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Physical Review A

Energy measurement and virial theorem for confined universal Fermi gases

John E. Thomas

Published Jul 23, 2008• 13 citations
Publisher

Abstract

Optically trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We show that the measured cloud profiles of both species determine the total energy of universal gases for any trapping potential $U$ and any spin mixture, without assuming either the local density approximation or harmonic confinement. A global proof of the virial theorem yields the total energy of the gas at all temperatures in the scale-invariant form $E=⟨ϵ\ensuremath{\partial}U/\ensuremath{\partial}ϵ⟩$, where $ϵ$ is an arbitrary energy scale in terms of which all length and energy scales that appear in the confining potential are written. This result enables model-independent energy measurement in any trap by observing only the cloud profiles, and provides a consistency check for many-body calculations in the universal regime.

DOI
10.1103/physreva.78.013630

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Optically trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We show that the measured cloud profiles of both species determine the total energy of universal gases for any trapping potential UUU and any spin mixture, without assuming either the local density approximation or harmonic confinement. A global proof of the virial theorem yields the total energy of the gas at all temperatures in the scale-invariant form E=⟨ϵ\ensuremath∂U/\ensuremath∂ϵ⟩E=⟨ϵ\ensuremath{\partial}U/\ensuremath{\partial}ϵ⟩E=⟨ϵ\ensuremath∂U/\ensuremath∂ϵ⟩, where ϵϵϵ is an arbitrary energy scale in terms of which all length and energy scales that appear in the confining potential are written. This result enables model-independent energy measurement in any trap by observing only the cloud profiles, and provides a consistency check for many-body calculations in the universal regime.
Optically-trapped two-component Fermi gases near a broad Feshbach resonance exhibit universal thermodynamics, where the properties of the gas are independent of the details of the two-body scattering interactions. We present a global proof that such a universal gas obeys the virial theorem for {\it any} trapping potential UUU and any spin mixture, without assuming either the local density approximation or harmonic confinement. The total energy of the gas is given in scale invariant form by E=E=E=, where εεε is an {\it arbitrary} energy scale in terms of which all length and energy scales that appear in the confining potential are written. This result enables model-independent energy measurement in traps that are anharmonic as well as anisotropic by observing only the cloud profile, and provides a consistency check for many-body calculations in the universal regime.
Unitary Fermi gases, where the scattering length is large compared to the interparticle spacing, can have universal properties, which are independent of the details of the interparticle interactions when the range of the scattering potential is negligible. We prepare an optically trapped, unitary Fermi gas of 6Li, tuned just above the center of a broad Feshbach resonance. In agreement with the universal hypothesis, we observe that this strongly interacting many-body system obeys the virial theorem for an ideal gas over a wide range of temperatures. Based on this result, we suggest a simple volume thermometry method for unitary gases. We also show that the observed breathing mode frequency, which is close to the unitary hydrodynamic value over a wide range of temperature, is consistent with a universal hydrodynamic gas with nearly isentropic dynamics.
We study the properties of an optically‐trapped, Fermi gas of 6Li atoms, near the center of a broad Feshbach resonance, where strong interactions are observed. Strongly interacting Fermi gases exhibit universal behavior, and are of interest as models of exotic systems ranging from high temperature superconductors to neutron stars and quark‐gluon plasmas. We measure the frequency and damping rate of the radial breathing mode of the trapped gas and consider quantum viscosity as a damping mechanism. We also demonstrate that the virial theorem holds and measure the heat capacity. In the experiments, energy is precisely added to the gas and an empirical temperature is determined from the spatial profiles of the cloud. Transitions are observed in both the damping rate and the heat capacity, measured as functions of the empirical temperature. Recent theory, using a pseudogap formalism, enables the first temperature calibration, and shows that the observed transition temperatures are close to that predicted for the onset of superfluidity in a strongly attractive Fermi gas.
Thermodynamic properties of an ultracold Fermi gas in a harmonic trap are calculated within a local density approximation, using a conserving many-body formalism for the BCS to Bose-Einstein condensate crossover problem, which has been developed by Haussmann et al. [Phys. Rev. A 75, 023610 (2007)]. We focus on the unitary regime near a Feshbach resonance and determine the local density and entropy profiles and the global entropy S(E)S(E)S(E) as a function of the total energy EEE. Our results are in good agreement with both experimental data and previous analytical and numerical results for the thermodynamics of the unitary Fermi gas. The value of the Bertsch parameter at T=0T=0T=0 and the superfluid transition temperature, however, differ appreciably. We show that, well in the superfluid regime, removal of atoms near the cloud edge enables cooling far below temperatures that have been reached so far.
We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T . We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏ n is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.
We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T. We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏn is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.