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arXiv:1710.08877

Cooperative parametric resonance of the spin one half system of the dense atomic gas

Yuri V. Rostovtsev, Vladimir L. Safonov, Marlan O. Scully

Published Oct 24, 2017• 1 citation
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Abstract

The cooperative resonance for a spin one half system interacting with dc and ac magnetic field is considered. This interaction in the system collective regime can result in parametic resonance and rapid excitation of the excited spin state of the dense atomic gas. The phenomenon is studied using the density matrix approach. We discuss the implementation of this effect and possible applications of the quantum amplification by superradiant emission of radiation.

DOI
10.48550/arxiv.1710.08877

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The cooperative resonance for a spin one half system interacting with dc and ac magnetic field is considered. This interaction in the system collective regime can result in parametic resonance and rapid excitation of the excited spin state of the dense atomic gas. The phenomenon is studied using the density matrix approach. We discuss the implementation of this effect and possible applications of the quantum amplification by superradiant emission of radiation.
Cooperative emission from a collection of atoms prepared in an initial state of complete inversion has been studied extensively in the past. In this paper we study the cooperative emission in dense atomic systems where there is a large average number of atoms per cubic resonance wavelength. For systems with such large densities, effects of the induced dipole-dipole interaction among neighboring atoms become important. Recently it has been shown that such interatomic interaction in a dense atomic system can lead to novel nonlinear effects.1,2 The induced dipole-dipole interaction for two-level atoms appears as a nonlinear inversion dependent renormalization of the atomic resonance frequency which gives rise to a set of modified Maxwell-Bloch equations. We study the phenomenon of superfluorescence (SF) and amplified spontaneous emission (ASE) using the modified Maxwell-Bloch equations. Statistical effects of amplified quantum stochastic processes are analyzed in SF and ASE. Phase wave statistics are analyzed in the linear regime of coherent pulse buildup. Amplified effects in the nonlinear regime in the SF to ASE transition region are statistically analyzed. Dipole dephasing due to collisions is found to play an important role.
We study the superradiance dynamics in a dense system of atoms each of which can be generally a spin-jjj particle, with jjj an arbitrary half-integer. We generalize Dicke's superradiance point of view to multiple-level systems and compare the results based on a novel approach we developed previously [Lin and Yelin, Adv. Atom. Mol. Opt. Phys. 61, in press (2012)]. Using this formalism we derive an effective two-body description that shows cooperative and collective effects for spin-jjj particles, taking into account the coherence of transitions between different atomic levels. We find that superradiance, which is well known as a many-body phenomenon, can also be modified by multiple-level effects. We also discuss the feasibility and propose that our approach can be applied to polar molecules, for their vibrational states have a multilevel structure which is partially harmonic.
When atoms are coupled to a common electromagnetic environment, the exchange of photons through dipole-dipole interactions leads to the emergence of cooperative effects. As a particular example, superradiance arises from spontaneous emission when this exchange leads to constructive interference of the emitted photons. Here, we introduce an integrated method for studying cooperative radiation in many-body systems. This method, which allows to study extended systems with arbitrarily large number of particles, can be formulated by an effective, nonlinear, two-atom master equation that describes the dynamics using a closed form which treats single- and many-body terms on an equal footing. We apply this method to a homogeneous gas of initially inverted two-level atoms, and demonstrate the appearance of both superradiance and subradiance, identifying a many-body coherence term as the source of these cooperative effects. We describe the many-body induced broadening -- which is analytically found to scale with the optical depth of the system -- and light shifts, and distinguish spontaneous effects from induced ones. In addition, we theoretically predict the time-dependence of subradiance, and the phase change of the radiated field during the cooperative decay.
Dicke's superradiance from a gas system of atoms and molecules was described in terms of two-level atoms, i.e., as an assembly of half-spin operators. In this system the magnitude of the total spin, which is called a cooperation number, is conserved at the maximum for the whole radiative process. We will answer in this paper how this superradiance is modified in the crystal in which an excitation can propagate from atom to atom through dipolar interactions. As a prototype of a crystal, we choose a linear chain of two-level atoms. The superradiance master equation of this system can be solved in terms of the exact solution of Lieb, Shultz, and Mattis for the spin system. The first effect is that the emitted frequency shows opposite shifts red and blue, respectively, for the first and second halves of the superradiance pulse, or vice versa, depending upon the sign of the transfer-matrix element of the excitation. The second effect is the appearance of a slow component in the emission tail, which originates from mixture of the states with smaller cooperation numbers or smaller oscillator strength under the transfer of the excitations. These results are demonstrated for a mesoscopic system of linear chains.
The present state of theoretical and experimental research on collective spontaneous emission (superradiance) in a system of radiators (atoms, molecules, or nuclei) is reviewed. The distinction between superradiance and the amplification of spontaneous emission is discussed. There is also a discussion of conditions under which the effect can be observed and of various theoretical methods for describing superradiance: the quantum single-mode and multimode models and the semiclassical approach. Theoretical papers on superradiance in systems with dimensions smaller than the wavelength of the radiation and also in extended systems are reviewed. It is shown that superradiance may occur in weakly amplifying media. A situation in which the superradiance is oscillatory is described. The possible use of superradiance to generate coherent emission in the x-ray and ? ranges is discussed. The superradiance accompanying Raman scattering of light in atomic and molecular media is studied. The theoretical results are compared with experimental observations of superradiance in the optical range. In an appendix, the nature of the phase transition in a system of radiators interacting through an electromagnetic field is discussed.