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arXiv:2608.10313 · American Journal of Physics

Experimental visualization of a Fermi gas

Inna Vishik

Published Oct 22, 2026• 0 citations
arXivHTMLPDF

Abstract

Angle-resolved photoemission spectroscopy (ARPES) can measure electrons' energy vs momentum relations in solids via the photoelectric effect. Here, we use experimental results from this technique as a tool for visualizing the Fermi gas model in quantum statistical mechanics. This model is an important starting point for understanding more complex electronic behaviors in real metals.

DOI
10.1119/5.0320045

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Angle-resolved photoemission spectroscopy (ARPES) can measure electrons' energy vs momentum relations in solids via the photoelectric effect. Here, we use experimental results from this technique as a tool for visualizing the Fermi gas model in quantum statistical mechanics. This model is an important starting point for understanding more complex electronic behaviors in real metals.
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The ability to study ultracold atomic Fermi gases holds the promise of significant advances in testing fundamental theories of many-body quantum physics. Of particular interest are strongly interacting Fermi gases in the BCS to BEC crossover that exhibit a transition to a superfluid state at temperatures near 0.2TF , where TF is the Fermi temperature. This transition, as a fraction of TF, is extremely high compared to any known superfluid or superconductor. These gases are also in a universal regime where the physics is independent of the details of the atomic interactions and is therefore relevant to fields as diverse as condensed matter, nuclear physics and astrophysics. In this thesis, I present an experimental probe of atomic gases that uses momentum-resolved RF spectroscopy to realize an analog of angle-resolved photoemission spectroscopy (ARPES) in materials. This measurement reveals the energy and momentum of single-particle states in the strongly interacting Fermi gas. In condensed matter, ARPES has proved to be one of the most powerful experimental techniques for studying the electronic structure of strongly correlated electron materials. The ability to perform analogous measurements in ultracold Fermi gases constitutes a significant advance in our ability to directly connect ultracold atomic gases to strongly correlated electron systems. Taking advantage of this new measurement technique, I investigate a long-standing problem in the field of strongly interacting fermions, namely whether a pseudogap state consisting of incoherent fermion pairs exists at temperatures above the critical temperature for superfluidity. The photoemission data I present provide strong evidence for this state and have implications for fundamental theories of strongly interacting Fermi gases and strongly correlated electron materials. I also discuss the experimental confirmation of recently predicted universal relations for strongly interacting Fermi gases, as well as some of the first experiments involving atomic Fermi gases with p-wave pairing.
In this review we discuss how theoretical momentum-resolved many-body spectral functions can help understanding the physics underlying angular resolved photoemission spectra (ARPES). Special focus is set on phenomena induced by electronic Coulomb correlations. Among these effects are transfers of spectral weight, the loss of quasi-particle coherence, and the sensitivity of these phenomena on external parameters, such as temperature or pressure. For the examples of the metallic phases of VO 2 and V 2 O 3 we review results obtained within dynamical mean-field theory, and assess the limits of band-structure approaches. Our discussion emphasizes the need for true many-body techniques even for certain metallic materials.
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The angle-resolved photoemission spectra (ARPES) of the spin-1/2 Holstein model at non-half-filling are calculated by using the adiabatic approximation and the classical Monte Carlo method. It is found that in the metallic state, the spectra take broad Gaussians at the band bottom, while evolving to sharp Lorentzians near the Fermi level, commonly in one, two, and three dimensions. We justify that this evolution in ARPES is connected with an electronic state transition from quasi-localized ones to the extended ones due to the scattering of electrons with the static lattice distortion.
Angle-resolved photoemission spectra (ARPES) are calculated in the Hubbard model by using cluster perturbation method. It is found that in a cluster of 12 sites, the local density of states displays the phase transition from normal conductor to Mott insulator with the increase of the electron-electron coupling. We show that a pseudogap develops from the metallic phase to the insulating phase. Evidence of spin-charge separation is also verified in the calculated single particle spectral functions.