Simulating ultracold matter: horizons and slow light
Abstract
This thesis explores the links between different ways of modelling the physical
world. Finite difference numerical simulations may be used to encode the behaviour of physical systems, allowing us to gain insight into their workings and
even to predict their behaviour. Similarly, one can investigate the properties of
gravitational black holes through the use of analogue black holes, physical systems
which share at least some part of the physics of the astronomical objects. Concentrating on black hole analogues using Bose-Einstein condensates, I show how
simulations of these systems may be greatly assisted through the use of a proper
absorbing boundary condition, the Perfectly Matched Layer. Such a boundary condition allows the effcient truncation of the computational domain, both saving computational time and increasing accuracy. I then apply this technique to
the simulation of the supersonic flow of a Bose-Einstein condensate through a
Laval nozzle, a black hole analogue, showing that such a flow should be stable and
observable in the laboratory. Moving to a related system, I investigate the optical
analogue of the Iordanskii force - the friction resulting from interaction between
excitations in a superfluid's normal component and a superfluid vortex - through
the simulation of such a vortex in a Bose-Einstein condensate illuminated by slow
light, which is light whose group velocity is on the order of metres per second.
The interaction of the slow light with the vortex should produce a momentum
transfer due to the optical Aharonov-Bohm effect, exerting a force on the vortex.
The coupled system of equations describing the condensate-slow light system is
simulated, giving some surprising results.
Type
Thesis, PhD Doctor of Philosophy
Rights
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