Doctor of Philosophy
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.
Summary for Lay Audience
Even in a pitch dark vacuum, the physics of the very small describes so-called quantum fluctuations of light. A particle possessing energy internal to itself can interact with these fluctuations and release its energy as a single unit of light known as a photon.
Sometimes, particles within a gas interact with quantum fluctuations of light independently. Other times, a collection of particles interacts with fluctuations in an exotic fashion whose whole cannot be understood as a sum of its parts. When the language of mathematical physics carefully tells the story of such a group, it cannot be said that any single member emits a photon; rather, the group itself collectively emits a photon. During this process the particles become tangled up together and lose their identities. This entangled group interacts strongly with quantum fluctuations of light and emits an intense stream of photons in a phenomenon known as superradiance.
Superradiance can describe some astrophysical observations, but such environments often possess wide spreads in their particles' velocities. Velocities shift particles' natural frequencies (similar to a passing train's pitch modulation) such that particles of different velocities talk to different photons, reducing their entanglement. This thesis analyses the effect of a wide velocity spread upon superradiance.
Certain mathematical objects describing a superradiant sample rotate at extremely fast rates. Computer simulation is simplified by spinning one's perspective, analogous to a strobe light bringing a spinning fan to a standstill. When multiple velocities are present, however, objects rotate at different rates and simulation is complicated by the lack of a shared ``strobe rate'' to simultaneously simplify all particles' mathematical descriptions. This thesis derives two novel simulation algorithms: one which transforms our approach to the spinning mathematical objects, and another which juggles a collection of strobes. Both methods dramatically improve simulation speed and are used to investigate superradiance in astrophysics.
Astrophysical sources can travel near the speed of light, which requires that superradiance be reformulated consistently with Einstein's special theory of relativity. This thesis derives a model of superradiance capturing relativistic time dilation and the relativistic transformation of light, and calculates consequences for observations.
Wyenberg, Christopher M., "Wideband and Relativistic Superradiance in Astrophysics" (2022). Electronic Thesis and Dissertation Repository. 8789.
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