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International Journal of Modern Physics B

PULSED SUPERRADIANT EMISSION FROM A MAGNETIC DIPOLE SYSTEM

Salomon Sylvain Mizrahi, MAURO A. MEWES

Published May 30, 1993• 9 citations
Publisher

Abstract

The superradiant emission is considered for a radiating system constituted by N dressed spin-1/2 magnetic dipoles, described by a nonlinear single particle Hamiltonian that is derived under a mean field approximation. This Hamiltonian describes adequately the transient regime of the emission process: The intensity of the radiation follows the sech2 law and its peak is proportional to N2. Then, one considers the application of a periodic time-dependent transverse magnetic field and we study the behavior of the emission that becomes periodically pulsed.

DOI
10.1142/s0217979293002882

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The superradiant emission is considered for a radiating system constituted by N dressed spin-1/2 magnetic dipoles, described by a nonlinear single particle Hamiltonian that is derived under a mean field approximation. This Hamiltonian describes adequately the transient regime of the emission process: The intensity of the radiation follows the sech2 law and its peak is proportional to N2. Then, one considers the application of a periodic time-dependent transverse magnetic field and we study the behavior of the emission that becomes periodically pulsed.
The atomic superradiant emission is treated in the single-particle mean-field approximation. A single-particle Hamiltonian, which represents a dressed two-level atom in a radiation field, can be obtained and it is verified that it describes the transient regime of the emission process. While the line-shape emission for a bare atom follows the sech2{\mathrm{sech}}^{2}sech2 law, for the dressed atom the line shape deviates appreciably from this law and it is verified that the deviation depends crucially on the ratio of the dynamic frequency shift to the transition frequency. This kind of deviation is observed in experimental results.
The superradiant phenomena is characterized by atomic dipoles ordering process in excited samples moderately denses, that occours due to the atomic induced correlations developed not directly but by the coherent radiation emitted by atoms themselves.The superradiant process evolves from a total disorder at t = 0, attain a maximum order in a time τ ∝ N -1 creating a radiation pulse whose intensity follows the sech 2 law and its peak is proportional to N 2 , thereafter the dipoles relax to a disordered equilibrium state.In this essay, we deal with the interaction between two cavity modes ω a and ω b and a classical pump with a system of N two-level atoms, whose atomic transition frequencies ω 0 .We consider a resonant interaction between atoms and mode ω a and a dispersive coupling of atoms with mode ω b , which couple the atomic sample, and the classical pump.In order to obtain how sech 2 law changes, we use the method of nonlinear small rotations to obtain effective Hamiltonian, expliciting dipolar interaction between atoms.Finally, after write the effective master equation, we use the mean-field approximation and Lewis and Riesenfeld method to obtain the mean features of this phenomena to our system.
The emission of radiation from a spatially extended amplifying medium is shown to exhibit new coherence effects when the medium is modeled by inverted atoms which possess a degeneracy allowing Q(J) transitions. In particular, it is predicted that media of this type for which J=2 can emit leading pulses which are doubly peaked or asymmetric within both the regimes of superfluorescence and oscillating fluorescence. Dissipative processes can radically alter the character of the emission; an output consisting of two well-separated pulses appears feasible, but the precise behavior in the present model depends upon the magnitude of the field losses and the initiation statistics.
We discuss the possibility of producing harmonics while the process of collective spontaneous emission (superradiance) takes place in a solid. Self correlations of dipole radiators induced by the emitted field lead to a reduction of the emission time and consequently to an increase of the intensity. Estimations of the superradiant energy flux show that, for crystalline densities of radiators, this flux may be comparable with the atomic unit. This assures the highly nonlinear behavior necessary to observe a pulse of high harmonics during superradiant pulse. We apply the Floquet–Bloch expansion to analyze the features of harmonic production in the framework of the two-level model.
We discuss the coherent behavior of a polarized, nuclear or electron, spin system for which the magnetic dipole radiation emitted in the radio-frequency region, has approximately quadratic dependence on the number of spins. An effective method of describing these phenomena is provided by computer simulation of a microscopic model of the spin system. Important aspects of this numeric simulation are described, together with a comparison with the theoretical predictions. The behavior of the transverse component of the magnetic moment, M+(t){M}^{+}(t)M+(t), in super-radiant conditions is studied. In addition, the role of dipole-dipole interactions in super-radiation phenomena is investigated in detail. It is shown that some important features of super-radiation cannot be described with the Bloch equations.
A spin system is considered with a Hamiltonian typical of molecular magnets, having dipole-dipole interactions and a single-site magnetic anisotropy. In addition, spin interactions through the common radiation field are included. A fully quantum-mechanical derivation of the collective radiation rate is presented. An effective narrowing of the dipole-dipole attenuation, due to high spin polarization is taken into account. The influence of the radiation rate on spin dynamics is carefully analysed. It is shown that this influence is completely negligible. No noticeable collective effects, such as superradiance, can appear in molecular magnets, being caused by electromagnetic spin radiation. Spin superradiance can arise in molecular magnets only when these are coupled to a resonant electric circuit, as has been suggested earlier by one of the authors in Laser Phys. 12, 1089 (2002).