Complete integrability of the quasi-one-dimensional quantum model of Dicke superradiance

The method of the quantum inverse scattering problem is used to show that the quasi-one-dimensional quantum model of superradiance is exactly integrable. The commutation relations are obtained for the transition matrix elements, and the eigenfunctions and eigenvalues of the motion integrals of the model are determined. The model includes a bound state of m particles; for sufficiently large m (m much greater than unity), the spectrum of the bound state (quantum soliton) is linear omega = k with a small correction proportional to the reciprocal of m. This state should be identified as the Dicke superradiance pulse.