One dimensional transport of ultracold fermions

Whelan, Rory (2021). One dimensional transport of ultracold fermions. University of Birmingham. Ph.D.

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Abstract

This thesis concerns the transport of fermions through a one-dimensional channel. I consider two three- dimensional reservoirs that contain BCS superconductors, that are connected via weak tunnelling junc- tions to a one-dimensional channel in which the fermions have attractive interactions. The current through the channel is entirely driven by the phase difference in the superconducting order parameters of the two reservoirs. I theoretically investigate the current as a function of phase difference and show that the flow has characteristics that are completely distinct from an equivalent system without attrac- tive interactions between fermions. As a perturbative solution fails for attractive fermions, I develop a non-pertubative mean field description of the fermionic current. With the inclusion of fluctuations in this mean field solution, I show that the system of fermions with attractive interactions can identically map onto a system of bosons in the same geometry, with Bose-Einstein condensate reservoirs. I show that the novel features of the bosonic flow are retained in the attractive fermionic system, namely the two seperate branches of the mean field solution. I show that these branches are degenerate at an applied phase difference of π, and that the degeneracy is robust against fluctuations. I compare this degeneracy in the attractive fermionic and bosonic systems to the topologically protected degeneracy in nanowires that host Majorana zero modes.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):