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arXiv:cond-mat/0610848 · Physical Review A

Renormalized mean-field theory for a two-component Fermi gas with s -wave interactions

Javier von Stecher, Chris H. Greene

Published Feb 20, 2007• 18 citations
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Abstract

A method is introduced to renormalize the zero-range interaction for use in mean-field and many-body theory, starting from two-body calculations. The density-renormalized $\ensuremath{\delta}$-function interaction is then applied using mean-field theory to a two-component fermion gas and compared with diffusion Monte Carlo simulations and conventional mean-field calculations. In the unitarity limit, the equation of state exhibits the expected behavior $\ensuremath{\mu}\ensuremath{\propto}{\ensuremath{\rho}}^{2∕3}$, with a parameter $\ensuremath{\beta}=\ensuremath{-}0.492$, which is consistent with recent experiments.

DOI
10.1103/physreva.75.022716

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A method is introduced to renormalize the zero-range interaction for use in mean-field and many-body theory, starting from two-body calculations. The density-renormalized \ensuremathδ\ensuremath{\delta}\ensuremathδ-function interaction is then applied using mean-field theory to a two-component fermion gas and compared with diffusion Monte Carlo simulations and conventional mean-field calculations. In the unitarity limit, the equation of state exhibits the expected behavior \ensuremathμ\ensuremath∝\ensuremathρ2∕3\ensuremath{\mu}\ensuremath{\propto}{\ensuremath{\rho}}^{2∕3}\ensuremathμ\ensuremath∝\ensuremathρ2∕3, with a parameter \ensuremathβ=\ensuremath−0.492\ensuremath{\beta}=\ensuremath{-}0.492\ensuremathβ=\ensuremath−0.492, which is consistent with recent experiments.
We develop a theoretical method going beyond the contact-interaction approximation frequently used in mean-field theories of many-fermion systems, based on the low-energy TTT matrix of the pair potential to rigorously define the effective radius of the interaction. One of the main consequences of our approach is the possibility to investigate finite-density effects, which are outside the range of validity of approximations based on $\ensuremath{\delta}$-like potentials. We apply our method to the calculation of density-dependent properties of an ultracold gas of 6{}^{6}6Li atoms at unitarity, whose two-body interaction potential is calculated using ab initio quantum chemistry methods. We find that density effects will be significant in ultracold gases with densities 1 order of magnitude higher than those attained in current experiments.
Single-component ultracold atomic Fermi gases are usually described using noninteracting many-fermion models. However, recent experiments reached a regime where ppp-wave interactions among identical fermionic atoms are important. In this paper, we employ variational and fixed-node diffusion Monte Carlo simulations to investigate the ground-state properties of single-component Fermi gases with short-range repulsive interactions. We determine the zero-temperature equation of state, and elucidate the roles played by the ppp-wave scattering volume and the ppp-wave effective range. A comparison against recently derived second-order perturbative results shows good agreement in a broad range of interaction strength. We also compute the quasiparticle effective mass, and we confirm the perturbative prediction of a linear contribution in the ppp-wave scattering volume, while we find significant deviations from the beyond-mean-field perturbative result, already for moderate interaction strengths. Finally, we determine ground-state energies for two-component unpolarized Fermi gases with both interspecies and intraspecies hard-sphere interactions, finding remarkable agreement with a recently derived fourth-order expansion that includes ppp-wave contributions.
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.
Interacting fermions are ubiquitous in nature, and understanding their thermodynamics is an important problem. We measured the equation of state of a two-component ultracold Fermi gas for a wide range of interaction strengths at low temperature. A detailed comparison with theories including Monte-Carlo calculations and the Lee-Huang-Yang corrections for low-density bosonic and fermionic superfluids is presented. The low-temperature phase diagram of the spin-imbalanced gas reveals Fermi liquid behavior of the partially polarized normal phase for all but the weakest interactions. Our results provide a benchmark for many-body theories and are relevant to other fermionic systems such as the crust of neutron stars.
We calculate the equation of state of a two-component Fermi gas with attractive short-range interspecies interactions using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. For a>0 and a smaller than the inverse Fermi wave vector our results show a molecular regime with repulsive interactions well described by the dimer-dimer scattering length a(m)=0.6a. The pair correlation functions of parallel and opposite spins are also discussed as a function of the interaction strength.
The ground-state properties of a two-component Fermi gas with attractive short-range interactions are calculated using the fixed-node diffusion Monte Carlo method. The interaction strength is varied over a wide range by tuning the value a of the s-wave scattering length of the two-body potential. We calculate the energy per particle, the one- and two-body density matrix as a function of the interaction strength. Results for the momentum distribution of the atoms, as obtained from the Fourier transform of the one-body density matrix, are reported as a function of the interaction strength. Off-diagonal long-range order in the system is investigated through the asymptotic behavior of the two-body density matrix. The condensate fraction of pairs is calculated in the unitary limit and on both sides of the BCS-BEC crossover.