Wideband and Relativistic Superradiance in Astrophysics
Abstract
In the quantum phenomenon of superradiance (SR) a population of inverted particles evolves, through its interaction with the quantized vacuum radiation field, into a highly entangled state capable of generating much greater radiative emission than predicted by the independent spontaneous decay of its constituent particles. The phenomenon has recently been applied to transient astrophysical processes but has thus far been restricted to particles sharing a common velocity. This thesis researches the effects of astrophysical velocity distributions upon SR, which are distinct from conventional regimes of the quantum optics literature in that they may possess extremely wide bandwidths, turbulent statistical properties, or highly relativistic mean velocities. An important result of this thesis is the derivation of two novel algorithms for simulating widely Doppler broadened SR, each offering improved numerical complexity scaling over conventional methods. In the first, a Fourier domain representation is derived for the velocity dependent partial differential equations describing a population inversion interacting with the radiation field; this representation generalises an existing quasi-steady state maser model to the transient SR regime. In the second, the electric field is represented by a collection of fields, each representing photon creation or annihilation on resonance with a particular velocity channel; the symmetry of this representation leads to a numerically advantageous algorithm for many velocity broadened systems. I apply this latter algorithm to investigate the effects of pumping mechanisms and velocity distribution statistics upon transient SR processes in widely broadened astrophysical media. I demonstrate that the orientation of the pumping mechanism as well as turbulent properties of the velocity distribution critically affect transient SR structure in a widely Doppler broadened sample. The final project of this thesis develops a relativistic model of SR built upon canonical quantization of a covariant Lagrangian for the matter-radiation interaction. I apply the diagrammatic method alongside numerical techniques to compute the particle state reduced density operator's time evolution from the relativistic two-particle SR Hamiltonian, and make quantitative conclusions regarding the effect of relativistic velocity coherence upon SR intensity measurements in the observer's frame.