ω2a+Ω2b)/2 and Ωa,Ωb are the Rabi frequencies of the two laser fields, respectively. Numerical calculations for selected values of the Rabi frequencies are graphically presented and discussed. The computed two-photon spectra are compared with those arising from the third-order nonlinear mixing of frequencies near ω=ωa+2ωb and ωb+2ωa, respectively, as well as with those of the stimulated Raman spectra near ω=±(ωa−ωb).