Abstract
We compute exactly the average spatial density for spinless noninteracting fermions in a harmonic trap rotating with a constant frequency in the presence of an additional repulsive central potential . We find that in the large- 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 and on the two parameters and leading to a rich phase diagram. Zooming in on the edge of the layer, we find that the edge density profile exhibits kinks located at the zeros of the Hermite polynomial. Interestingly, in the large- 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.
3 More- Received 17 October 2020
- Revised 15 February 2021
- Accepted 18 February 2021
DOI:https://doi.org/10.1103/PhysRevA.103.033321
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