The one-dimensional Fermi gas with repulsive short-range interactions provides an important model of strong correlations in few- and many-particle systems. However, in the presence of a harmonic potential, no exact solution is known in general for strongly interacting fermions. We have recently shown that this problem in the regime of strong repulsion can be mapped onto a Heisenberg spin chain, where approximate analytic expressions for the spin-spin interactions may be derived [1]. This effectively allows one to solve the problem for the case of a single spin-down impurity in a spin-up Fermi sea, a scenario that has recently been considered in cold-atom experiments [2].
The aim of this project is to generalise the above approach for spin-1/2 fermions to that of SU(N) Fermi gases, where there are N different flavours of fermions instead of just two.
References
[1] J. Levinsen, P. Massignan, G. M. Bruun, & M. M. Parish, Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential, Science Advances volume 1, number 6, 2015. [2] A. N. Wenz et. al., From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time, Science volume 342, number 6157, 2013Supervisor: A/Prof. Meera Parish and Dr Jesper Levinsen
See https://www.monash.edu/science/schools/physics/honours/honours-project to apply.