Topological Density Correlations in a Fermi Gas
- URL: http://arxiv.org/abs/2310.03737v1
- Date: Thu, 5 Oct 2023 17:57:58 GMT
- Title: Topological Density Correlations in a Fermi Gas
- Authors: Pok Man Tam and Charles L. Kane
- Abstract summary: 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 topology of a $D$ dimensional Fermi sea is physically encoded in the $D+1$ point equal time density correlation function.
We make use of the topological $D+1$ point density correlation to reveal universal structures of the more general $M$ point density correlation functions in a $D$ dimensional Fermi gas.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 $\chi_F$ of the Fermi sea serves to
topologically classify these gapless fermionic states. The topology of a $D$
dimensional Fermi sea is physically encoded in the $D+1$ point equal time
density correlation function. In this work, we first present a simple proof of
this fact by showing that the evaluation of the correlation function can be
formulated in terms of a triangulation of the Fermi sea with a collection of
points, links and triangles and their higher dimensional analogs. We then make
use of the topological $D+1$ point density correlation to reveal universal
structures of the more general $M$ point density correlation functions in a $D$
dimensional Fermi gas. Two experimental methods are proposed for observing
these correlations in $D=2$. In cold atomic gases imaged by quantum gas
microscopy, our analysis supports the feasibility of measuring the third order
density correlation, from which $\chi_F$ can be reliably extracted in systems
with as few as around 100 atoms. For solid-state electron gases, we propose
measuring correlations in the speckle pattern of intensity fluctuations in
nonlinear X-ray scattering experiments.
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