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arXiv:1301.1139 · Physical Review A

Pauli paramagnetism of an ideal Fermi gas

Ye-Ryoung Lee, Tout T. Wang, Timur M. Rvachov, Jae-Hoon Choi, Wolfgang Ketterle, Myoung-Sun Heo

Published Apr 24, 2013• 21 citations
arXivHTMLPDF

Abstract

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 ${}^{6}$Li, 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.

DOI
10.1103/physreva.87.043629

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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.
We report on the measurement of the equation of state of a two-component Fermi gas of 6Li^{6}\mathrm{Li}6Li atoms with resonant interactions. By analyzing the in situ density distributions of a population-imbalanced Fermi mixture reported in a recent experiment [Y. Shin et al., Nature 451, 689 (2008)], we determine the energy density of a resonantly interacting Fermi gas as a function of the densities of the two components. We present a method to determine the equation of state directly from the shape of the trapped cloud, where the fully polarized, noninteracting ideal Fermi gas in the outer region provides the absolute calibration of particle density. From the density profiles obtained at the lowest temperature, we estimate the zero-temperature equation of state.
We report the experimental determination of the scattering parameters for a ppp-wave Feshbach resonance in a single-component Fermi gas of 6{}^{6}6Li atoms in the lowest spin state. The time scale of the cross-dimensional relaxation reflects the elastic-scattering rate of the atoms, and scattering parameters are determined from the scattering rate as a function of magnetic field by taking into account the momentum distribution and inhomogeneous density profile of the atoms in a trap. Precise determination of the scattering parameters for a ppp-wave Feshbach resonance is an important step toward the realization of a ppp-wave superfluid in an ultracold atomic gas.
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.
We report on a study of the superfluid state of spin-polarized atomic 6{}^{6}6Li confined in a magnetic trap. Density profiles of this degenerate Fermi gas and the spatial distribution of the BCS order parameter are calculated in the local-density approximation. The critical temperature is determined as a function of the number of particles in the trap. Furthermore, we consider the mechanical stability of an interacting two-component Fermi gas, in the case of both attractive and repulsive interatomic interactions. For spin-polarized 6{}^{6}6Li we also calculate the decay rate of the gas and show that within the mechanically stable regime of phase space, the lifetime is long enough to perform experiments on the gas below and above the critical temperature if a bias magnetic field of about 5 T is applied. Moreover, we propose that a measurement of the decay rate of the system might signal the presence of the superfluid state.
We systematically studied the two-body loss in a two-component Fermi gas of 6Li^{6}\mathrm{Li}6Li atoms near a ppp-wave Feshbach resonance. The two-body loss rate constants were measured for various temperatures and magnetic fields using atoms trapped in three-dimensional and quasi-two-dimensional traps. Our results were nicely reproduced by a theoretical model that incorporates the two-body loss as an imaginary part to the inverse of the scattering volume in the scattering amplitude expression. The observed loss suppression in quasi-two-dimensional traps may provide a promising strategy to realize a ppp-wave superfluid in a system of ultracold atoms.
rf spectroscopy is one of the most powerful probing techniques in the field of ultracold gases. We report on a novel rf spectroscopy scheme with which we can detect very weak signals of only a few atoms. Using this method, we extended the experimentally accessible photon-energies range by an order of magnitude compared to previous studies. We directly verify a universal property of fermions with short-range interactions which is a power-law scaling of the rf spectrum tail all the way up to the interaction scale. We also determine, with high precision, the trap average contact parameter for different interaction strength. Finally, we employ our technique to precisely measure the binding energy of Feshbach molecules in an extended range of magnetic fields. These data are used to extract a new calibration of the Feshbach resonance between the two lowest energy levels of ^{40}K.