Topological Density Correlations in a Fermi Gas
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916362247471104 |
|---|---|
| author | Tam, Pok Man Kane, Charles L. |
| author_facet | Tam, Pok Man Kane, Charles L. |
| contents | 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 $χ_F$ 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 $χ_F$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03737 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological Density Correlations in a Fermi Gas Tam, Pok Man Kane, Charles L. Quantum Gases Mesoscale and Nanoscale Physics Quantum Physics 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 $χ_F$ 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 $χ_F$ 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. |
| title | Topological Density Correlations in a Fermi Gas |
| topic | Quantum Gases Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2310.03737 |