Dynamics of Multi-Boson Decay

Abstract

A number of problems in quantum optics can be formulated in terms of the Hamiltonian

$$ H\left( {q,p} \right) = {\omega _0}a_0^\dag {a_0} + \sum\limits_{k = 1}^p {{\omega _k}a_k^\dag } {a_k} + \gamma a_0^\dag \sum\limits_{k = 1}^p {{a_k} + h.c.1)} $$

((1))

describing a q-photon decay into p different Bose fields. The examples of processes inkier consideration are provided by the model of parametric process with classical pumping¹ (at q = 0, p = 2), pure guantnnl model of Raman scattering² (at q = 1, p = 2), and quantum model of degenerate hyper-Raman scattering³ (at q = p = 2). Although some of that models can be solved exactly⁴⁵ the numerical methods remain the main approach in investigation of their qua.ntnm properties⁶.