Superradiance from a Relativistic Source

• URL: http://arxiv.org/abs/2207.05570v1
• Date: Tue, 12 Jul 2022 14:42:40 GMT
• Title: Superradiance from a Relativistic Source
• Authors: Christopher Wyenberg, Fereshteh Rajabi, Martin Houde
• Abstract summary: We construct a model of cooperative superradiant emission from a highly relativistic multi-particle source. We adapt the standard diagrammatic framework to compute time evolution and density operators from our Hamiltonian. We evaluate velocity coherence requirements for a sample to demonstrate enhanced superradiant emission in the observer frame.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct a model of cooperative superradiant emission from a highly relativistic multi-particle source. We revise an existing model of the literature for a relativistic two-level particle, and construct from it a Hamiltonian describing relativistic velocity dependent multi-particle superradiance. We adapt the standard diagrammatic framework to compute time evolution and density operators from our Hamiltonian, and demonstrate during the process a departure from standard results and calculation methods. In particular, we demonstrate that the so-called vertical photon result of the literature is modified by the relativistic Lorentz factor of the sample; we also introduce a set of coupled differential equations describing certain propagators in the velocity-dependent small sample framework, which we solve numerically via a hybrid fourth order Runge-Kutta and convolution approach. We demonstrate our methods for the simple case of two highly relativistic particles travelling with slightly differing velocities simulated at varying relativistic mean sample $\beta$ factors, and evaluate velocity coherence requirements for a sample to demonstrate enhanced superradiant emission in the observer frame. We find these coherence requirements to become increasingly restrictive at higher $\beta$ factors, even in the context of standard results of relativistic velocity differential transformations.

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