Topological Density Correlations in a Fermi Gas

A Fermi gas of non-interacting electrons, or ultra-cold fermionic atoms, has a quantum ground state defined by a region of occupancy in momentum space known as the Fermi sea. The Euler characteristic of the Fermi sea serves to topologically classify these gapless fermionic states. In this talk, we establish a universal structure of a D + 1 point equal time density correlation function that reflects the Fermi sea topology in D spatial dimensions [1]. We further argue that, for two dimensions, ultracold fermionic gases imaged by quantum gas microscopy provides a feasible platform to measure the third order density correlation, from which the 2D Fermi sea topology can be reliably extracted in systems with as few as around 100 atoms.

[1] Tam and Kane, arXiv:2310.03737