Cooperative effect in the radiation process has been studied in for more than half acentury. It is important in the sense of both basic physics and applied science.In this work, we study the dynamics of the cooperative spontaneous emissionfrom an ensemble of N atoms which is uniformly excited by absorbing a single photon.We reveal that there are two different regimes in which the system exhibitstotally different behaviors. One of them is the superradiance type of behavior: thesystem decays much quicker than single atom decay, with a decay rate proportionalto N(?/R)2, where N is the atom numbers, R is the size of the atom cloud, and ?is the wavelength. We call it Markovian regime because the sytem does not persistmemory effect. The other regime is called non-Markovian regime and the system oscillateswith effective Rabi oscillation frequency while slowly decaying with a rateproportional to the photon escaping rate. The effective Rabi oscillation is a new typeof dynamics which analogs well known Cavity QED behavior.Particularly in the Markovian regime, we study the system dynamics as a manybodyeigenfunction and eigenvalue problem. For a dense cloud, we find analytical solutions for the eigenstates and corresponding eigenvalues, which can help to generallydescribe the system dynamics for any initial conditions in this regime.One of the applications is in atom microscopy. We propose a scheme to measurethe distance between two atoms/molecules beyond diffraction limit. It covers thewhole range from half the wavelength to sub-nanometers, utilizing both the atomlocalization technique and the collective frequency shift effect due to the cooperativeeffect in the radiation of the two atoms.Another application that we propose is to generate Coherent XUV radiation usingRaman-type superradaince. We prove that intense short pulses of XUV radiation canbe produced by Raman type superradiance from an ensemble of atoms/ions drivenby visible or IR laser pulses.
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