Super-radiance from a relativistic source

Cooperative super-radiant emission from a highly relativistic multi-particle source is modeled and solved for the simple case of two particles. An existing model of a single relativistic two-level particle is used to construct a Hamiltonian describing relativistic velocity dependent multi-particle super-radiance. The standard diagrammatic framework is applied to the calculation of time evolution and density operators from this Hamiltonian, demonstrating during the process a departure from standard results and calculation methods. In particular, the so-called vertical photon result of the literature is shown to be modified by the relativistic Lorentz factor of the sample; additionally, a set of coupled differential equations describing certain propagators in the velocity-dependent small sample framework are introduced and solved numerically via a hybrid fourth order Runge–Kutta and convolution approach. The model is applied to the simple case of two highly relativistic particles travelling with slightly differing velocities simulated at varying relativistic mean sample β factors, and velocity coherence requirements for a sample to demonstrate enhanced super-radiant emission in the observer frame are evaluated. These coherence requirements are found to become increasingly restrictive at higher β factors, even in the context of standard results of relativistic velocity differential transformations.