| 研究実績の概要 |
In order to secure the long-term goals of the Fellowship, a code capable of simulating the physics of two-dimensional dipolar Bose-Einstein condensates has been written and tested by the awardee. This will in due course allow us to simulate a two-dimensional ring (an effective periodic structure) of solitons, where it is hoped the individual solitons mutual interaction will in turn facilitate a novel form of nonlinear lattice known as the ‘Toda’ lattice, as described in the original proposal. Presently, the code is able to simulate the dynamical evolution of up to three such solitons in a ring configuration; and also track the individual positions of the solitons. In due course this will be extended and the resulting dynamics compared to the analytical generalized Toda lattice equations.
Complimentary to the above activities, since taking up my Fellowship I have also become involved in an independent project studying a novel form of the so-called Tonks- Girardeau gas, an unusual form of ultracold matter where Bosonic atoms are confined and their mutual interaction made exceptionally strong, so that they behave as a gas of non-interacting spinless Fermions. Here, I have performed numerical calculations to understand the interaction of and dynamics of (weakly interacting) bright solitons with such a Tonks-Girardeau gas. In particular, we have looked at how a single bright soliton may act as a type of defect known as a Polaron; which could lead to a new understanding of regimes where weakly and strongly interacting ultracold matter can co-exist.
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