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arXiv:1204.0048 · Physical Review A

Direct observation of the Fermi surface in an ultracold atomic gas

Tara E. Drake, Yoav Sagi, Rabin Paudel, John T. Stewart, John Gaebler, D. S. Jin

Published Sep 6, 2012• 26 citations
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Abstract

The ideal (i.e., noninteracting), homogeneous Fermi gas, with its characteristic sharp Fermi surface in the momentum distribution, is a fundamental concept relevant to the behavior of many systems. With trapped Fermi gases of ultracold atoms, one can realize and probe a nearly ideal Fermi gas; however, these systems have a nonuniform density due to the confining potential. We show that the effect of the density variation, which typically washes out any semblance of a Fermi surface step in the momentum distribution, can be mitigated by selectively probing atoms near the center of a trapped gas. With this approach, we have directly measured a Fermi surface in momentum space for a nearly ideal gas, where the average density and temperature of the probed portion of the gas can be determined from the location and sharpness of the Fermi surface.

DOI
10.1103/physreva.86.031601

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The ideal (i.e., noninteracting), homogeneous Fermi gas, with its characteristic sharp Fermi surface in the momentum distribution, is a fundamental concept relevant to the behavior of many systems. With trapped Fermi gases of ultracold atoms, one can realize and probe a nearly ideal Fermi gas; however, these systems have a nonuniform density due to the confining potential. We show that the effect of the density variation, which typically washes out any semblance of a Fermi surface step in the momentum distribution, can be mitigated by selectively probing atoms near the center of a trapped gas. With this approach, we have directly measured a Fermi surface in momentum space for a nearly ideal gas, where the average density and temperature of the probed portion of the gas can be determined from the location and sharpness of the Fermi surface.
The collective behavior of an ensemble of strongly interacting fermions is central to many physical systems, and its theoretical description is challenging due to the many-body nature of the problem. The ultracold Fermi gas is an ideal model system to shed light on this issue, as it provides excellent controllability, reproducibility, and unique detection methods. One of the problems, however, which complicates the interpretation of such experiments is the inherent density inhomogeneity of the gas due to harmonic confinement. We have developed a technique to overcome this difficulty by selectively probing atoms near the center of a trapped gas while still retaining momentum resolution. In this contribution to the 21th International Conference on Laser Spectroscopy (ICOLS 2013), we give an overview of this technique and some of the observations that have resulted from its implementation.
This thesis presents experiments probing the physics of strongly interacting fermionic atoms in the BCS-BEC crossover. Ultracold atom experiments bring the ability to arbitrarily tune interatomic interactions, which allows for unprecedented access to the regime of strongly interacting physics. The majority of cold atom experiments, however, are carried out in an atom trap that imprints an inhomogeneous density on the cloud of atoms. Many phenomena, especially the signatures of phase transitions, are significantly modified by this non-uniform density. In this thesis, I present a novel imaging technique that allows us to probe a region of nearly homogeneous density within a larger, inhomogenenous cloud. Using this technique, I present new results for strongly interacting fermionic atoms, including the first measurements of the contact and the occupied spectral function of a homogeneous Fermi gas, and the first direct observation of the "textbook" momentum distribution of an ideal Fermi gas.
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We report on the creation of homogeneous Fermi gases of ultracold atoms in a uniform potential. In the momentum distribution of a spin-polarized gas, we observe the emergence of the Fermi surface and the saturated occupation of one particle per momentum state: the striking consequence of Pauli blocking in momentum space for a degenerate gas. Cooling a spin-balanced Fermi gas at unitarity, we create homogeneous superfluids and observe spatially uniform pair condensates. For thermodynamic measurements, we introduce a hybrid potential that is harmonic in one dimension and uniform in the other two. The spatially resolved compressibility reveals the superfluid transition in a spin-balanced Fermi gas, saturation in a fully polarized Fermi gas, and strong attraction in the polaronic regime of a partially polarized Fermi gas.
We show how to use trapped ultracold atoms to measure the magnetic susceptibility of a two-component Fermi gas. The method is illustrated for a noninteracting gas of 6{}^{6}6Li, using the tunability of interactions around a wide Feshbach resonance. The susceptibility versus effective magnetic field is directly obtained from the inhomogeneous density profile of the trapped atomic cloud. The wings of the cloud realize the high-field limit where the polarization approaches 100%, which is not accessible for an electron gas.
Thermometry is essential for studying many-body physics with ultracold atoms. Accurately measuring low temperatures in these systems, however, remains a significant challenge due to the absence of a universal thermometer. Most widely applicable methods, such as fitting of in situ density profiles, are limited by the requirement of global thermal equilibrium and inapplicability to homogeneous systems. In this Letter, we introduce a novel in situ thermometry for quantum gases, leveraging single-atom-resolved measurements via quantum gas microscopy, and demonstrate it on an ideal Fermi gas. By analyzing number fluctuations in probe volumes containing as little as one atom on average, we extract both global and local temperatures over a broad dynamic range. Our method does not rely on the fluctuation-dissipation theorem and is based instead on the exact relationship between number fluctuations and density-density correlations. In the low-temperature regime, it allows us to observe significant deviations from fluctuation-dissipation predictions, uncovering subextensive fluctuations. Our method is applicable to systems with arbitrary trapping potentials, requiring neither precise trap calibration nor global thermal equilibrium. This thermometer for quantum gases overcomes key limitations of existing techniques, paving the way for more accurate and versatile temperature measurements in ultracold quantum systems.