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Physical Review A

Effect of short-range Coulomb interaction on cooperative spontaneous emission

Brian J. Coffey, Richard M. Friedberg

Published Mar 1, 1978• 70 citations
Publisher

Abstract

We follow in detail the spontaneous decay of fully excited samples of two and three resonant two-level atoms separated by distances much smaller than a wavelength. We include both the static dipole-dipole interaction and an in rinsic detuning (inhomogeneous broadening) of the atoms. We find that the Coulomb interaction may have both a decohering and a recohering effect. The decohering effect is seen in three atoms not equivalently placed. Here the Coulomb interaction diminishes super-radiance by subjecting the different atoms to different frequency shifts. The recohering effect is seen in all cases and consists in a protection of super-radiance against an inhomogeneous broadening far in excess of the inverse radiation time. Both effects have analogs in small many-atom samples studied in previous literature.

DOI
10.1103/physreva.17.1033

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For pt.II see ibid., vol.19, p.2109 (1986). This paper is the third in a theoretical study of subradiance, i.e. the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. The paper is devoted to the problem of the cooperative spontaneous emission of atomic samples with linear dimensions much smaller than the wavelength of the emitted light. The treatment, which is based on a fully quantum mechanical description of the problem, corroborates the results obtained in a semiclassical treatment by Friedberg and Hartmann (1974). Starting from a master equation describing both the cooperative spontaneous emission and the dipole-dipole interaction, a statistical treatment of the latter is introduced and the corresponding symmetry relaxation is studied. The evolution of the atoms is described in three typical cases that correspond to different sample geometries and/or atomic distributions. In one of these cases, in particular, the symmetry is first conserved and the atoms follow Dicke's predictions for a time. A 'retarded' symmetry breaking then occurs suddenly, near the zero value of the collective energy, as in Friedberg and Hartmann's calculations for a small sphere. With regard to the further evolution of the atoms in this case, which cannot be studied in a semiclassical model, it is shown that the decay rate quickly becomes much smaller than the incoherent decay rate. An unquestionable subradiance phenomenon is thus predicted in this case.

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We follow in detail the spontaneous decay of fully excited samples of two and three resonant two-level atoms separated by distances much smaller than a wavelength. We include both the static dipole-dipole interaction and an in rinsic detuning (inhomogeneous broadening) of the atoms. We find that the Coulomb interaction may have both a decohering and a recohering effect. The decohering effect is seen in three atoms not equivalently placed. Here the Coulomb interaction diminishes super-radiance by subjecting the different atoms to different frequency shifts. The recohering effect is seen in all cases and consists in a protection of super-radiance against an inhomogeneous broadening far in excess of the inverse radiation time. Both effects have analogs in small many-atom samples studied in previous literature.
The interaction between electromagnetic radiation and two three-level atoms is investigated. The atom-atom separation is assumed to be smaller than the corresponding mean resonance wavelength. The total radiance rate of the atomic system is calculated as a function of time. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some act as photon-trapping states. Instead of exponential decay, the oscillations appear in the time evolution of the radiation rate due to the correlation between atoms. The decay constants and coupling decay constants show strong effects on the emission rates. Completely differing from two identical double-level atoms, the cooperative effects always exist in the three-level atomic system except for the case in which the coupling decay constants ${\ensuremath{\gamma}}_{12}$ and ${\ensuremath{\gamma}}_{21}$ are zero.
Spontaneous emission from two non-identical two-level atoms is examined from the viewpoint of quantum beats and super-radiant effects. Our analytical solution, illustrated graphically, shows that the total radiation rate exhibits temporal sinusoidal modulation (beats). The beats result from the fact that the atoms have different transition frequencies and different natural linewidths. For small interatomic separations, the total radiation rate is greater than its initial value. This ‘super-radiant’ property is absent in the case of noninteracting atoms, as well as for two identical atoms. In the case when the atoms are separated by distances much smaller than the resonant wavelength, the population trapping effect can take place in such a system.
The cooperative spontaneous emission from three identical, initially excited two-level atoms separated by distances much smaller than the resonance wavelength is studied taking into account the dipole-dipole near-field interaction. Approximate expressions are obtained for the time evolution of the atomic system, the radiated intensity and the one-time intensity correlation function. As a new result the authors find that the near-field interaction may lead to the occurrence of beats in the intensity. Moreover, the destructive effect of the near-field interaction on the coherence properties of the emitted radiation is discussed.
For pt.II see ibid., vol.19, p.2109 (1986). This paper is the third in a theoretical study of subradiance, i.e. the cooperative inhibition of spontaneous emission by a destructive interatomic interference, a phenomenon which has recently been observed. The paper is devoted to the problem of the cooperative spontaneous emission of atomic samples with linear dimensions much smaller than the wavelength of the emitted light. The treatment, which is based on a fully quantum mechanical description of the problem, corroborates the results obtained in a semiclassical treatment by Friedberg and Hartmann (1974). Starting from a master equation describing both the cooperative spontaneous emission and the dipole-dipole interaction, a statistical treatment of the latter is introduced and the corresponding symmetry relaxation is studied. The evolution of the atoms is described in three typical cases that correspond to different sample geometries and/or atomic distributions. In one of these cases, in particular, the symmetry is first conserved and the atoms follow Dicke's predictions for a time. A 'retarded' symmetry breaking then occurs suddenly, near the zero value of the collective energy, as in Friedberg and Hartmann's calculations for a small sphere. With regard to the further evolution of the atoms in this case, which cannot be studied in a semiclassical model, it is shown that the decay rate quickly becomes much smaller than the incoherent decay rate. An unquestionable subradiance phenomenon is thus predicted in this case.
The influence of the dipole–dipole inter-atomic coupling on collective spontaneous emission has been considered by many authors using both semiclassical and quantum theories. Specific results have been obtained for simple cases of regular atomic systems with a finite number of atoms. For disordered systems it has been found that the dipole–dipole coupling causes relaxation of the polarization phase (the effect of de-phasing), thus suppressing super-radiance. The main object of this chapter will be a regular linear chain of identical two-level atoms fully excited in the initial moment of time. The chapter considers the super-radiance of a regular linear chain of atoms. Such a system is the limiting case of a multi-atomic system characterized by a small Fresnel number. The dipole–dipole inter-atomic coupling modifies the super-radiance dynamics only slightly, but has a strong effect on the shape and width of the spectrum.
We study the collective spontaneous emission of three identical two-level atoms initially prepared in the excited states by measuring Glauber's third-order photon correlation function. Assuming two atoms at subwavelength distance from each other such that they are subject to the dipole-dipole interaction while the third one is located several wavelengths away, we observe super- and subradiant decay alike, depending on the direction of observation. Unlike the case where no remote atom is introduced or no conditional measurements are performed, the spontaneous emission behavior of the conditioned three-atom system is strongly modified, i.e., differing from the single-atom and the canonical two-atom configuration. The conditional measurements associated with the three-photon correlation function in combination with the dipole-dipole interaction between the adjacent atoms lead to quantum interference among the different decay channels allowing one to engineer the spontaneous emission in space and time.