We compute exactly the average spatial density for $N$ spinless noninteracting fermions in a $2d$ harmonic trap rotating with a constant frequency $\mathrm{\Omega }$ in the presence of an additional repulsive central potential $\gamma /r^2$. We find that in the large-$N$ limit, the bulk density has a rich and nontrivial profile—with a hole at the center of the trap and surrounded by a multilayered “wedding cake” structure. The number of layers depends on $N$ and on the two parameters $\mathrm{\Omega }$ and $\gamma$ leading to a rich phase diagram. Zooming in on the edge of the $k\mathrm{th}$ layer, we find that the edge density profile exhibits $k$ kinks located at the zeros of the $k\mathrm{th}$ Hermite polynomial. Interestingly, in the large-$k$ limit, we show that the edge density profile approaches a limiting form, which resembles the shape of a propagating front, found in the unitary evolution of certain quantum spin chains. We also study how a newly formed droplet grows in size on top of the last layer as one changes the parameters.

• Received 17 October 2020
• Revised 15 February 2021
• Accepted 18 February 2021

DOI:https://doi.org/10.1103/PhysRevA.103.033321