Finite temperature dynamics of a degenerate Fermi gas with unitarity limited interactions

We derive the elastic collision rate for a harmonically trapped Fermi gas in the extreme unitarity limit where the s-wave scattering cross section is $\ensuremath{\sigma}(k)=4\ensuremath{\pi}{/k}^{2},$ with $\ensuremath{\Elzxh}k$ the relative momentum. The collision rate is given in the form $\ensuremath{\Gamma}=\ensuremath{\gamma}{I(T/T}_{F})$---the product of a universal collision rate $\ensuremath{\gamma}{=k}_{B}{T}_{F}/(6\ensuremath{\pi}\ensuremath{\Elzxh})$ and a dimensionless function of the ratio of the temperature T to the Fermi temperature ${T}_{F}.$ We find that I has a peak value of $\ensuremath{\simeq}4.6$ at ${T/T}_{F}\ensuremath{\simeq}0.4,$ $I\ensuremath{\simeq}82{(T/T}_{F}{)}^{2}$ for ${T/T}_{F}<~0.15,$ and $I\ensuremath{\simeq}{2(T}_{F}{/T)}^{2}$ for ${T/T}_{F}>1.5.$ We estimate the collision rate for recent experiments on a strongly-interacting degenerate Fermi gas of atoms.We derive the elastic collision rate for a harmonically trapped Fermi gas in the extreme unitarity limit where the s-wave scattering cross section is $\ensuremath{\sigma}(k)=4\ensuremath{\pi}{/k}^{2},$ with $\ensuremath{\Elzxh}k$ the relative momentum. The collision rate is given in the form $\ensuremath{\Gamma}=\ensuremath{\gamma}{I(T/T}_{F})$---the product of a universal collision rate $\ensuremath{\gamma}{=k}_{B}{T}_{F}/(6\ensuremath{\pi}\ensuremath{\Elzxh})$ and a dimensionless function of the ratio of the temperature T to the Fermi temperature ${T}_{F}.$ We find that I has a peak value of $\ensuremath{\simeq}4.6$ at ${T/T}_{F}\ensuremath{\simeq}0.4,$ $I\ensuremath{\simeq}82{(T/T}_{F}{)}^{2}$ for ${T/T}_{F}<~0.15,$ and $I\ensuremath{\simeq}{2(T}_{F}{/T)}^{2}$ for ${T/T}_{F}>1.5.$ We estimate the collision rate for recent experiments on a strongly-interacting degenerate Fermi gas of atoms.

arXiv:cond-mat/0304633Physical Review AJul 23, 200338 citations

Dynamics of a Highly-Degenerate, Strongly-Interacting Fermi Gas of Atoms

John E. Thomas, S. L. Hemmer, Joseph M. Kinast +3 more

Journal of Low Temperature PhysicsJan 1, 20042 citations

The degenerate Fermi gas with density-dependent interactions in the large-Nlimit under the K-harmonic approximation

Seth T. Rittenhouse, Chris H. Greene

We present a simple implementation of a density-dependent, zero-range interaction in a degenerate Fermi gas using hyperspherical coordinates in the large particle number limit. The method produces a 1D effective potential that accurately describes the ground-state energy as a function of the hyperradius of the two spin component gas throughout the vicinity of the unitarity regime. In the unitarity regime the breathing mode frequency is found to limit to the non-interacting value. A dynamical instability, similar to the Bosenova, is predicted to be possible for a gas containing more than three spin components, for large, negative, two-body scattering lengths. While the situation is less clear for the gas with three components, collapse might also be possible.We present a simple implementation of a density-dependent, zero-range interaction in a degenerate Fermi gas using hyperspherical coordinates in the large particle number limit. The method produces a 1D effective potential that accurately describes the ground-state energy as a function of the hyperradius of the two spin component gas throughout the vicinity of the unitarity regime. In the unitarity regime the breathing mode frequency is found to limit to the non-interacting value. A dynamical instability, similar to the Bosenova, is predicted to be possible for a gas containing more than three spin components, for large, negative, two-body scattering lengths. While the situation is less clear for the gas with three components, collapse might also be possible.

Journal of Physics B Atomic Molecular and Optical PhysicsOct 6, 20089 citations

The degenerate Fermi gas with renormalized density-dependent interactions in the K harmonic approximation

Seth T. Rittenhouse, Chris H. Greene

We present a simple implementation of a density-dependent, zero-range interactions in a degenerate Fermi gas described in hyperspherical coordinates. The method produces a 1D effective potential which accurately describes the ground state energy as a function of the hyperradius, the rms radius of the two spin component gas throughout the unitarity regime. In the unitarity regime the breathing mode frequency is found to limit to the non-interacting value. A dynamical instability, similar to the Bosenova, is predicted to be possible in gases containing more than three spin components, for large, negative, two-body scattering lengths.We present a simple implementation of a density-dependent, zero-range interactions in a degenerate Fermi gas described in hyperspherical coordinates. The method produces a 1D effective potential which accurately describes the ground state energy as a function of the hyperradius, the rms radius of the two spin component gas throughout the unitarity regime. In the unitarity regime the breathing mode frequency is found to limit to the non-interacting value. A dynamical instability, similar to the Bosenova, is predicted to be possible in gases containing more than three spin components, for large, negative, two-body scattering lengths.

arXiv:physics/0702161Feb 20, 20070 citations

Observation of a Dynamical Phase Transition in a Quantum Degenerate Fermi Gas

Ana María Rey

Bulletin of the American Physical SocietyMay 30, 20191 citation

{T}_{F}.

We find that I has a peak value of $\ensuremath{\simeq}4.6$ at ${T/T}_{F}\ensuremath{\simeq}0.4,$ $I\ensuremath{\simeq}82{(T/T}_{F}{)}^{2}$ for

{T/T}_{F}<~0.15,

and $I\ensuremath{\simeq}{2(T}_{F}{/T)}^{2}$ for

{T/T}_{F}>1.5.

We estimate the collision rate for recent experiments on a strongly-interacting degenerate Fermi gas of atoms.